Mohammad Bagher Ghomi

Definition has the following features in Aristotle’s philosophy: 1. Each thing has only one definition and ‘it is impossible that there should be more than one definition for the same thing.’ (To., Z, 5, 142b^25; cf. To., Z, 4, 141a26) 2. Definition is ‘a formula of the essence’ (Met., H, 1042a17-18) and, thus, signifies the essence of the thing. (To., I, 5, ^101b30-) About the relation between definition and essence Aristotle regards three possibilities (PsA., B, 94a11-14): a) A definition as an indemonstrable statement of essential nature. b) A definition as a syllogism of essential nature differing from demonstration in grammatical form. c) A definition as the conclusion of a demonstration giving essential nature. 3. ‘The definition is a formula and a formula has parts.’ (Met., H, 1042a18-20) Therefore, only the composite substances are definable and the primary parts of a composite substance are not definable. The reason is that ‘a definitory formula predicates something of something and one part of the definition must play the part of matter and the other that of form.’ (Met., H, 1043b28-32) Thus, definition is a sort of number: a divisible including indivisible parts. (Met., H, 1043b32-36) 4. To define a thing, one should give the species or the genera of the thing which are the only other things that can be substances of it and not its accidents. (Cat., 5, 2b31-36) Aristotle also brings differentiae into the definition: ‘There is nothing in the definition except the first-named genus and the differentiae. The other genera are the first genus and along with this the differentiae that are taken with, e.g. the first may be animal, the next animal which is footed, and again animal which is two-footed and featherless and …’ (Met., Z, 1037b28-33) Among genera the nearer genera are more informative because they are more distinctive and less general. (Cat., 5, 2b10-13 and b32-34) However, to give the species is always more informative and apt than giving the genus. (Cat., 5, 2b8-10) 5. Primary substances admit the definition of the species they are their individuals and of their genera. In the same way, species admit the definition of the genus. The reason is that everything said of the predicate can be said of the subject. (Cat., 5, 3b2-6) Therefore, everything admits the definition of its higher classes. 6. ‘Both the species and the individuals admit the definition of the differentia.’ (Cat., 5, 3b6-7) 7. A formula exhibiting the cause of a thing’s existence is a definition. (PsA., B, 10, 93b38-94a1) 8. It is possible to achieve the definition by division only if we keep three conditions in view (PsA., B, 97a23-26): a) The admission only of elements in the definable form. b) The arrangement of these elements in the right order c) The omission of no element in the definable form The process of division (PsA., B, 97a37-b6) is the process of dividing the genus by its differentia to the right species, the one that the subject accepts as its predicate, and again dividing the whole such searched by its right differentia to a predicable species. This process will be continued until we reach to that which is not further divisible, ‘i.e. that as soon as we have taken the last differentia to form the concrete totality, this totality admits of no division into species.’ In this way we achieve to a series of elements all in the definable forms without superfluous addition and without omission of any necessary element. This series includes the primary genus with all the differentia until it achieves to that which would admit of no division. The second condition, the right order, is the order in which that which is posited as primary be the one that is predicable of all of the other and not vice versa. The order must, then, be from more predicables to less predicables: ‘The right order will be achieved if the right term is assumed as primary, and this will be ensured if the term selected is predicable of all the other but not all they of it; since there must be one such term. Having assumed this, we at once proceed in the same way with the lower terms; for our second term will be the first of the remainder, our third the first of those which follow the second in a ‘contiguous’ series, since when the higher term is excluded, the term of the remainder which is ‘contiguous’ to it will be primary, and so on.’ (PsA., B, 97a26-34) 9. Things that are not the same must have different definitions. However, this does not mean that things that are the same must necessarily have the same definition. (To., I, 5, ^102a17-) 10. ‘Everything applicable to property and genus and accident will be applicable to definition as well.’ (To., I, 6, 102b27-) 11. ‘A name, e.g. ‘round’, means vaguely a sort of whole: its definition analyses this into its particular senses.’ Definition must be done through terms that are prior and more familiar and ‘anyone who has not defined a thing through terms that are prior and more familiar has not defined it at all.’ (To., Z, 4, 141a26-) It is indeed this very point that is the basis of definition by genus and differentiae: ‘A correct definition must define a thing through its genus and its differentiae, and these belong to the order of things which are without qualification more familiar than, and prior to, the species.’ (To., Z, 4, 141b^15-) This more familiarity, however, must be without qualification, i.e. not more familiar to certain people or in certain times. Otherwise, definition could not come always to be one and the same. (To., Z, 4, ^142a1-)

Aristotle’s rare hints to act and to to be acted upon are as follows: 1. Senses of ‘to be acted upon.’ Aristotle distinguishes between two senses of ‘to be acted upon’ (So., B, 5, 417b2-5): a) The extinction of one of two contraries by the other b) The maintenance of what is potential by the agency of what is actual and already like what is acted upon 2. Possessing knowledge is ‘to become’ an actual knower. This becoming, Aristotle asserts, must be a transition and this transition either is not alteration or if it is alteration, it must be so in a quite different sense. Thus, ‘it is wrong to speak of a wise man as being ‘altered’ when he uses his wisdom.’ (So., B, 5, 417b5-9) 3. ‘That which starting with the power to know learns or acquires knowledge through the agency of one who actually knows and has the power of teaching either ought not be said ‘to be acted upon’ at all- or else we must recognize two senses of alteration: a) Change to conditions of privation, and b) Change to a thing’s disposition and to its nature.’ (So., B, 5, 417b9-16) 4. Feeling versus thinking. Aristotle resembles feeling to affirmation and negation and in contrast with thinking: ‘To perceive then is like bare asserting or thinking; but when the object is pleasant or painful, the soul makes a sort of affirmation or negation, and pursues or avoids the object. To feel pleasure or pain is to act with the sensitive mean towards what is good or bad as such.’ (So., Γ, 7, 431a8-11)

Aristotle’s points about taking ‘more or less’ (μᾶλλον καὶ ἧττον) are as following: 1. Substances do not admit of the more and the less. This is supposed to mean that a man is not more a man either than itself or than another man. This is not, however, the case between different substances because one substance can be more a substance than another. (Cat., 5, 3, 3b33-4a2) In Metaphysics, Aristotle tells us that substance in the sense of form does not admit of the more and the less ‘but if any substance does, it is only the substance which involves matter.’ (Met., H, 1044a9-11) 2. Quantities, including numbers, do not admit of a more and a less. (Cat., 6, 6a19-25; Met., H, 1044a9-10) 3. Some qualities, but not all of them, admit the more and the less. For example, one thing can be called paler or more beautiful than another. This is not, however, true about the shape: neither things that admit nor those that do not admit the definition of a shape, e.g. triangle or circle, is called more a triangle or a circle. (Cat., 11a5-) Moreover, a thing can admit of more or less of a quantity than itself in a different time. (Cat., 5, 4a3-9) 4. Some, but not all, relatives admit of a more and a less. For example, while a thing is called more or less similar or more or less unequal to another thing, what is double is not spoken more double or less double. (Cat., 7, 6b20-27) 5. Doing and being affected admit of a more and a less. It is possible, for example, to heat more or to be heated more or less. (Cat., 9, 11b1-7) 6. Aristotle speaks of the possibility of being more false or less false. (Met., Γ)

Aristotle says that ὑπαρχειν has as many senses as ‘to be true’ (PrA. , A, 36, 48b2-9) and as many ways as there are different categories. (PrA., A, 37, 49a6-9) This may mean that for every ‘is’ there is a ὑπαρχειν. Τhe reason is that Aristotle uses ὑπαρχειν in converse direction of ‘is’. The equal statement of ‘A is B’ with ὑπαρχειν is ‘B ὑπαρχει to A.’ Allen Bāck points to the difference between the use of the verb with dative case and its use with a subject alone in Greek language. When it is used with the dative, it retains its basic meaning, that is, ‘be already present’ or ‘exist really.’ ‘So to say that P belongs to S is to say that P exists in S, or, if you like, that P has its being in S.’ He believes that Aristotle uses this construction to insist that primary substances alone are the fundamental being and all other things only are ‘in’ substances. Thus, when the verb is used with the dative, it expresses dependent substance relation. But when it is used with a subject alone, e.g. in ‘S ὑπάρχει,’ it expresses that the subject really exists. (OI., 17a24 and 17b2) Thus, while it is the subject which is said to be the predicate, it is the predicate which ὑπάρχει to the subject. The formula of ‘τὸ Α ὑπάρχει τῷ Β’ is equivalent to ‘τὸ Β ἐστι Α.’ He uses the word for the predication of a category on substance (e.g. Met., α, 993b24-25; Met., Z, 1029a15-16; Cat., 5, 3b24-25), the predication of secondary substance on primary substance (e.g. Met., Z, 1038b21-23; Cat., 5, 2a14-19), the predication of primary substance on nothing else but itself (e.g. Met., Z, 1040b23-24), the belonging of a verb to the subject, the belonging of axioms to a single science (Met., 1005a22-23) , the belonging of PNC to all things that are (Met., IV, 3) , in the sense of really existing (Cael. 297b22, Met., 1041b4. Cf. B503, 125-126) or merely in the sense of the predication of a predicate on a subject (e.g. OI., I, 5, 17a22-24) and especially and much more repeatedly than anywhere else in his discussion of syllogism. (e.g. PrA., A, 36, 48a40-b2; PrA., B, 22, 67b28-30; PrA., A, 24a26-28) It is also used in some related senses like mere belonging (e.g. Met., A, 989a10-14; K, 1060a9-10) or to be there. (So., B, 5, 417b23-26) Some of its derived forms are also used by Aristotle. For example, ἐνυπαρχον in the sense of the thing that is ‘in’ something; (e.g. Met., A, 991a13-16; Met., Z, 1038b29-33 and 1039a3-5) ὑπερέχον in the sense of that which contains and ὑπερεχόμενον in the sense of that which is contained in something else. (e.g. Met., Δ, 1020b26-28) In a sense, the extent of the application of ὑπαρχειν is wider than ‘is’ since it is not restricted to the nominative form in which ‘is’ is used but is applicable to other cases as well: ‘For ‘That does not belong to this’ does not always mean that ‘This is not that’ but sometimes that ‘this is not of that’ or ‘for that.’ (PsA., A, 36, 48b28-33) Allen Bāck (B503, 124) points that in the Prior Analytics Aristotle uses ‘ὑπάρχει τῷ’ and ‘κατηγορεῖσθαι κατά’ interchangeably. (e.g. at 25b37-26a4) Referring to its converse construction in respect of μετέχει (if A belongs to B, then B participates in A) as a probable reason that it may have Platonist foundations. But the question is: why does Aristotle uses this construction (B belongs to A) instead of simply saying A is B? Alexander of Aphrodisias (Apr 54.21-29) wonders why Aristotle had to adhere to such artificial language, entirely unnatural for ordinary speakers of Greek. As Jonathan Barnes points out, all the three formulas of ‘τὸ Α ὑπάρχει τῷ Β,’ ‘τὸ Α κατηγορεῖται κατὰ τοῦ Β’ and ‘τὸ Α λέγεται κατὰ τοῦ Β’ are artificial in the sense that no Greek who wanted to say that pleasure was good would normally have expressed himself by way of any of them.’ Bāck thinks Aristotle may have used it ‘to stress the primacy of primary substances as the ultimate subjects.’ He also mentions the probability that it may be to emphasize that the terms are being coupled in predication without any existence condition, a suggestion he is not himself inclined with. Robin Smith notes for Aristotle that ‘belonging to’ construction is wider than ‘predicated of’ construction because it can be used for cases that cannot easily be treated as categorical sentences. While predication is restricted to cases in which the subject term is in the nominative case, belonging can indicate, as he quotes Mignucci (480-481), ‘any possible grammatical construction for a predicative relation’

Like (ὃμοιος) has the following functions in Aristotle’s philosophy: 1. We know from Aristotle that some thinkers believed that ‘like is known by like.’ (ἡ δέ γνῶσις τοῦ ὁμοίου τῷ ὁμοίῳ). (Met. , B, 1000b5-6 and So., A, 5, 410a27-29 about Empedocles; So., A, 2, 404b16-18 about Plato; So., A, 2, 405b12-16 and b26-28 about those who define the soul by its power of knowing) This, however, is a problematic theory in Aristotle’s point of view. One major problem is that it is in contradiction with saying that like is not capable of being affected by like (though there are some who believe in this: So., B, 5, 416b35-36) simply because knowing and thinking are ways of being affected on their own views. (So., A, 5, 410a23-26) Another reason being that this theory entails that error must be a ‘contact with the unlike’ because it is the opposite of the knowing of like by like. (So., Γ, 3, 427a26-b5) Aristotle also mentions that some thinkers believe that like is fed by like, though there are some others who believe in its converse. (So., B, 4, 416a29-32) He also mentions a theory he assigns to ‘Antisthenes and other such uneducated people’ based on which it is not possible to say what a thing is (τί μέν ἐστι) and its definition but it is possible to say what a thing is like’ (ὃτι δ᾿ οἷον καττίτερος). (Met., H, 1043b23-28) 2. Aristotle posits likeness as distinguished from sameness: things are the same whose substance is one but those are like whose quality is one.’ (Met., Δ, 1021a11-12) Quality is the only basis of similarity and dissimilarity: ‘It is only based on one of the qualities that things are called similar and dissimilar (ὃμοια δὲ καὶ ἀνόμοια κατὰ μόνας τὰς ποιότητας λέγεται). A thing is not similar to another in virtue of anything but that in virtue of which it is qualified.’ (ὃμοιον γὰρ ἓτερον ἑτέρῳ οὐκ ἔστι κατ᾿ ἂλλο οὐδὲν ἢ καθ᾿ ὃ ποιόν ἐστιν) (Cat., 8, 11a15-18) Also, things that are not without difference in their compound substances and thus are not absolutely the same but are the same in their form, are called alike. (Met., I, 1054b3-7) 3. Family resemblance. Aristotle says that some kinds of sameness that are not one due to the sameness of species ought still to be ranked in the same class because they seem to be one family based on a certain likeness and resemblance. (To., I, 7, ^103a10-25) 4. Aristotle distinguishes between two kinds of likeness: a) Likeness between things belonging to different genera with such a formula: as one is to one thing, so is another to something else (e.g. knowledge to object of knowledge and perception to object of perception). (To., I, 17, 108a7-10) b) Likeness between things belonging to the same genus: they are alike in so far as they have any identical attribute. (To., I, 17, ^108a14-17) 5. The contrary of likeness and unlikeness seems to be at least an alternative for primary difference and contrariness. Aristotle asserts that all contraries refer to the primary differences and contraries: ‘Since everything that is may become referring to some one common nature, each of the contraries also may become referring to primary differences and contraries of being, whether the first differences of being are plurality any unity or likeness and unlikeness, or some other differences.’ (Met., K, 1061a10-15; cf Met., K, 1061b11-15; Met., Γ, 1005a6-8)

Common (κοινὸν) has the following features in Aristotle’s works: 1. ‘That which is common ὑπαρχει in many things at the same time,’ which show that it cannot be one thing because that which is one cannot be in many things at the same time. (Met. , Z, 1040b25-27) Although the common is common between different things, it is indeed different for each of them (ἓτερον ἑκατέρῳ τοῦτο αὐτο τὸ ζῷον). Animal, e.g., which is common between horse and man, is specifically different in them (τὸ κοινὸν ἓτερον ἀλλήλων ἐστὶ τῷ εἴδει). Thus, man and horse are different having difference of genus, an otherness that makes the genus itself different (ἀνάγκη ἄρα τὴν διαφορὰν ταύτην ἑτερότητα τοῦ γένους εἶναι. λέγω γὰρ γένους διαφορὰν ἑτερότητα ἣ ἓτερον ποιεῖ τοῦτο αὐτό). (Met., I, 1058a2-8) 2. The common indicates a ‘such’ (τοιόνδε) and not a ‘this’ (τόδε τι). (Met., B, 1003a7-9) One reason of this is that every single thing has several commons with other things and if each of these commons were to be a this, every single thing would be several things. (Met., B, 1003a9-12; cf. Met., Z, 1038b34-1039a11) 3. To investigate the definition of a thing, we must stablish the common element in all members of all the species of that which is to be defined and the common of the commons until we reach to a single formula, which will be the definition. (PsA., B, 13, 97b7-13) The same is true about the investigation of essential nature: to inquire the essential nature of a thing, we should search for what is common in instances. (PsA., B, 13, 97b15-25) 4. The process of the selection of analyses and divisions is based on lying down the common genus of all the subjects of investigation by analyzing the common properties and especially essential properties of subgenera classes. (psA., B, 14, 98a1-12) 5. We must distinguish between two ways of commonship: being based on a common (καθ᾿ ἓν) or being related to or referred to a common (πρὸς ἓν or πρὸς μίαν). (Met., B, 1003b12-15) 6. Things that have common nature, fall under one science. (Met., K, 1060b33-36)

Some forms of defining PNC in Aristotle’s works are as follows: a) Everything must be either affirmed or denied (φάναι ἢ ἀποφάναι). (Met., B, 996b28-29) or: it will not be possible to assert and deny the same thing truly at the same time. (Met., Γ, 1008a36-b1) In other words, ‘contradictory statements (ἀντικειμένας φάσεις) are not at the same time true. (Met., Γ, 1011b13-14) Also, ‘It is impossible that contradictories (ἀντίφασιν) should be at the same time true of the same thing.’ (Met., Γ, 1011b15-16) Also, ‘Opposite statements (ἀντικειμένας φάσεις) can never be true of the same subjects.’ (Met., K, 1062a33-34; 1063b15-17) Also, ‘Of all affirmation or negation one is impossible. (PsA., A, 11, 77a22) b) A thing cannot at the same time be and not be. (Met., B, 996b30-31; Γ, 1006a3-5) This can also be extended to many other similar pairs of opposites: ‘The same thing cannot at the same time be and not be, or admit any other similar pair of opposites.’ (Met., K, 1061b34-1062a2) Also, ‘It will be possible for the same thing to be and not to be, except in virtue of an ambiguity.’ (Met., Γ, 1006b18-19) This is also asserted in another similar way: it is impossible that it should be at the same time true to say the same thing is a thing and is not a thing.’ (Met., Γ, 1006b33-34) c) ‘The same attribute cannot at the same time belong (ὑπάρχειν) and not belong to the same object in the same respect.’ (Met., Γ, 1005b19-21) d) Those positive and negative propositions are said to be contradictory which have the same subject and predicate. (OI, I, 7, 17a33-35) The opposition between an affirmation and a denial makes contradictories (ἀντίφασεως). (PsA., A, 2, 72a11-14) Based on Aristotle’s definition, ‘An affirmation is opposed to a denial in the sense which I denote by the term ‘contradictory’ (ἀντίφατικως), when, while the subject remains the same, the affirmation is of universal character and the denial is not.’ (OI., I, 7, 17b16-19) 1) Characteristics of PNC a) It is the most certain (Met., Γ, 1005b22-23 and b11) and the most indisputable (Met., Γ, 1006a5-6) of all principles. b) It is impossible: to believe its contrary (Met., Γ, 1005b24-30); to be really in that position (Met., Γ, 1008b11-13); and to defend it. (OI, I, 9, 18b17-19) Nonetheless, Aristotle thinks that many of the writers about nature assert the contrary of PNC and use a language opposite to it. (Met., Γ, 1005b35-1006a3) c) It is the starting point of all the other axioms. (Met., Γ, 1005b32-34) d) It is not hypothetical. (Met., Γ, 1005b13-17) e) Contradictories are extremely opposed to each other. (Met., Γ, 1007a1-4) f) Believing in PNC saves substance and essence and not believing in it makes all attributes accidents and there will be nothing as being essentially something. The reason is that something which essentially is a being cannot avoid being that thing. (Met., Γ, 1007a20-29 and b16-18) g) PNC supports plurality of things because otherwise all things will be one: ‘If all contradictories are true of the same subject at the same time, evidently all things will be one. For the same thing will be a trireme, a wall, and a man, if it is equally possible to affirm and deny anything of anything.’ (Met., Γ, 1007b18-22) In fact, PNC supports difference: ‘For if contradictories can be predicated alike of each subject, one thing will in no wise differ from another; for if it differs, this difference will be something true and peculiar to it.’ (Met., Γ, 1008a25-27) h) To accept truth and falsity, whether in an absolute sense (e.g. A is more true than B; or C is less true than D) entails PNC. (Met., Γ, 1008b2-7 and b31-35; 1009a2-5) In fact, PNC is entailed by accepting true affirmation. (Met., K, 1062b7-11) i) Judging and choosing between at least two things entails PNC: you cannot choose one as better than another without a previous judging that one is A and the other not A. (Met., Γ, 1008b18-24) The same is true about avoiding. (Met., Γ, 1008b24-29) j) PNC guarantees speaking and saying anything intelligible because otherwise e.g. saying ‘yes’ means both yes and no. (Met., Γ, 1008b7-13) k) Contradictories do not accept intermediates that means we must either affirm or deny a predicate on a subject and there is no third option. (Met., Γ, 1011b23-24; Met., I, 1055b1-2; PsA., A, 2, 72a11-14; Met., I, 1057a33-36) l) PNC is applicable also to the future time. (OI., I, 9, 19a28-29) m) PNC is presupposed by the least semantic of words. If we accept that each word has a meaning and, thus, signifies something definite, we cannot accept that it has the contradictory meaning and signies contradictory things and this approves PNC. Thus, Aristotle asks the opponent of PNC to say just one word, a significant word and takes this as the demonstration of PNC because by saying the word e.g. ‘man’ you have already signified man and not-man. (Met., Γ, 1005a11-13 and a18-22; 1006a28-31 and b13-15) Therefore, signification entails PNC: ‘He, then, who says this is and is not denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible. Therefore, if ‘This is’ signifies something, one cannot truly assert the contradictory.’ (Met., K, 1062a16-20) He says again: ‘If the word signifies something and this can be truly asserted of it, it necessarily is this; and it is not possible that that which is necessary should ever not be: it is not possible therefore to make the opposed assertions truly of the same subject.’ (Met., K, 1062a20-23; cf. Met., K, 1062a24-31) n) At Met., 4, 3, 1005b9-10 (check???) PNC is called as principle of things (ἀρχὰς τοῦ πράγματος). (quoted from B215, 517)

The following are the characteristics of a genus: 1. Those to which the same figure of predication applies are one in genus. (Met. , Δ, 1016b32-35) 2. Things that are one in genus are all one by analogy while things that are one by analogy are not all one in genus. (Met, Δ, 1016b35-1017a3) 3. A genus includes contraries. (Met., Δ, 1018a25-31) 4. All the intermediates are in the same genus as one another and as the things they stand between. (Met., I, 1057a18-30; 1057b31-34) 5. Not every predicate is a genus of what it is predicated on; for this would equate a genus with one of its own species. (PsA., A, 22, 83b7-10) 6. The opposite of the genus should always be the genus of the opposite. (To., Δ, 4, ^125a27-29) 7. A genus divides the object from other things. (To., Z, 3, 140a^24) 8. None of unity and being is a genus. (Met., B, 998b22-27; Met., K, 1059b31-34; PsA., B, 7, 92b12-14) 9. There is no necessity or even no possibility that things that are the same specifically or generically should be numerically the same. (To., H, I, 152b30-) 10. To be called one due to having one genus is in a way similar to be one due to having the same matter. (Met., Δ, 1016a24-28) 11. The substance of a thing involves its genus, and thereby all the higher genera are predicated of the lower. (To., Z, 5, 143a^20- ) 12. Being falls immediately into genera. (Met., Γ, 1004a4-6) A. Characteristics of relations between genera The characteristics of relations between genera, the relations between genera and species excluded, are as follows: 1. Genus is not an element in the composition of things. (Met., I, 1057b20-22) 2. Things resulting from the same division of the same genus are simultaneous by nature. (Cat., 13, 15a3-4) 3. Processes of proof cannot pass from one genus to another. (PsA., A, 23, 84b14-18) 4. It is not necessary for subordinate genera to have different accounts. (To., I, 15, ^107a19-) E.g. when we say a raven is a bird, we also say it is a certain kind of animal. 5. It is necessary for genera that are not subordinate one to the other to have different accounts. (To., I, 15, ^107a27-30) E.g. whenever we call a thing an engine, we do not call it an animal, nor vice versa. 6. If one of the genera is predicated in what it is, all of them, both higher and lower than this one, if predicated at all of the species, will be predicated of it in what it is; so that what has been given as genus is also predicated in what it is. (To., Δ, 2, ^122a10) 7. The same object cannot occur in two genera of which neither contains the other. (To., Z, 139b32-140a2) 8. Those to which the same figure (σχῆμα) of predication applies, are the same in genus. (Met., Δ, 1016b32-35) 9. Attributes that inhere always in each several things can be divided to two groups: those that are wider in extent but not wider than its genus and those wider than its genus. (PsA., B, 13, 96a24-27) 10. The relation between A and B must be extendable in respect of all the genera of A. Thus, if A is double of B, it must also be in excess, the genus of double, to B. Aristotle accepts, however, that this may be objectable in some cases: while knowledge is called knowledge of an object of knowledge, it cannot be called a state and disposition (which is the genus of knowledge) of an object of knowledge. In fact, it is a state and disposition of the soul. (To., Δ, 4, 124b28-34) B. Characteristics of species The following are the characteristics of species: 1. Things are said to be other in species if they are of the same genus but are not subordinate the one to the other. (Met., Δ, 1018a38-b2; Met., I, 1057b35-37) 2. Contraries are other than one another in species. (Met., Δ, 1018b5-7; Met., I, 1058b26-) 3. It is not sufficient for a difference to be the basis of distinguishing species in a genus because it belongs to the genus in virtue of its nature as, e.g., the difference between men and women belongs to animal in virtue of its nature. It must also be a modification peculiar to the genus (οἰκεῖα πάθη τοῦ γένους) in the strongest sense. (Met., I, 1058a29-37) Thus, contraries which are in the formula (ἐν τῷ λόγῳ) make a difference in species, but those which are in the compound material thing do not make one as e.g. being male and female is a difference in matter. (Met., I, 1058a37-b23) 4. Some things are peculiar to the species as distinct from genus: there are attributes peculiar to each distinct species. (PrA., A, 27, 43b27-29) 5. There is no necessity or even no possibility that things that are the same specifically should be the same numerically. (To., H, I, 155b30-) C. Characteristics of relations between genera and species The following are the characteristics of relations between genera and their species: 1. Although species predicated of individuals seem to be principles rather than the genera, it is hard to say, Aristotle asserts, in what sense species are to be taken as principles. (Met., B, 999a14-21) 2. Things that are one in species are all one in genus, while things that are one in genus are not all one in species. (Met., Δ, 1016b35a1) 3. The relation of a species to its genus is like the relation of primary substance to all others: the species is a subject for the genus (ὑπόκειται γὰρ τὸ εἴδος τῷ γένει) and the genera are predicated of the species but the species are not predicated of them. (Cat., 5, 2b17-22) 4. Of the species themselves- those which are not genera- one is no more a substance than another: a certain horse is no more a substance than another horse. (Cat., 5, 2b22-26) 5. Genera are prior to species since they do not reciprocate as to implication of existence (κατὰ τὴν τοῦ εἶναι ἀκολούθησιν). For example, if there is a fish there is an animal, but if there is an animal there is not necessarily a fish. (Cat., 13, 15a4-7) 6. What belongs both to a species and to its genus, it belongs to the species more properly indeed than to the genus. (PrA., A, 27, 43b29-32) 7. A predicate drawn from the genus is never ascribed to the species in a derived form and as its genus. Thus, e.g. coloured cannot be a genus of ‘white’ when we say ‘white is coloured.’ (To., B, I, ^109b1-5) 8. Genera are predicated of their species synonymously because the species take on both the name and the account of their genera. (To., B, I, ^109b3-6) 9. All the attributes that belong to the species belong to the genus as well but there is no necessity that all the attributes that belong to the genus should belong also to the species. (To., B, 4, 111a20-32) 10. Those things of which the genus is predicated must also of necessity have one of its species predicated of them. (To., B, 4, 111a33-) 11. The higher genus should be predicated of the species in what it is. (To., Δ, 2, ^122a6) 12. The species, or any of the things which are under the species, is not predicated of the genus because the genus is the term with the widest range of all. (To., Z, 6, 144a27f.) 13. The same species cannot be in two genera neither of which contains the other. (To., Z, 6, 144b14f.) 14. None of the species of a genus is prior or posterior to other species but they are thought to be simultaneous by nature. (Cat., 13, 14b38-15a1) 15. Daniel W. Graham points that sometimes Aristotle speaks of species as classes (Cat., 5, 2a14-17) and sometimes as properties or a certain character (ποιόν τι) of substances, which is difficult to be distinguished from the category of quality. (Cat., 3b13-22) D. Characteristics of differentia 1. The last differentia will be the substance, the definition and the form of the thing. (Met., Z, 1038a18-28) 2. If we divide according to accidental qualities, there will be as many differentiae as there are processes of division. (Met., Z, 1038a25-28) 3. The differentia divides the object from any of the things contained in the same genus. (To., Z, 3, 140a24-) 4. A. C. Lloyd argues that Aristotle’s logic of classification contains a vicious circle because: ‘For a genus to be predicated unequivocally and essentially of a species the specific differentiae have to be ‘appropriate’; but in order to know whether a proposed differentia is appropriate we have to know whether the genus is predicable essentially of the species thus defined.’ The predication of differentia on primary substance seems to make difficulties in Aristotle’s system, as Terence Irwin points out. It seems to violate the distinction of strong predication and inherence, a distinction between predication of count-nouns and predication of characterizing adjectives. Irwin says that this violation is only apparent because although the differentia-term is an adjective, its gender agrees with the gender of the understood genus-term and not with that of the subject term. ‘Man is biped’ is indeed ‘Man is a biped animal.’ This shows, Irwin asserts, ‘why Aristotle can still mention that strong predication is nominal and inherence is adjectival.’ Differentiae are not, however, secondary substances, as Aristotle himself insists. A differentia does not say what the thing is, as secondary substances do, but only what it is like or what sort it is. (ποιον: To., 122b12-17; 128a20-29; 139a28-31; 142b25-29) Nonetheless, differentiae are not qualities because they are not inherent. Thus, they cannot be regarded in any of the ten categories. Irwin thinks that this anomaly is unnecessary because Aristotle could give good reasons for taking differentiae to be second substances. E. Characteristics of relations between differentia and genera or species 1. It is not possible for the genus to be predicated of the differentia taken apart from the species. (Met., B, 998b23-25; Met., K, 1059b31-33; To., VI, 6, 144a32-b1) 2. It is not possible for the species of the genus to be predicated of the proper differentiae of the genus. (Met., B, 998b24-26) 3. Where the differentia is present, the genus accompanies it, but where the genus is, the differentia is not always present. (Met., Δ, 1014b12-14) 4. The number of species are equal to the number of differentiae. (Met., Z, 1038a15-18) 5. The differentiae of genera which are different and not subordinate one to the other are themselves different in kind. (Cat., 3, 1b16-20; To., I, 15, ^107b19-) 6. There is nothing to prevent genera subordinate one to the other from having the same differentia. (Cat., 3, 1b20-22) 7. Since the higher genera are predicated of the genera below them, all differentiae of the predicated genus will be differentia of the subject also. (Cat., 3, 1b21-24) 8. The definition of the differentia is predicated of that of which the differentia is said. (Cat., 5, 3a25-28) 9. In giving what a thing is it is more fitting to state the genus than the differentia. For example, anyone who says that man is an animal shows what man is better than who describes him as terrestrial. (To., Δ, 6, ^128a24-27) 10. The differentia always signifies a quality of the genus, but the genus does not do this of the differentia. (To., Δ, 6, 128a27-29; To., Z, 6, 144a20-23) 11. A specific differentia, along with the genus, always makes a species. (To., Z, 6, 143b^1-) 12. A genus is always divided by the differentiae that are co-ordinate with it in a division and the differentiae that are co-ordinate in a division are all true of the genus. (To., Z, 6, 143b^1-) 13. Differentia cannot be predicated of the genus because genus is the term with the wider range. (To., Z, 6, 144a27-) In fact, genus is predicated, not of the differentia, but of the object of which the differentia is predicated. (To., Z, 6, 144a^31-b3) 14. Neither species nor the objects under it can be predicated of the differentia because the differentia is a term with a wider range than the species. (To., Z, 6, 144b4-) 15. The differentia is posterior to genus but prior to the species. (To., Z, 6, 144b^9-) 16. The same differentia cannot be used of two genera neither of which contains the other and if they do not both fall under the same genus. Otherwise, the same species will be in two genera neither of which contains the other, which is impossible. (To., Z, 6, 144b14-) 17. Genus and differentia are prior to and more familiar than the species: ‘For annul the genus and the differentia; and the species too is annulled, so that they are prior to the species. They are also more familiar; for if the species is known, the genus and differentia must of necessity be known as well (for anyone who knows what a man is knows also what animal and terrestrial are), whereas if the genus or the differentia is known it does not follow of necessity that the species is known as well; thus the species is less intelligible.’ (To., Z, 4, 141b15-) F. Characteristics of relations in series of classes 1. Mutually exclusive series. If no term in the series ACD… is predicable of any term in the series BEF…, and if G- a term in the former series- is the genus of A, clearly G will not be the genus of B; since, if it were, the series would not be mutually exclusive. (PsA., A, 15, 79b6-11) 2. Atomic disconnection of series. Of two mutually exclusive series ACD and BEF, if neither A nor B has a genus and A does not inhere in B, this disconnection must be atomic. (PsA., A, 15, 79b6-14) G. Characteristics of relations of individuals 1. No individual in a species is more substance than another individual in another species. (Cat., 5, 2b26-28) An individual man, for instance, is no more a substance than an individual ox. 2. Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 3. Not distinguishing between class membership and class inclusion? Some commentators like Vlastos and Ackrill (1963, 76) criticized Aristotle because he, they believe, did not distinguish between class membership (between species and particulars) and class inclusion (between genera and their species). Having accepted this point, Daniel W. Graham believes it is ‘question-begging in a curious way.’ Phil Corkum thinks that Aristotle employs mereological notions. (This criticism seems so strange because all the Aristotle’s point in distinguishing species 2 from genera is strictly the distinction of class membership and class inclusion as they call them so.

Aristotle’s points about sameness or identity are as follows: 1. Aristotle speaks of different senses of same (ταὐτόν) in some of his works but it seems that the most comprehensive division is found in Topics (I, 7, 103a7-25) where he mentions three kinds of sameness: numerically, specifically and generically besides a fourth kind he calls ‘in view of unity of species.’ The numerically sameness on which there is the greatest agreement (To. , I, 7, ^103a25) and is the strictest sense of sameness (To., H, 1, 151b26-27) occurs when there is more than one name but only one thing. Specific sameness occurs when while there is more than one thing, they present no differences in respect of their species. Likewise, generic sameness occurs when there is more than one thing but they fall under the same genus. Aristotle also speaks of a sameness ‘in view of unity of species’ like the sameness of water from the same spring. We discussed this under the name of ‘family resemblance.’ In Metaphysics (I, 1054a32-b2) he also speaks of a sameness ‘both in formula and in number as well as a sameness in the formula of the primary substance. We also observe Aristotle distinguishing sameness from likeness because the former occurs in substance while the latter in quality. (Met., Δ, 1021a11-12) There are several other senses of sameness in book Δ of Metaphysics. One sense is accidental sameness in which two things are called the same either because they are accidents of the same thing or because one is the accident of the other. (Met., Δ, 1017b27-29) In another sense, a complex notion is considered as the same of either of the simple notions. (Met., Δ, 1017b30-33) He also speaks of a general rule of being the same: ‘Things are said to be the same by their own nature in as many ways as they are said to be one’ like being one in matter or substance. (Met., Δ, 1018a4-7) 2. ‘We know things in so far as they have the same unity and identity and in so far as some attribute belongs to them universally (ᾗ καθόλου τι ὑπάρχει).’ (Met., B, 999a28-29) 3. Herman Weidemann believes that in Met., Z, 11 (1037a33-b7) only primary substances are considered to be identical with what it is for each of them to be. This, however, is not the same as primary substance in Categories but is rather meant to cover the individualized substantial form of each thing (τὸ εἶδος τὸ ἐνον), like the soul of a man (1037a28-29). Therefore, ‘if we take substance which is ‘primary’ in this sense and ‘say just what it is,’ we must indeed be producing a statement of identity. … To say of a man that he is essentially an animal of such and such a kind is not to mean, however, that the man in question is identical with what he is said to be essentially.’ Thus, while an essential predication in which the subject is the primary substance of Metaphysics Z (i.e. substantial form) and the predicate just what it is, is ‘genuine statement of identity,’ the predication in which the subject is primary in the sense of the Categories and the predicate its secondary substance, is a predicative statement in a strict sense.

Aristotle differentiates between otherness (ἑτερότης) and difference (διαφορὰ). Otherness has no definite respect: one thing is other than another thing only because they are not the same. Every two things which are not the same are other than each other. Therefore, two things other than each other do not need something in which they are other than each other. Difference, on the other hand, has a definite respect and one thing is different from another thing in some respect. Thus, there must be something identical whereby two different things differ. (Met. , I, 1054b23-27) Therefore, there is no difference between anything and the things outside its genus. (Met., I, 1055a26-27) 1) Difference Aristotle takes two things as identical things in which difference occurs: genus and species. All things that differ differ either in genus or in species. (Met., I, 1054b27-28) a) Difference in genus Two things are different in genus if they ‘have not their matter in common and are not generated out of each other,’ which means that they belong to different figures of predication. (Met., I, 1054b28-29) They have no way to one another and are too far distinct and are not comparable. (Met., I, 1055a6-8) b) Difference in species Two things are different in species if they have the same genus (Met., I, 1054b29-30) but are not subordinate one to the other. (Met., Δ, 1018a38-b7) 2) Contrariety Aristotle mentions five senses. In the first sense he calls contraries ‘those attributes that differ in genus, which cannot belong at the same time to the same subject.’ (Met., Δ, 1018a25-27) Three senses emphasize on having the most difference either in the same genus, the same receptive material or the same category, all similar to genus. The fifth sense also insists on having the greatest difference but mentions species besides genus as where difference occurs. (Met., Δ, 1018a27-31) It seems that Aristotle is more inclined to the second sense as his definition in Metaphysics, I, 1055a27-29 might concede: ‘The things in the same genus which differ most are contraries; for the complete difference is the greatest difference among these,’ though he agrees with the third sense too and regards those that differ most in the same receptive material also as contraries. (Met., I, 1055a29-30) In fact, Aristotle speaks of all kinds of contraries within, without or in genera: ‘All contraries must either be in the same genus or in contrary genera or be themselves genera.’ Their corresponding examples are white and black (in the same genus), justice and injustice (in contrary genera) and good and bad (themselves genera). (Cat., 11, 14a19-25) To speak generally, as one of the four kinds of opposition, contraries are those that cannot belong at the same time to the same thing. (Met., Γ, 1011b15-18) Thus, contrariety (ἐναντιότης) is complete difference (Met., I, 1055a16-17) and contraries are the extremes of things that differ in species for which generation takes place and have the greatest distance. (Met., I, 1055a8-10; Δ, 1018a38-b7) Since contraries have the extreme difference, there cannot be more than one contrary and extreme for each thing. (Met., I, 1055a19-21) Thus, the things in the same genus which differ most are contraries. (Met., I, 1055a27-28) Aristotle says that the meaning of calling two things ‘other in species’ is that they are contrary and this being other in species he posits versus being the same in species. (Met., I, 1058a17-28) Aristotle even calls ‘the difference between things which differ in species’ a difference that belongs only to things in the same species. (Met., I, 1058a26-28) The reason is that ‘all things are divided by opposites and … contraries are in the same genus … and every difference in species is a difference from something in something … Hence also all contraries which are different in species … are … other than one another in the highest degree- for the difference is complete-, and cannot be present along with one another.’ The conclusion is that ‘The difference, then, is a contrariety.’ (Met, I, 1058a8-16) There are some characteristics for contraries in Aristotle’s philosophy: a) One thing cannot have more than one contrary for there can be neither anything more extreme than the extreme, nor more than two extremes for the one interval. (Met., I, 1055a19-21) b) The primary contrariety is the contrariety between state and complete privation. (Met., I, 1055a33-37) Aristotle regards privation both as a kind of contradiction (Met., I, 1055b3-11) and as that of which contrariety is a kind: all contrariety is a privation but not all privation is contrariety. (Met., I, 1055b11-17) In fact, every contrariety involves a privation as one of its items (Met, I, 1055b17-19 and b25-29): ‘of the contraries, no less than of the contradictories, one is a privation- and a privation of substance; and privation is the denial of a predicate to a determinate genus.’ (Met., Γ, 1011b18-20) Nonetheless, the relation between contrary, privation and contradictory seems to be even more complex:’For within a single identical genus the contrary of a given attribute is either its privative or its contradictory; e.g. within number what is not odd is even, inasmuch as within this sphere even is a necessary consequent of not-odd.’ (PsA., A, 4, 73b21-24) c) A contrary cannot be an intermediate because otherwise it would not be a perfect contrary, which must be based on definition. (Met., I, 1056a12-14) d) Contraries always accept intermediates between themselves. (Met., I, 1056a14-15 e) ‘Contraries do not involve one another in their composition, and are therefore first principles.’ (Met., I, 1057b22-23) f) ‘All the inferior classes, both the contraries and their intermediates, will be compounded out of the primary contraries.’ (Met., I, 1057b31-34) g) None of the intermediables can be predicated of either of the contraries. (Met., K, 1063b19-22) h) Contrary propositions (as defined in OI, I, 7, 17b3-6) can never both be true because they state contrary conditions which cannot subsist at one and the same time in the same subject. (OI, II, 14, 24b7-) 3) Otherness in kind Aristotle also speaks of things other in kind (ἓτερα τῷ γένει) by which he means an otherness between things ‘whose ultimate substratum is other and one cannot be analysed to the other nor both into the same thing. His example of this otherness in kind is the otherness of form and matter. (Met., Δ, 1024b9-12) 4) Network of difference and wholism Aristotle speaks of a theory based on which the knowledge of each thing depends on the knowledge of its differentiae distinguishing it from every single other thing. Therefore, to know and define one thing we need to know the whole existence. (PsA., B, 13, 97a6-11) Aristotle rejects this theory based on the fact that ‘not every differentia precludes identity’ and, thus, many differentiae inhere in things specifically identical, though not in the substance of these nor essentially.’ (PsA., B, 13, 97a11-14) 5) Knowledge and difference There must be some kind of relation between knowledge and difference in Aristotle’s saying that sight, more than other senses, makes us know and bring in light many differences between things. (Met., A, 980a24-27)

A. Accident 1. We call an accident (συμβεβηκὸς) that which attaches to something and can be truly asserted, but neither of necessity nor usually.’ (Met. , Δ, 1025a14-16) 2. Whenever an accident attaches to a subject, it attaches to it not because it is that subject (μὴ διότι τοδὶ ἧν). (Met., Δ, 1025a21-24) 3. ‘There is no definite cause for an accident, but a chance cause, i.e. an indefinite one.’ (Met., Δ, 1025a24-25) 4. ‘The accident has happened or exists, -not in virtue of itself, however, but of something else. (Met., Δ, 1025a28-29) 5. ‘What attaches to each thing in virtue of itself but is not in its substance is an accident.’ (Met., Δ, 1025a30-32) 6. ‘An accident is something which, though it is … neither a definition nor a property nor a genus, yet belongs to the thing.’ (To., I, 5, 102b4-) 7. An accident is ‘something which may either belong or not belong to any one and the self-same thing, as (e.g.) being seated may belong or not belong to some self-same thing.’ (To., I, 5, 102b4-) 8. ‘There is nothing to prevent an accident from becoming a temporary or relative property … [and] there is nothing to prevent an accident from becoming both a relative and a temporary property; but a property absolutely it will never be.’ Aristotle’s example is ‘being seated.’ That it is a temporary property is evident. It is also a relative property to those who are not seating when he is the only person sitting. Therefore, it is a temporary and also a relative property. 9. ‘In the case of accidents and in no other it is possible for something to be true in a certain respect and not universally’ and ‘there is nothing to prevent an attribute belonging in part’ so that it is open to dispute accidents e.g. being white or just about a man because he might be white or just in part only. Thus, ‘conversion is not a necessary process in the case of accidents.’ (To., B, 1, 109a9-) B. Essential versus accidental Aristotle distinguishes between two senses of being (τὸ ὄν): accidental sense (κατὰ συμβεβηκός) and essential sense (καθ᾿ αὑτό). The accidental sense happens when something is said to be another thing while there is in fact a third thing which is both of them. Thus, being the first thing is not by itself the second thing. a) Aristotle speaks of three ways in which one thing is said in an accidental sense to be another. (Met., Δ, 1017a8-22) i) When both the subject and the predicate are accidents of a third thing and it is in fact the third thing which ‘is’ by its own. Thus, when it is said e.g. that ‘The just is musical’ it is said accidentally because it is in fact a third thing, Socrates for example, which is just and musical. (Met., Δ, 1017a13-19) ii) When that to which the attribute belongs is. The example of this must be ‘the man is musical’ because it is in fact the man which is. iii) When the subject which has as an attribute that of which it is itself predicated, itself is. The example of this must be Aristotle’s third example: ‘The musical is man.’ b) Aristotle rejects the essential sense to categories: ‘Those things are said in their own right to be that are indicated by the figures of predication; for the senses of ‘being’ are just as many as these figures.’ (Met., Δ, 1017a22-24) Aristotle does not give us any example of the essential sense. Daniel W. Graham suggests that while essential predication is of the logical form of ‘S is P,’ the logical form of the accidental predication is ‘S has P.’ Although he concedes that the is/has contrast is not Aristotle’s, for which he thinks Aristotle prefers ‘said of’/’in’ terminology, he points to the discussion of ‘have’ in Cat. 15 as an evidence of its potential value for an analysis of predication. Kirwan analyses the distinction of essential and accidental predicate as such: while essential predicates ‘are identical with the subjects of which they are predicated; other predications are true in virtue of the fact that two distinct items, e.g. a substance and a quality, ‘coincide.’ Herman Weidemann believes ‘what divides a predicative statement which predicates essentially from a predicative statement which predicates accidentally is the fact that the former does- whereas the latter does not- answer the question what its subject cannot fail to be without ceasing to exist, as the somewhat its subject goes on existing, no matter what happens to be true of it during its existence, or, what kind of things its subject must be in order to be identifiable as one and the same object as long as it exists.’ C. Essential 1. Either the formula or the name of the subject of an essential attribute is involved in it. For example, animal is involved in female but not in white. (Met., Z, 1030b23-26) 2. Essential attributes, combined together, form a unity. Thus, e.g. animal and biped form a unity because they are both essential of man. (OI., II, 11, 21a14-16) 3. Aristotle distinguishes between two kinds of essential attributes (PsA., A, 4, 73a34-b3; 22, 84a12-17): a) Those attributes that belong to their subject as elements in its essential nature as e.g. line belongs to triangle or point to line. Here the very being of triangle is composed of line or that of line is composed of points: line is contained in the formula of triangle and point in that of line. b) Those attributes whose subjects are contained in their own defining formula as e.g. straight is an essential attribute of line because line is part of the defining formula of straight or odd belongs to number because number is part of the defining formula of odd. Every attribute that is related in neither of these two ways to its subject, it is not an essential but an accidental attribute. (PsA., A, 4, 73b3-5) 4. That attribute which is not predicated of a subject other than itself is an essential attribute. A substance cannot be predicated of anything but itself and is, thus, essential. (PsA., A, 4, 73b5-10) 5. A thing consequently co-stated with anything is essential. For example, if a beast dies when its throat is being cut, its death is also essentially connected with the cutting because the cutting was the cause of death, not death a coincidence of cutting. (PsA., A, 4, 73b10-15) 6. Essential attributes in both of this sense, either in the sense that their subjects are contained in them or in the sense that they are contained in their subjects, are necessary as well as consequently co-stated with their subjects. The reason is that it is impossible for them to inhere in their subjects either simply or in the qualified sense (that one or other of a pair of opposites must inhere in the subject as e.g. one of straight or curve must be necessarily predicable of a line or one of odd or even of number). (PsA., A, 4, 73b16-21; 6, 74b5-12; B, 96b1-5) 7. Only those attributes that are within a genus are essential and possessed by their respective subjects as such and, thus, are necessary. Thereupon, both the conclusion and the premises of demonstrations which produce scientific knowledge are essential. (PsA., A, 6, 75a28-31) Therefore, ‘the extreme and the middle terms must be drawn from the same genus; otherwise, as predicated, they will not be essential and will thus be accidents.’ (PsA., A, 6, 75b10-12) Also, the theorems of a science can be demonstrated by means of another science only when they are related as subordinate to superior. (PsA., A, 6, 75b13-) 8. Our knowledge of the connexion of an attribute with a subject is essential only when ‘we know that connexion through the middle term in virtue of which it inheres (καθ᾿ὃ ὑπἀρχει), and as an inference from basic premises essential and ‘appropriate’ to the subject.’ The essential belonging of the middle to the minor has a necessary connexion with its belonging to the same genus of the major and minor: ‘If that middle term also belongs essentially to the minor, the middle must belong to the same genus as the major and minor terms (ἀνάγκη τὸ μέσον ἐν τῇ αὐτῇ συγγενείᾳ εἶναι). (PsA., A, 9, 76a4-9) 9. In an essential predication, the predicate is signified of a subject identical with itself or with a species of itself. Since only predicates which signify substance signify that the subject is identical with the predicate or with a species of the predicate, predicates signifying substance are essentially predicated and any other predicate is accidental or coincidental. Thus, while animal is essentially predicated of man because man is identical with a species of animal, white is accidentally predicated of man because man is neither identical with white nor a species of it. (PsA., A, 22, 83a24-32) Weidemann discusses the confusion between essential predications and statements of identity. He warns that the expression ‘(to be) just what a man is’ (analogous to the Greek phrase ‘(εἶναι) ὃπερ ἀνθρώπον) ought not to be confused with the expression ‘just what it is for a man to be,’ which renders the phrase τὸ ὃπερ ἀνθρώπῳ εἶναι’ (1007a22, 23, 27-28); a confusion Kirwan discusses. 10. ‘Demonstration proves the inherence of essential attributes in things.’ (PsA., A, 22, 84a11-12) 11. ‘Nothing which does not happen to belong to the genus is essentially the genus; e.g. a white man is not essentially a color.’ Thus, while justice falls within the genus, a just man does not. (To., Γ, 1, ^116a24-) 12. There is no syllogism of essence (ti esti). Nevertheless, we come to know ti esti through a demonstration. (93b15-20; cf. 93b25-28) D. Accidental 1. An accidental attribute cannot be predicated of a subject universally. Thus, we cannot say ‘Every man is musical.’ The reason is that ‘universal attributes belong to things in virtue of their nature.’ Therefore, accidental predicates are predicated only of the individuals. (Met., Δ, 1017b33-1018a2) 2. An accidental is a mere name. (Met., E, 1026b13-) 3. An accidental is obviously akin to non-being. (Met., E, 1026b21) 4. ‘That which is neither always nor for the most part we call accidental.’ (Met., E, 1026b27-33) 5. The matter (ὕλη) is the cause of the accidental because it is matter which is capable of being otherwise than as it for the most part is. (Met., E, 1027a13-16) In fact, there is cause or principle of the incidental of the same kind as there are of the essential because if there were, everything would be of necessity. (Met., K, 1065a6-8) The causes of accidental are unordered and indefinite. (Met., K, 1065a25-26) 6. Since all science is either of that which is always or of that which is for the most part, there is no science of the accidental. (Met., E, 1027a19-24; K, 1064b30-1065a6) Therefore, since an accident may also not inhere and, thus, it is impossible to prove its inherence as a necessary conclusion, there is no demonstrative knowledge of accidents. (PsA., A, 6, 75a18-23) 7. The accidental is not necessary but indeterminate. (Met., K, 1065a24-26) 8. The co-positing of a subject and a predicate which are accidental either to the same subject or to one another, whiteness and being musical for instance, does not form a unity. (OI, II, 11, 21a7-14) 9. Negative predicates, i.e. predicates including a ‘not,’ are accidental predicates. Thus, if good be an essential predicate of a subject, ‘not bad’ cannot be essential but is accidental. (OI., II, 14, 23b15-20) 10. Every attribute which does not belong to its subject in either of two senses of essential attribute (cf. PsA., A, 4, 73a34-b3), namely, belonging to their subjects as an element of its formula or their subjects belonging to them as an element of them, is an accidental attribute. (PsA., A, 4, 73b3-5) 11. Those attributes that are predicated of a subject other than themselves are accidental attributes. Thus, everything except substance is an accidental in this sense. (PsA., A, 4, 73b5-10) 12. A thing not consequentially connected with anything is accidental. For example, in ‘while he was walking it lightened,’ the lightening was not due to his walking but was a coincidence. (PsA., A, 4, 73b10-15) 13. Those attributes that are not within a genus are accidental attributes. (PsA., A, 6, 75a28-31) Therefore, the extreme and middle terms that are not drawn from the same genus are accidents. (PsA., A, 6, 75b10-12) Moreover, to apply an attribute to subjects in different genera afford knowledge of the attribute, only as inhering accidentally, not as belonging to its subject as such.’ (PsA., A, 9, 75b38-76a3)

Abstraction (ἐξ ἀφαιρέσεως) or abstracting (χωρίζειν) have the following characteristics in Aristotle: 1. Abstraction is a process of eliminating (περιελὼν) everything else to reach to a single attribute; a process usually done by mathematicians abstracting the quantitative by eliminating all the sensible qualities like weight, lightness, hardness, etc. (Met. , K, 1061a28-b3) 2. Having eliminated every other attribute of a thing in order to have only one abstract thing, we have the thing qua (ᾗ) the abstracted which is an indivisible thing. (Met., K, 1061a28-b3; Met., M, 1078a21-26; So., Γ, 7, 431b12-17) 3. Abstracting the subject of inquiry and investigating it as abstracted is the best way of investigation. The reason is that in our investigation of a thing, if we abstract it from every other thing so that we reach to it qua it as an individual thing, we can best investigate if an attribute belongs to that indivisible thing or not. (Met., M, 1078a21-28) 4. Although Aristotle calls the abstract thing neither prior nor posterior to the thing, (Met., M, 1077b9-11), he calls sciences dealing with abstracts more precise (Met., M, 1078a11-17) and investigations of them the best. (Met., M, 1078a21-26) 5. Supposing things separated from their attributes in abstractions does not make our inquiry to fall in error for this reason. (Met., M, 1078a17-21; Phy., B, 2, 193b32-194a1) 6. ‘The mind, when it is thinking the objects of mathematics, thinks of them as separate though they are not separate.’ (So., Γ, 7, 431b14-16) At least we can say that in thought, objects of mathematics are separable from motion. (Phy., B, 2, 193b32-194a1) 7. The relatives abstracted having anything accidental to them stripped off (καταλειπομένον), will always be spoken of in relation to each other if they are properly given. For example, when everything accidental to a master is stripped off and only being a master is left, a slave will always be spoken of in relation to that. (Cat., 7, 7a31-37) 8. Holders of the theory of Forms used to abstract by separating the objects of physics, which are less separable than those of mathematics. (Phy., B, 2, 193b32-194a1)

We have a basic definition of genus in Topics (I, 5, 102a31-35): ‘A genus is what is predicated in what a thing is of a number of things exhibiting differences in kind. We should treat as predicate in what a thing is all such things as it would be appropriate to mention in reply to the question “what is the object in question?”; as, for example, in the case of man, if asked that question, it is appropriate to say “He is an animal.”’ He indicates that ‘of the common predicates that which is most definitely predicated in what the thing is, is likely to be the genus.’ (To. , I, 18, ^108b22) From this definition, what is demonstrative in the definition of genus, Aristotle asserts, is ‘what is common to all the cases.’ (To., I, 18, ^108b22) This common thing is ‘one identical thing which is predicated of both and is differentiated in no merely accidental way.’ (Met., I, 1057b37) This means that the things in which the genus is common must be essentially different. In fact, this very common genus must be essentially different in the things it is their genus. Therefore, things that are identical in a genus are at the same time different in that very genus. This means that though the genus is the same in them, it is indeed different in them and they are not the same as each other in that very same genus but specifically different from each other: ‘For not only must the common nature attach to the different things, e.g. not only must both be animals, but this very animal must also be different for each (e.g. in the one case horse, in the other man), and therefore this common nature is specifically different for the two things (διὰ τοῦτο τὸ κοινὸν ἓτερον ἀλλήλων ἐστι τῷ εἴδει). One then will be in virtue of its own nature one sort of animal, and the other another, e.g. one a horse and the other a man. This difference then must be an otherness of the genus. For I give the name of ‘difference in the genus’ to an otherness which makes the genus itself other.’ A. Characteristics of genera The following are the characteristics of genera: 1. Those to which the same figure of predication applies are one in genus. (Met. , Δ, 1016b32-35) 2. Things that are one in genus are all one by analogy while things that are one by analogy are not all one in genus. (Met, Δ, 1016b35-1017a3) 3. A genus includes contraries. (Met., Δ, 1018a25-31) 4. All the intermediates are in the same genus as one another and as the things they stand between. (Met., I, 1057a18-30; 1057b31-34) 5. Not every predicate is a genus of what it is predicated on; for this would equate a genus with one of its own species. (PsA., A, 22, 83b7-10) 6. The opposite of the genus should always be the genus of the opposite. (To., Δ, 4, ^125a27-29) 7. A genus divides the object from other things. (To., Z, 3, 140a^24) 8. None of unity and being is a genus. (Met., B, 998b22-27; Met., K, 1059b31-34; PsA., B, 7, 92b12-14) 9. There is no necessity or even no possibility that things that are the same specifically or generically should be numerically the same. (To., H, I, 152b30-) 10. To be called one due to having one genus is in a way similar to be one due to having the same matter. (Met., Δ, 1016a24-28) 11. The substance of a thing involves its genus, and thereby all the higher genera are predicated of the lower. (To., Z, 5, 143a^20- ) 12. Being falls immediately into genera. (Met., Γ, 1004a4-6) 13. They do not exist apart from the individuals. (Met., B, 999a29-32; Met., I, 1053b21-22) 14. A genus is not a simple qualification but marks off the qualification of substance. (Cat., 5, 3b18-21) 15. Genera are criteria of difference when ‘the things have not their matter in common and are not generated out of each other.’ (Met., I, 1054b27-31) 16. The genus of a thing is its matter (ὓλη). (Met., I, 1058a23-25) 17. A genus is applicable to a wider range than its species. (Cat., 5, 3b21-23) 18. A genus is prior to its species in existence: while a genus reciprocates on the existence of its species, they do not reciprocate on the existence of their genus. (Cat., 13, 15a3- ) Aristotle’s example is this: if there is a fish there is an animal, but if there is an animal, there is not necessarily a fish. 19. The genus of a thing expresses ‘what it is’ and its essence. (To., I, 5, 102a31- ; To., Z, 5, 143a^20- ) 20. A genus is most familiar than its differentia and may be them all. (To., Z, 9, 149a16) 21. The genus is more substantial than its species. (Met., H, 1042a13-16) 22. One, being and substance cannot be classes. (Met., I, 1053b21-24; cf. 1054a8-11) 23. Aristotle draws a distinction between a simple and a composite concept in their falling within a genus. While a simple one can, a composite one cannot. He discusses this between ‘justice’ and ‘just man’: ‘the former falls within the genus, whereas the other does not … for nothing which does not happen to belong to the genus is essentially the genus; e.g. a white man is not essentially a color.’ (To., Γ, 1, ^116a24) 1) Genus and universal ‘Genera are universals’ (Met., Λ, 1069a26-27; Δ, 1014b9-10) and more universal than differentia and species (Met., Δ, 1014b9-12), but it is evident that not all universals are genera. (Met., A, 992b10-13) 2) Co-ordinate species The species resulting from the same division are co-ordinate species. They are the results of the same division in the same genus. Thus, none of them is prior or posterior to others but they are simultaneous by nature. (Cat., 13, 14b33-15a3) 3) Priority of genus to species Aristotle defines prior (λοιπόν) based on reciprocation as to implication of existence: ‘Τhat from which the implication of existence does not hold reciprocally is thought to be prior.’ (Cat., 12, 14a32-34) His examples are genera and species: ‘genera are always prior to species since they do not reciprocate as to implication of existence.’ (Cat., 13, 15a4-6) Τhus, if there is a fish, there is an animal, but if there is an animal, there is not necessarily a fish. 4) Generic versus non-generic attributes As the above discussions illustrates, not all attributes can be genera of their subjects. Thus, we ought to distinguish between generic and non-generic attributes of each subject. K. J. Spalding distinguishes between substantive and classificatory attributes, a distinction that, he believes, is absent from the Aristotelian logic. Classificatory attributes are those that originate and exist in class alone, and are generic like ‘human’ and ‘animal.’ These attributes do not belong to the individual as individual. For example, animal belongs to the Socrates not as Socrates but as man. Substantive attributes, on the other hand, are those that belong to Socrates as Socrates and not as a class. Attributes like sense attributes that originate independently of generic structure and ‘do not involve a necessary relation to or dependence on a class’ are substantive attributes.

The concept of universal in Aristotle’s philosophy has several aspects. 1) Universal and plurality Aristotle posits universal (καθόλου) versus particular (καθ᾿ ἕκαστον) each covering a range of elements: some elements are universal while others are particulars. Aristotle defines universal as ‘that which by nature is predicated (κατηγορεῖσθαι) of many subjects’ and particular as ‘that which is not’ so. (OI ., I, 7, 17a38-b1) The plurality of possible subjects of universal is what Aristotle insists on. The inclusion of the notion of ‘plurality’ in the definition of universal might make us expect to have ‘singularity’ in the definition of particular. So, when Aristotle says that universal is that which is naturally predicable of many subjects, we expect him to define the particular as ‘that which is predicable of one subject only.’ Nonetheless, Aristotle does not and indeed cannot define it this way. We cannot find a text in which he defines particular as such simply because particulars are not predicable of any subject unless we regard their predication of themselves a predication, which Aristotle does not, at least in a genuine sense. Thus, he defines a particular only negatively. Hence, the capability of predication of a plurality is indeed the capability of predication itself because the particular cannot be predicated of anything. A particular is that which cannot be predicated of anything (or: of anything else, if saying of a thing of itself is to be considered as predication). It is ‘numerically one’ and what of which the universal is predicated (Met., B, 999b34-1000a1). Those that cannot be predicated of anything, or particulars, are of two kinds: primary substances and individual accidents. Besides Categories we can hardly find a text where Aristotle discusses individual accidents maybe because they are of much less importance for him compared with substances. However, substances are what he mentions repeatedly so that we can confine particulars to substances. In fact, it is substance that Aristotle considers so repeatedly as what cannot be predicated. As the main particulars and individuals, substances are posited as the main things that are not universal. The closeness of the two concepts of ‘substance’ and ‘unpredicability’ is to the extent that he ignores individual accidents and makes these concepts equal and as the opposite of universal: ‘what is not predicated of a subject is said a substance (οὐσία λέγετα τὸ μὴ καθ᾿ ὑποκειμένου) but what is always said of some subject is called a universal.’ (Met., Z, 1038b15-16. cf. Met., B, 1003a7-9) Therefore, since particulars cannot be predicated of any subject and, thus, every predication is necessarily a predication of a plurality of subjects, the inclusion of ‘plurality’ in the definition of universal is either i) in the sense of ‘representation’ or it must be regarded as ii) an unnecessary addition mentioned just for clarification or iii) only for avoiding cases where something is predicated of itself. By the first we mean this: though a substance is not said of anything, it represents some one thing and there is some one thing that is that substance. A universal, on the other hand, can represent a plurality of things. There is, however, a third possibility that has no essential difference with the sense of representation. Aristotle might have ‘arbitrary predication’ in mind when he suses ‘plurality’ in the definition of universal: while a particular can be the arbitrary predicate of just one thing, a universal can be predicated, both really and arbitrarily, of many things. Whatever Aristotle’s intention was, what is important for our investigation is this: Aristotle uses the notion of plurality in the definition of universal in spite of the fact that it is not necessary. What this implies is that this notion is so important for Aristotle that albeit every predictability is a predictability of a possible plurality, he adds the notion of plurality. What makes this notion important, I believe, is that he has something like a class in mind when he defines a universal because the notion of plurality is indistinguishable from a class. 2) Universal and whole; particular and part In Aristotle, the concepts of universal and whole are so close: ‘That which is true of a whole class and is said to hold good as a whole (which implies that it is a kind of whole) is true of a whole in the sense that it contains many things by being predicated of each, and that each and all of them, e.g. man, horse, god, are one because all are living things (τὸ μὲν γὰρ καθόλου καὶ τὸ ὃλως λεγόμενον ὡς πολλὰ περιέχον τῷ κατηγορεῖσθαι καθ’ ἑκάστου καὶ ἓν ἃπαντα εἶναι ὡς ἑκαστον, ...). Phil Corkum points to Aristotle’s distinction between quantitative and integral wholes in Met., 5, 26, 1023b26-33 where a quantitative whole is called homoiomerous, as the sum of animal while an integral whole, e.g. a house, is called heteromerous. He links the notion of homoiomerous to the notion of indivisibility of individuals (in 1b6-9 and 3b10-18) and indivisibility of universals. He believes that in PrA., I, 4, 25b32-26a2 it is the transitivity of mereological containment that is discussed. 3) Universal is common between instances Universal is common (κοινόν) between all the plurality of subjects it can be predicated of because what belongs to more than one thing must be common between them. (Met., Z, 1038b10-12) In the Same way, what is common cannot be a particular and, thus, a substance. (Met., Z, 1040b23-24) An individual or substance is a ‘this’ and a ‘this’ cannot be what common indicates simply because it is here in ‘this’ and can be nowhere else while common must be common between several things. In fact, what can be indicated by a common is indeed a ‘such.’ (Met., B, 1003a7-9) 4) Universal is the same in its instances We have a universal i) in all of its instances and ii) in the same way (ταὐτὸ ἐπὶ πὰντων). (Met, Γ, 1005a9-10) While the first point is evident (otherwise how could it be their universal?), the second point might seem not only ambiguous but the cause of many problems. For Aristotle, therefore, a universal must be ‘one’ in number and not many. This numerically one universal is the very universal for all its instances. It is the same universal that is predicated on each of its instances. This sameness is not, however, a mere homonymous sameness or the sameness of a homonymous word. All these three points, namely oneness, sameness and rejection of mere homonymous sameness are asserted in Aristotle’s own words τι ἕν καὶ τὸ αὐτὸ ἐπὶ πλειόνων μη ὁμώνυμον. (PsA., A, 11, 77a8-9) This non-homonymous unity is asserted also in PsA., A, 24, 85b15-16. 5) Universal as predicate Contrary to substance that cannot be a predicate, universal is what cannot be prevented from being in the place of predicate. Therefore, Aristotle distinguishes universal from subject because while the latter must necessarily be capable of being a predicate, though it might take the position of subject as well, the latter does not necessarily have such a capability especially when it is a this because it cannot be a predicate in such a case: ‘For the subject and universal differ in being or not being a ‘this’; like man and body and soul are the subject of accidents while the accident is something like musical or white.’ (Met., Θ, 1049a27-30) This indicates that a universal is basically different from subject and although it can be posited in the place of subject, it is the position of predicate that is its position as a universal. In Metaphysics, Z, 13, Aristotle asserts that ‘no universal can be substance.’ The same is asserted in Met., I, 1053b16-17 cf. 1060b21. As James H. Lesher points out, Aristotle’s position is that ‘nothing predicated universally is a substance.’ 6) Universal in substance In Met., 10388b8-9 Aristotle says that no universal is a substance. While a universal cannot be a substance in the way essence (to ti en einai) is, it is, Aristotle asserts, ‘in’ it (ἐν τούτῳ δὲ ἐνυπάρχειν) (Met., Ζ, 1038b16-18). Aristotle’s examples are: animal in man and horse. A universal is ‘in’ the thing it is its universal. But in what sense a universal can be in a thing? It cannot be in it as ‘in a subject’, which is denied in Categories for secondary substances. If we check the senses of being in, we can find some other senses of ‘being in’ some of which are compatible with this sense of ‘being in.’ Michael J. Loux believes that contrary to his earlier works like Peri Ideaon and Organon in which the immanence of universals signals a reproduction of the platonic two worlds picture, in his later works like Physics and Metaphysics, when Aristotle tells us that universals are in particulars he means that they are ‘components of or ingredients in sensible particulars.’ In Metaphysics (Δ, 1014b3-9) Aristotle compares elements with universals and call them ‘the most universal things because elements are present either in all or in many things. 7) Logos is of universal Not only universals have logos (Met., Z, 1038b18-19) but ‘Every logos and every science is of universals and not of particulars.’ (Met., K, 1059b25-26) The reason is that they are the same: the logos of the unjiversal ‘circle’ is nothing but ‘being circle’ and the logos of the universal ‘soul’ is ‘being soul.’ (Met., Z, 1035b33-1036a2) The same is said about definition. (Met, Z, 1036a27-29) 8) Universal: in the soul Contrasting individuals, universals are in the soul (So., 3, 5, 417b22-23; cf. PsA., B, 19, 100a6-7). Aristotle also says that the form, i.e. the essence, of the artwork is in the soul. (met., Z, 1032a32-b2) Moreover, as Michael J. Loux points out, ‘the Peri Ideon tells us that we need universals to serve as the objects of noetic acts.’ 9) Universal: not beside individual In spite of the fact that demonstration creates the opinion that demonstrating is based on the existence of universals as existing among the existing things, they do not have existence besides individuals (PsA., A, 24, 85a31-35; Met, Λ, 1071a19-23). Aristotle believes that universals of a P-series (B203, 71) are not παρὰ τὰ εἴδη: 999a6ff. Also check De Anima, II, 3, 414b20-25 10) Primary or commensurate universal Aristotle distinguishes ‘πρῶτον καθόλού’ (PsA., B, 17, 99a33-35) literally meaning ‘primary universal’ but mostly, and truly, translated as commensurate universal. While a universal merely ‘μὴ ἀντιςτρέφει,’ a primary universal ‘ᾧ ἓκαςτον μὲν μὴ ἀντιςτρέφει’ (PsA., B, 17, 99a33-35). Aristotle mentions three conditions for a commensurate universal. It is an attribute that i) belongs to every instance of its subject (without exception!!!), and this belonging is ii) essentially and iii) qua that subject itself (ᾗ αύτό). (PsA., A, 4, 73b26-28) However, he insists that the second and the third conditions are indeed the same. (PsA., A, 4, 73b28-30) The first condition he paraphrases as ‘to belong to any random instance of that subject’ and the second and the third as ‘when the subject is the first thing to which it can be shown to belong.’ (PsA., A, 4, 73b32-74a3) Aristotle’s example is ‘the equality of its angles to two right angles’. This attribute is not a commensurate universal of figure due to the first condition: it cannot be demonstrated of any figure. Nonetheless, though it can be demonstrated of every isosceles because every isosceles has angles equal to two right angles, it is not a commensurate universal of isosceles due to the other conditions: it is not predicated of isosceles qua isosceles but qua triangle. These conditions seem to be like regulators: they organize everything to match to the right group. The method of finding commensurate universal is like test and error method based on elimination: you must eliminate each of the higher or lower universals and check if the attribute remains or not. The commensurate universal is that which remains in between eliminated universals. (cf. PsA., A, 5, 74a37-b4) Brad Inwoodpresents an understanding of commensurate universal that is different from what I have understood and, thus, must be checked: ‘These universals are propositions in which, for example, ‘all A are B’ is true and which are still true universal statements if converted: ‘all B are A’ is also true.’

Aristotle classifies opposition (ἀντικεῖσθαι) into four groups: relatives (τὰ πρός τι), contraries (τὰ ἐναντία), privation and possession (στρέσις καὶ ἓξις) and affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) His example of relatives are the double and the half. Aristotle’s description of relatives as a kind of opposition is as such: ‘Things opposed as relatives are called just what they are, of their opposites (αὐτὰ ἃπερ ἐστι τῶν ἀντικειμένων λέγεται) or in some other way in relation to them. For example, the double is called just what it is double of the other (οἷον τὸ διπλάσιον, αὐτὸ ὃπερ ἐστίν, ἑτέρου διπλάσιον λέγεται). Again, knowledge and the knowable are opposed as relatives, and knowledge is called just what it is, of the knowable, and the knowable too is called just what it is, in relation to its opposite, knowledge; for the knowable is called knowable by something-by knowledge.’ (Cat., 10, 11b24-30) 2) Senses of relatives In Met., Δ, 1020b26-32 Aristotle distinguishes three senses of relatives: i) That which contains something else many times to that which is contained many times in something else, and that which exceeds to that which is exceeded. E.g. double to half ii) The active to the passive; e.g. that which can heat to that which can be heated iii) The measurable to the measure, e.g. the knowable to knowledge and the perceptible to perception. 3) Relatives and contraries Aristotle’s discussion of relatives is unbelievably ambiguous. While he enumerates relatives besides contraries, privation-possession and affirmation-negation as four types of opposition (Cat., 10, 11b15-23), not only does not he restrict relatives to oppositions but he also does not totally differentiate it from contraries. Aristotle distinguishes between two senses of relatives one of which is contraries: ‘We have distinguished elsewhere the two senses in which relatives are so called-some as contraries (ὡς ἐναντία), others as knowledge to things known, a term being called relative because what is said one to the other is said by the other to itself (τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό). (Met., I, 1056b34-1057a1) It seems that this differentiation is the same as, and maybe the one he himself refers to, the differentiation between the second and the third senses of relatives in Met., Δ, 1021a27-32: ‘Relative terms which imply number or capacity, therefore, are all relative because their very essence includes in its nature a reference to something else, not because something else is related to it (πρός τι πὰντα ἐστὶ πρός τι τῷ ὃπερ ἐστὶν ἄλλου λέγεσθαι αὐτὸ ὃ ἐστιν, ἀλλὰ μὴ τῷ ἄλλο πρὸς ἐκεινο); but that which is measurable or knowable or thinkable is called relative because something else is related to it. For the thinkable implies that there is thought of it, but the thought is not relative to that of which it is the thought; for we should then have said the same thing twice.’ Although Aristotle confirms contrariety in relatives (e.g. virtue to vice and knowledge to ignorance), he denies that there is a contrary ‘to every relative’ as there can be no contrary to what is double or treble. (Cat., 7, 6b15-19) The fact that Aristotle dedicates one sense of relatives to contraries means that the fourfold division of oppositions is not such a strict division without any kind of community between them. In his example of the first sense, however, Aristotle says: ‘One and number are in a sense opposed, not as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the other measurable, they are opposed.’ (Met., I, 1057a4-6) Now, the question is: Is Aristotle’s first sense of relative a contrary or not? Aristotle tells us that the opposition in this sense of relatives is the opposition of measure and measurable. The second sense has two differences with the first one: i) it is not a contrary and ii) what is said by one of the relatives to the other is also said by the latter to the former. To differentiate it from the first sense, when the one is the measure of the other, the latter will be the measure of the former as well: ‘But though knowledge is similarly spoken of as related to the knowable, the relation does not work out similarly for while knowledge might be thought to be the measure, and the knowable the thing measured, the fact is that all knowledge is knowable, but not all that is knowable is knowledge, because in a sense knowledge is measured by the knowable.’ (Met., I, 1057a7-12) Aristotle’s assertion at Met., I, 1057a36-37 that ‘of relative terms, those which are not contrary have no intermediate’ ensures us that we must take the first sense as contraries. Here he mentions a criterion of differentiation between two senses: while the first sense accepts intermediates (as, for example, great and small do), the second one does not. (Met., I, 1057a37-b1) It seems, however, that it is only the second sense that is the essential sense of relatives because the first sense, Aristotle says, is an accidental sense: ‘The one is opposed then to the many in numbers as measure to things measureable; and these are opposed as relatives which are not from their very nature relatives.’ (Met., I, 1056b32-34) 4) Definition of relative Aristotle’s first definition of the category of relative (πρός τι) is as such: ‘We call relative all such things as are said to be just what they are, of or than other things, or in some other way in relation to something else (Πρός τι δὲ τὰ τοιαῦτα λέγεται, ὃσα αὐτὰ ἃπερ ἐστὶν ἓτερων εἶναι λέγεται, ἢ ὁπωσοῦν ἄλλως πρὸς ἓτερον). (Cat., 7, 6a36-37; repeated almost without any change in: Cat., 7, 6b6-8) Aristotle’s examples are larger (because it is what it is than something else (τοῦθ᾿ ὃπερ ἐστὶν ἑτέρου λέγεται) that means it is called larger than something) and double. (Cat., 7, 6a37-b1) Aristotle’s aporia regarding relative is about their relation with substances: whether no substance is spoken of as a relative, or whether this is possible with regard to some secondary substances. (Cat., 7, 8a13-15) In the case of primary substances, it seems that he is confident, at least at first, that neither themselves nor their parts are spoken of in relation to anything: neither an individual man is called someone’s individual man nor an individual hand is called someone’s individual hand (but someone’s hand). (Cat., 7, 8a15-21) Although it is obvious that most of secondary substances are not spoken of as relatives (a man is not called someone’s man) (Cat., 7, 8a21-25), there are some with them there is room for dispute: a head is someone’s head and a hand is called someone’s hand, which seem to be relatives. (Cat., 7, 8a25-28) Aristotle thinks this must be due to the previous definition’s being problematic: with that definition ‘it is either exceedingly difficult or impossible to reach the solution that no substance is spoken of as a relative.’ (Cat., 7, 8a28-32) Thus, Aristotle changes his previous definition to a new one: ‘Those things are relatives for which being is the same as being somehow related to something’ (ἔστι τὰ πρός τι οἷς τὸ εἶναι ταὐτόν ἐστι τῷ πρός τί). (Cat., 7, 8a32-34) Although the first definition does indeed apply to all relations, its problem is that it does not take ‘their own being relative’ (τῷ πρός τι αὐτοῖς εἶναι) the same as ‘their being what they are of other things’ (ἃπερ ἐστὶν ἑτέρων λέγεσθαι). (Cat., 7, 8a34-37) Although this change of definition is to exclude all substances from being relative, what Aristotle says in Topics (To., Z, 8, 146a39- ), seems to ignore this: ‘For of everything relative the substance is relative to something else, seeing that the being of every relative term is identical with being in a certain relation to something.’ 5) Necessary knowledge of the related Knowledge of that in relation to which a relative is spoken of is necessary when one knows the relative: it is impossible to know a relative and at the same time not to know that in relation to which it is spoken of. (Cat., 7, 8a37-b3) To prove this, Aristotle adheres to the definition of relatives: ‘If someone knows of a certain ‘this’ that it is a relative, and being for relatives is the same as being somehow related to something, he knows that also to which this is somehow related.’ (Cat., 7, 8a37-b3; cf. 7, 8b3-15 for Aristotle’s examples) This necessary knowledge of the related, if we call it so, dedicates Aristotle an epistemological reason, besides the ontological one mentioned in his definition, for the exclusion of substances. As we noted in our discussion of Aristotle’s definition of relatives, he changed his first definition to exclude all substances from being relatives. Therefore, it is evident that for him relatives must not include substances, either primary or secondary. Aristotle does have no problem with primary substances simply because it is evident for him that they cannot be relatives. The same can be said about most of the secondary substances as well. The problem for which he changed the definition of substances was about some secondary substances like ‘head’ or ‘hand’: the fact that it is possible to know a hand or head without necessarily knowing definitely that in relation to which it is spoken of proves that they are not relatives. (Cat., 7, 8b15-21) 6) Reciprocation Aristotle regards reciprocation (ἀντιστρέφειν) necessary in all relations: ‘All relatives are spoken of in relation to correlatives that reciprocate.’ (Cat., 7, 6b28-29; cf. Cat., 10, 12b21-24) The sense of reciprocation is clear by his own examples: ‘The slave is called slave of a master and the master is called master of a slave; the double double of a half, and the half half of a double.’ (Cat., 7, 6b29-31) Reciprocation of relatives is so necessary that if there seems that we do not have reciprocation, it must necessarily be due to a mistake and that in relation to which something is spoken of must have not been given properly. (Cat., 7, 6b36-7a1) Aristotle’s example is this: If a wing is given as of a bird, ‘bird of a wing’ does not reciprocate because it has not been given properly: a wing is of a winged and not of a bird; a wing is wing of a winged and a winged is winged with a wing. (Cat., 7, 7a1-5) Even if we do not have a proper name to have a proper reciprocation, Aristotle points, we must invent names. (Cat., 7, 7a5-15 and 7b10-14) Thus, having proper names is the condition of necessary reciprocation: ‘All relatives are spoken of in relation to correlatives that reciprocate, provided they are properly given.’ (Cat., 7, 7a22-23) This condition is also said in another way: there is no reciprocation if a relation is given as related to some chance thing or to something that is accidentally the related thing like when, for example, a slave is given as of a man or a biped instead of being given as of a master. (Cat., 7, 7a25-31) 7) Simultaneity of relatives Aristotle believes that in most cases relatives are simultaneous: double and half or master and slave must exist at the same time: when there is a half, there is a double and when there is a slave, there is a master. (Cat., 7, 7b10-14) However, this receives some exceptions like knowable, which is prior and can, thus, exist before and without knowledge. (Cat., 7, 7b22-27) What approves this non-simultaneousness for Aristotle is that the destruction of knowledge does not carry the knowable to destruction. (Cat., 7, 7b27-31) The same is said about perception and perceptible. (Cat., 7, 7b35-8a9) Aristotle attaches simultaneity to reciprocation. This reciprocation, however, is not a simple reciprocation but ‘reciprocation as to implication of existence’ (ἀντιστρέφει μὲν κατὰ τὴν τοῦ εἶναι) with the condition that neither be in any way the cause of the other’s existence. (Cat., 13, 14b27-29; the same is said also at: Cat., 13, 15a4-11) Aristotle’s examples are the double and the half because when there is a double there is a half and when there is a half there is a double but neither is the cause of the other’s existence. (Cat., 13, 14b29-32) (We have ‘reciprocation as to implication of existence’ also in relation between genus and species but it seems that this has a totally different sense there. 8) Having no independent reality That a relative cannot be a substance, either a primary or a secondary substance, is discussed in our review of both the definition of relatives and their reciprocation. The differentiation of relatives and substances are so deep for Aristotle that after questioning the possibility of any common element or principle for substances and relatives (Met., Λ, 1070a33-36), he asserts that no substance, on the one hand, is the element of relatives and none of the relatives, on the other hand, is the element of substances. (Met., Λ, 1070b3-4) Aristotle does not, however, suffice to this. For him, relatives have the least substantiality, which is, for him, almost the same as reality: ‘The relative is least of all categories a real thing (φύσις τις) or substance, and less than quality and quantity; and the relative is an affection of quantity.’ (Met., M, 1088a22-25) Aristotle believes that an evidence of this least reality (ὄν) and substantiality is that relatives have no proper generation, destruction or movement while each of substance, quality and quantity have them. (Met., M, 1088a29-35) Moreover, neither motion (Phy., E, 1) nor any kind of change is applicable to relatives so that relatives are neither themselves alterations nor the subject of alterations (Phy., Z, 3) and the process of losing and acquiring states cannot be considered as alterations because these are the result of the alterations of non-relative things of which they are states. (Phy., Z, 3) Relative is not even matter but is something different. (Met., M, 1088a24-25) The reason is that the matter is potentially of a nature but relative is neither potentially nor actually of a nature. (Met., M, 1088b1-2) To understand the status of relatives in Aristotle’s world, we have to make a tripartite classification; a classification that though Aristotle himself did not make, his assertions approve it. Based on this division, there are three kinds of being in the world: i) Independent beings: This class includes only substances. ii) Dependent beings: This class includes qualities and quantities. Although they are real, they are ‘in’ substances and cannot exist without them. iii) Super dependent beings: This class includes at least relatives. The fact that relatives must be considered in a third class different from substances, on the one hand, and qualities and quantities, on the other hand, is obvious not only from the previously mentioned texts (Met., M, 1088a22-25, 29-35 and b1-2) in which relatives’ reality is considered less than all substances, qualities and quantities and different from matters but from this text: ‘For there is nothing either great or small, many or few, or, in general, relative which is not something (τι ὄν) different (ἓτερον) [that is also] many or few or great or small’. (Met, N, 1088a27-30) Therefore, super dependent beings are those beings that must necessarily be also something else, i.e. an independent or dependent being. Ackrill (1963, 99) points that some of the words used by Aristotle to exemplify relational entities, e.g. slave, are endowed with a complete sense and do not need to be supplemented by a correlate. (Thus, the linguist criterion of incompleteness would be deficient. Some other instances of relative entities like ‘state,’ ‘knowledge’ and perception are not necessarily followed by the genitive case. 9) Extent of relatives What is the extent of relatives? What are or are not included in relatives either among categories or among other concepts? Which concepts or things Aristotle regard as relative? i) Aristotle includes state (ἓξις) and position (θέσις) among relatives. (Cat., 7, 6b2-6; Cat., 7, 6b11-14; Cat., 8, 11a20-24) ii) Although relative is not matter but is something different (Met., M, 1088a24-25), matter is ‘non-being’ only in virtue of an attribute (Phy., A, 9) and is, thus, a relative term. (Phy., B, 2, 194b9) 10) Property and relativity Aristotle draws a contrast between two types of giving a property, absolute and relative: ‘A property is given either in its own right and for always or relative to something else and for a time.’ (To., E, 1, ^128b15-18) Being a civilized man, for example, is an absolute property for man while to command is a relative property for the soul. The absolute property, however, is considered not only potential to be discussed or observed in relation to many things or periods of time, it in fact ‘belongs to its subject relatively to every single thing that there is, so that if the subject is not distinguished relatively to everything else, the property will not have been given correctly.’ (To., E, 1, 129a18-20) Therefore, an absolute property is a property that ‘is ascribed to a thing in comparison with everything else and distinguishes it from everything else.’ (To., E, 1, 128b33- ) An absolute property is, then, absolutely relative and not conditionally relative, i.e. relative to a specific thing. This is what differentiates it from a relative property, which is relative to a certain thing: ‘A property relative to something else is one which separates its subject off not from everything else but from a particular definite thing.’ (To., E, 1, 128b33- ) One important difference between absolute and relative properties is that while an accident can be a relative property, it can never be an absolute property. (To., I, 5, ^102b20-36) For example, sitting, which is an accident, is also a property relatively to those who are not sitting. (To., I, 5, ^102b20-36) 11) Platonic theories as relatives At least three of Platonic theories Aristotle attaches to relatives: i) Forms ‘It seems that a Form is always spoken of in relation to a Form-this desire itself is for the pleasure itself, and wishing itself is for the good itself.’ (To., Z, 8, 147a^10) Moreover, the theory of Forms takes the relative prior to the absolute as, for example, it takes not the dyad but the number as first. (Met., A, 990b15-17) Aristotle believes that this is against not only the necessities of the case but only the Platonists’ opinion because Forms must be substances only, if they can be shared. (Met., A, 990b27-29) There are, however, things like ‘equal’ which are only relative: they are only in relation to something else. Now the theory that ideas are supposed to be substances only should entail the substantiality of merely relatives. The reason being that Forms are not shared incidentally but each thing shares in that which is not predicated of a subject. (Met., A, 990b29-31) ii) Unequal The Platonic theory of great and small or unequal, which we know more from Aristotle and has, in Platonic philosophy, a role like that of matter in Aristotelian philosophy, is also called relative by Aristole. (Met., M, 1089b4-15) iii) Potentiality Aristotle says that Platonists take what potentially is a ‘this’ and a substance but not actually so a relative because it is ‘neither potentially the one or being, nor the contradictory of the one nor of being, but one among beings.’ (Met., N, 1089b15-20) 12) All things as relative Aristotle attaches the theory that ‘everything is true’ to relativity and thinks the consequence of believing in this theory is that everything is true: ‘He who says all things that appear are true, makes all things relative.’ (Met., Γ, 1011a17-20) 13) Genera and species of relatives There are some genera, Aristotle hints, that are relative but their species are not relative. In such cases, the genera are spoken of in relation to something, but none of the particular cases are so spoken. (Cat., 8, 11a20-36) Aristole’s examples are knowledge and grammar of which the former is a relative but the latter is a quality. The consequence of this is that there is nothing absurd for a thing to be in both genera of relative and quality. (Cat., 8, 11a37- ) However, when the species is a relative, the genera will be a relative too. (To., Δ, 4, 124b15- ) Moreover, Aristotle asserts that ‘the differentiae of relative terms are themselves relative.’ (To., Z, 6, 145a14-16) Things that are called relative are called so, Aristotle says, ‘because the classes that include them are of this sort, e.g. medicine is thought to be relative bcs its genus, knowledge, is thought to be relative,’ (Met., Δ, 1021b4-6) 14) Relatives as indefinite? Fabio Morales takes 1088a29-b1 as a textual evidence supporting the assumption that Aristotle regarded relational terms as indefinite.

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32)

There are four ways in which things are said to oppose (ἀντικεῖσθαι) each other: as relatives (τὰ πρός τι), as contraries (τὰ ἐναντία), as privation and possession (στρέσις καὶ ἓξις) and as affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) Aristotle’s examples are: double and half for relatives, good and bad for contraries, blindness and sight for privation and possession and ‘He is sitting’ and ‘he is not sitting’ for affirmation and negation. We discussed relatives separately thus we ignore it here. A. Contraries Contraries (ἐναντία) have the following features: 1) They are not said of each other (οὐδαμῶς πρὸς ἄλληλα λέγεται) as relatives are said of each other. (Cat., 10, 11b15-23) 2) Contraries are of two kinds: a) Non-intermediables: Those that it is necessary for one or the other of them to belong to the things they naturally occur in or predicated of and accept no intermediate between themselves. Since it is necessary for one of e.g. health and sickness to occur in an animal’s body or odd and even to belong to a number, there is no intermediate between health and sickness or odd and even. (Cat., 10, 11b38-12a9; 12b28-34) b) Intermediables: Those that it is not necessary for one of them to belong to the things they naturally occur in or predicated of and accept intermediates between themselves. It is not necessary for one of e.g. black and white to belong to a body and there may be some intermediates between them. (Cat., 10, 12a9-25; 12b34-40) 3) Contraries can change to one another when the thing capable of receiving them is there. (Cat., 13a18-21) The only exception is when one of the contraries belongs to something by nature. In such cases, change is not possible as the hotness of fire cannot change to coldness while fire is still there. 4) Contraries belong to the same thing, either the same in species or in genus as e.g. sickness and health in an animal’s body or whiteness and blackness in body simply. (Cat., 10, 14a15- ) In Metaphysics (I, 1058a8-10) Aristotle asserts that contraries are in the same genus. 5) There are three possibilities about the genera of contraries: they either are in the same genus, e.g. black and white, or in the contrary genera, e.g. justice and injustice, or are themselves genera, e.g. good and bad. (Cat., 11, 14a19-25) 6) Doing and being affected admit of contrariety, e.g. heating is contrary to cooling. (Cat., 9, 11b1-4) 7) Substances only are able to receive contraries. (Cat., 5, 4a10-17) 8) There is nothing contrary to a substance, whether primary or secondary. (Cat., 5, 3b24-27) Thus, neither man nor an individual man has a contrary. 9) There is no contrary to a quantity: e.g. four-foot ot ten has no contrary. (Cat., 5, 3b27-32) 10) Otherness in species means to be contraries. (Met., I, 1058a17-20) 11) Contrariety is complete difference. Two things that have the same genus but are different in species are other than one another in the highest degree and their difference is complete, i.e. they cannot be present along with one another. (Met., I, 1058a10-16) 12) One of the contraries is a privation, which is a denial of a predicate to a determinate genus. (Met., Γ, 1011b18-20) 13) ‘Neither true judgments nor true propositions can be contrary the one to the other.’ (OI., II, 14, 24b6-7) B. Privation and possession Privation and possession are said in connection with the same thing in which the possession naturally occurs. Only that thing which is capable of receiving a possession and only when it is entirely absent from that which naturally has it and only at the time when it is natural for it to have it, is called to be deprived of it. (Cat., 10, 12a26-30) A thing is not called e.g. blind if it has never had or was not supposed to have sight. That privation and possession are not relatives is obvious from the fact that none is called just what it is, of its opposite. (Cat., 10, 12b16-21) Moreover, while relatives reciprocate, they do not. (Cat., 10, 12b21-25) That they are not contraries is explained by the classification of contraries to intermediable and non-intermediable contraries. The latter are different from privation and possession because it is necessary for one of such contraries to be predicated of absolutely everything while it is not the case about privation and possession because they are necessary only in things naturally capable of their predication. Intermediable contraries are different from privation and possession because while the former are not necessary the latter are necessary in their subject matters. (Cat., 13a3-17) Unlike contraries for each of which it is possible to change to the other, change in privation and possession is allowed only from possession to privation and not vice versa: neither a blind man gets sight nor a bald man regain his hair. (Cat., 13a18-36) C. Affirmation and negation Aristotle regards the reception of truth and falsity as the main difference affirmation and negation opposition has in respect of other three kinds of opposition: it is only affirmation and negation that it is always necessary for one of them to be true and the other to be false (Cat., 13a37-b26), no matter the subject of affirmation or negation exists or not. (Cat., 10, 13b27-35) ‘It is impossible that contradictory propositions should both be true of the same subject.’ (OI., II, 12, 21b17-18) It is evident both about relatives and those contraries that include no co-positing, e.g. health and sickness. The only cases that resemble affirmation and negation are those contraries that are said with co-positing, e.g. ‘Socrates is well’ and ‘Socrates is sick.’ Yet, Aristotle points, not even with these is it necessary always for one to be true and the other false because if Socrates does not exist, neither will be true. (Cat., 10, 13b12-19) This is true also about privation and possession: neither ‘Socrates has sight’ nor ‘Socrates is blind’ are true if he does not exist. Moreover, it is not necessary for one or the other of them to be true or false even if he exists because until the time when it is natural for Socrates to have sight, both are false. (Cat., 10, 13b20-26)

Contrary to nouns and verbs that either do not include a co-positing of parts, including nouns and some verbs, or if they are, their parts do not significate separately, a sentence (λόγος) is a ‘significant portion of speech by co-positing, its parts signify something separately, though not as a positive or negative judgment but as utterance.’ (OI ., I, 4, 16b26-28). Therefore, every utterance in language that i) includes parts, ii) its signification is based on the co-positing of its parts, iii) each of its parts is separately significant but iv) the signification of its parts is the signification of an utterance and not a judgment, is a sentence. This definition distinguishes a sentence from: a) Nouns: because they do not have parts; b) Verbs: because they either do not have parts or if they have, their parts do not significate separately; c) Those co-positings of words whose significance is not based on their co-positing. Thus a co-positing like ‘wall tree house’ is not a sentence because it has no significance on the basis of its co-positing; d) Those co-positings that the signification of at least some of their parts is the signification of judgments. Thus, ‘Socrates is from Athens and is a philosopher’ is not a sentence because at least one of its parts, e.g. ‘Socrates is from Athens’ signifies a judgment. Those sentences that either of truth or falsity belongs to them are propositions (ἀπόφανσις or λόγος ἀπόφαντικὸς). (OI., I, 4, 17a2-3) It is this and only this kind of sentence that is the subject of study in philosophy. (OI., I, 4, 17a5-7) The primary forms of a proposition are, firstly, an affirmation (κατάφασις) and then a negation (ἀπόφασις). (OI., I, 4, 17a8-9) To have an affirmation or a denial and, thus, a proposition, what firstly is necessary is a verb or the tense of a verb (OI, I, 4, 17a9-12; I, 10, 19b12-13; OI, I, 4, 16b28-30) and a noun (OI, I, 10, 19b10-12). Aristotle draws a contrast between single and plural proposition: a) Single proposition: a proposition that ‘indicate a single fact, or the conjunction of the parts of which results in unity.’ (OI., I, 5, 17a15-16) b) Plural propositions: a proposition that ‘are separate and many in number, which indicate many facts, or whose parts have no conjunction.’ (OI., I, 5, 17a16-17) He also differentiates between simple and composite propositions (OI, I, 5, 17a20-22): a) Simple proposition: ‘that which asserts or denies something of something’; b) Composite propositions: ‘that which is compounded of simple propositions.’ A simple (ἁπλῆ) proposition is a statement about the belonging or not belonging of something (OI, I, 5, 17a22-24). Affirmation and denial are indeed kinds of simple proposition, one affirming the belonging and the other not belonging. An affirmation or denial may be single or non-single. A single affirmation or denial ‘signifies some one fact about some one subject. This singularity is destroyed neither by the universality of subject nor by the universal character of the statement. The only thing that destroys this singularity is that one part signifies more than one thing, which makes the proposition more than one proposition (OI, I, 8, 18a13-27). In other words, neither ‘predication of one thing of many subjects’ nor ‘many things of the same subject’ results in a unitary proposition. (OI., II, 11, 20b13-16) There is also another cause that might destroy the unity of predicate and thus the unity of proposition, namely when one of the parts of the predicate is implicit in the other. Thus, e.g. animal-man does not form a unity because the notion ‘animal’ is implicit in ‘man.’ (OI., II, 11, 21a16-18) The following are characteristics of propositions: 1. That about which an affirmation signifies something is a noun, whether definite or indefinite. (OI., I, 10, 19b5-12) Moreover, there can be no affirmation or denial without a verb. (OI., I, 10, 19b12-19) Therefore, a proposition must involve at least a noun and a verb. 2. Contrary propositions: since both belonging and not belonging of something to something is possible, we are able to make a negative proposition out of an affirmative one and vice versa. (OI., I, 5, 17a26-31) Therefore, ‘every affirmation has an opposite denial’ and vice versa. (OI., I, 6, 17a31-33) The contradictory of each proposition is made by changing the positivity or negativity of the verb ‘to be’ to its opposite but not by changing the subject to its opposite. Thus, the contradictory of ‘man is white’ is ‘man is not white’ and not ‘not-man is white.’ (OI., II, 11, 21a38-b5) What happens in the mentioned wrong form of contradictory propositions is that they change the subject while the denial must be the contrary of the affirmation about the same subject. (cf. OI., II, 14, 24b1-6) This is made plain in propositions involving a verb other than ‘to be’. What must be changed in these propositions is the verb and not the noun or the subject. Thus, the contradictory of ‘Socrates runs’ is ‘Socrates does not run’ and not ‘not-Socrates runs.’ 3. Conversion possible: ‘Out of conversion (μετατιθεμένου) of the name and the verb, the same affirmation and denial is generated. (OI., I, 10, 20b10-12) In other words, the two affirmations or denials ‘signify the same thing.’ (OI, I, 10, 20b1-2)

For Aristotle, a verb (ῥῆμα) is that which a) besides a proper meaning b) carry with it the notion of time; c) its parts do not significate separately and d) is a sign of something said of something else (OI ., 2, 16b6-8). This comprehensive definition distinguishes verbs from both nouns (since they do not carry the notion of time with themselves) and sentences or co-positings of words (since they have parts with independent meanings). Based on this definition, a verb signifies three things: i) A main or proper meaning which is the meaning of the verb, e.g. running or sleeping; ii) time and iii) co-positing (or positing away). Although it is not asserted that one part is responsible for prossignification of time, its responsibility is given to co-positing-is. This might seem to be in contradiction with (c). However, it seems that (c) cannot include prossignifications of time and co-positing. What Aristotle means in (c) is just that parts of a verb cannot separately signify a meaning. Therefore, it is better to distinguish between signification, which is about meaning and prossignification, which is generally about anything but meaning. Hence, while the parts of the verb cannot have separate signification, they can have separate prossignification. Aristotle distinguishes between different kinds of verbs: 1) Definite verbs: those verbs that have definite nouns as their verb-name. 2) Indefinite verbs: those verbs that do not have definite nouns as their verb-name (OI., I, 3, 16b12-14; 10, 19b10-11). Aristotle’s examples of an indefinite verb are ‘is not-healthy’ and ‘is not-ill’. 3) Tenses of verbs: ‘was healthy’ and ‘will be healthy’ are tenses of the verb ‘is healthy’ because a verb indicates only the present time (OI., I, 3, 16b16-18). For Aristotle, almost all verbs either are composed of or can be analyzed to parts. An example of the former is ‘is healthy’ and of the latter is ‘runs,’ which can be analyzed to two parts: ‘is running.’ (OI., I, 10, 20a3-5; II, 12, 21b5-8). Thus, for him a verb either includes or can be analyzed to two parts: a part that includes the meaning and is, or is shown, by a name we call ‘verb-name’ (a), and a part that includes the co-positing of that meaning with the subject of the verb, which is or is shown by ‘is’, which we call ‘co-positing-is’ (d). The verb ‘runs’, for example, can be analyzed to a verb-name, ‘running’ and a co-positing-is (Note: Aristotle distinguishes between the verb ‘is’ in the sense of ‘exists’ and the co-positing ‘is’. Whereas in the former ‘is’ is a verb, having a signification of its own, which is ‘existing’, besides signifying time (OI., I, 10, 19b12-19), the ‘is’ in the latter is not a verb (Aristotle calls it ‘incidental’ is (OI., II, 11, 21a25-28) and is not sure whether to call it a verb or a noun (OI., I, 10, 19b22-24)) because it does not signify existing and, thus, need something else to be added. This something else is the meaning we are discussing. Therefore, it is only after the addition of the meaning to this ‘is’ that we have a verb. This is, I believe, the sense of the so much controversial text of OI, I, 3, 16b22-25: ‘For being and not being signify the existence of a thing not τὸ ὄν εἴπῃς αὐτὸ καθ᾿ ἑαυτὸ ψιλόν. For it does not indicate anything but prossignifies some co-positing (σύνθεσίν). Aristotle’s words at 16b24 about co-positing-is that it ‘prossignifies some co-positing’ (προσσημαίνει δὲ σύνθεσίν τινα) is an explicit evidence that she cannot be right.) and is not a concept apart from the things co-posited (συγκειμένων).’ This text, however, is so controversial. Originating from Ammonius and Boethius after him, who used the verb ‘copular’ for ‘est’ and Abelard, some commentators like Weidemann, Oehler, Francisco Ademollo take ‘is’ as having a copulative function. Allen Bāck notes that Aristotle does not separate off ‘is’ from other verbs as a mere copula but takes it ‘as the basic, paradigmatic form of the verb.’ He believes that in his interpretation of Aristotle (in: OI., 55, 19-24) Ammonius also took it as the paradigm for all verbs. Francisco Ademollo criticizes the standard view of taking ‘is’ as copula here and is inclined to take it as essential. David Ross thinks that although Aristotle is aware of the distinction between the existential and the copulative is, he has as yet no very clear idea of their relation. Although Jonathan Barnes agrees that the copula is surely present in de Interpretation, he thinks that at 16b22-25 Aristotle ought to be talking of existential εἶναι. Marie De Rijk Lambartus believes that there is no copula in Aristotle’s philosophical analysis of the elementary sentences and it is a mere corpus alienum in Aristotle’s semantics. Allan Bȃck believes that the copulative theory is not Aristotle’s and ‘may have come to dominate as a result of the neoPlatonizing interpretations of Aristotle’s works by Proclus, Ammonius and Boethius, which is the sign of the relation of running with a subject, e.g. Socrates in ‘Socrates runs’. Nonetheless, none of these parts significate separately. This is supposed to mean that a verb is a single signification. However, it is evident that each of the parts can signify if we use them in a different context as both of ‘running’ and ‘is’ in ‘runs’ or both of ‘is’ and ‘healthy’ in ‘is healthy’ can do. It might seem now that the first mentioned definition of verb might be contradictory. While Aristotle asserts that the parts of verb do not signify separately (d), he considers two other significations for a verb: the signification of time and relation. As it is obvious, both of these significations are done by one part of the verb, that is the co-positing-is. Therefore, in a verb e.g. ‘is healthy’ we have three significations: the significations of meaning, time and co-positing. Aristotle uses prossignification both for time (προσσημαῖνον χρόνον, OI., 2, 16b4) and co-positing (προσσημαίνει δἑ σύνθεσὶν τινα, OI, I, 3, 16b23-24). Since the copula part of a verb has no signification and does not form any conception, a verb is indeed its verb-name. Thus we see Aristotle saying that ‘verbs are in and by themselves names and signify something’ and like names, he adds, they arrest the hearer’s mind and fix his attention (OI., I, 3, 16b19-22). We can conclude then that verbs are names said of something else and carrying time. In other words, verbs are words that though have one single signification, as names have, they also have two other prossignifications: time and relation.

Aristotle’s analysis of language is, firstly, on the basis of co-positing and positing away: this is the starting point of analysis: what is asserted in language either involves a co-positing or does not (Cat. , 2, 1a16-17). Although he does not explain what he means by co-positing, we can see that he considers something like a sentence (his examples: man runs, man wins) and not merely a co-positing of two words like not-man, which he calls an indefinite noun (OI., 2, 16a30-32). Aristotle and his contemporaries had no word for ‘word.’ The closest words for ‘word’ are ὄνομα and λόγος. ὄνομα is distinguished from ῥῆμα (verb) and, thus, cannot mean word. λόγος means a sentence or statement. Daniel W. Graham (Aristotle’s Two Systems, 1987, Oxford University Press, 38, fn.27) renders λεγομενον as ‘word.’ The problem with this suggestion is that, as Aristotle asserts in Categories, it is used both for single words and the composition of several words and even sentences. Aristotle distinguishes a noun from all the followings: a) A co-positing of words: noun is a word that is said without co-positing. (Cat., 2, 1a16-19) b) Inarticulate sounds: the sounds like those that brutes produce are not considered as nouns, though Aristotle believes that they are significant. (OI., 2, 16a28-29) c) Verbs: words that carry with them the notion of time. (OI., 2, 16b6-8) So far, a noun is a word said without co-positing, without the notion of time and distinguished from inarticulate sounds. What remains in language, however, is not necessarily a proper noun, though it is related with noun. What remain are different kinds of names: 1) Noun (ὄνομα) or definite noun: a sound that is significant by convention and of which no part is significant from the rest (OI., I, 1, 16a19-20) unless not having an independent meaning, the parts contribute to the meaning of the whole (OI., I, 1, 16a22-27). This latter condition is indeed a division made by Aristotle between two kinds of nouns: a. Simple nouns: a word in which the part is in no way significant. b. Composite nouns: a word in which though the part may be significant, i) it contribute to the meaning of the whole and ii) it does not have an independent meaning. 2) Indefinite noun: expressions like ‘not-man’ that i) have no recognized term by which denote the expression and ii) are not a sentence or denial by themselves (OI, 2, 16a28-29; 10, 19b8-10). 3) Cases of a noun. This is what used in languages like Greek language that have different cases. They show the senses that are asserted by other elements like prepositions in languages like English in a form or case of the name. Thus, e.g. Φίλωνος means ‘of Philo’ while Φίλωνι means ‘to Philo’. The cases of a noun have the same definition as the noun itself. However, they are not able to combine with any of the different tenses of the verb ‘is’ so that a true or false preposition results. (OI., 2, 16ab4-5). Aristotle thinks convention (συνθήκην) is the basis of the formation of nouns: ‘The limitation ‘by convention’ was introduced because nothing is by nature a noun- it is only so when it becomes a symbol.’ (OI., I, 1, 16a27-28) In Greek language, Francesco Ademollo notes (B508, 34), onoma has a close etymological connection with any transitive verb. Thus, it seems that an onoma is essentially ‘an expression that names or refers to something. It is strange that Aristotle does not distinguish proper from improper noun. We find no text in which Aristotle made such a distinction. In fact, it seems nouns are essentially improper for him: ‘A name, e.g. ‘round,’ means vaguely a sort of whole: its definition analyses this into its particular senses. Similarly, a child begins by calling all men ‘father’ and all women ‘mother’ but later on distinguishing each of them.’ (Phy., A, 1) Nouns necessarily are applicable to others: ‘If one were defining you, he would say ‘an animal which is lean’ or ‘white’ or something else which will apply to someone other than you.’ (Met., Z, 1040a12-14)

Plato Seeking for “One Real Explanation” in Phaedo Abstract: This essay intends to discuss what Plato was seeking as an explanation in Phaedo. In this dialogue, we observe Socrates criticizing both the natural scientists’ explanations and Anaxagoras’ theory of Mind because they could not explain all things, firstly, in a unitary and, secondary, in a real way. Thence, we are to call what Plato is seeking as his ideal explanation in Phaedo “One Real Explanation”. He talks at least about three kinds of explanation, two of which, the confused and foolish way of explanation by Forms and the explanation by Forms appealing to essence, are just "second best" and lower degrees of explanation. His ideal explanation is an explanation that can explain all things by one thing and in a real way. Though he cannot show, at least in Phaedo, how this One Real Explanation can work, we can see Plato completing the theory by the Form of the Good in Republic. Key words: Plato; explanation; cause; good; Form I Having discussed the immortality of human soul in Phaedo, Socrates says that their arguments do not prove the soul to be immortal but only being long-lasting (95c). He pauses 'for a long time, deep in thought' (95e7) to find a way for the soul’s immortality. He knows that it is a crucial problem that requires 'a thorough investigation of the cause of generation and destruction' [ὅλως γὰρ δεῖ περὶ γενέσεως καὶ φθορᾶς τὴν αἰτίαν διαπραγματεύσασθαι] (95e9-96a1). Socrates’ wonderful keen for the wisdom of natural science, he says, was because he thought it splendid to find out the causes of everything, 'why it comes to be, why it perishes, and why it exists' (96a9-10). Socrates is thus searching for i) the explanation of everything and ii) an explanation that tells him about being, generation, and destruction of things. One simply can expect these from those natural scientists based on what they were to present: explaining all things’ being, becoming, generation, and destruction by one or some elements. Their explanations not only were not satisfactory but made him even 'quite blind to those things which he and others thought that [he] clearly knew it before' (96c3-5). But why their explanations made him so? Let have a look at his three kinds of examples of what he had thought he knew before- but became blind to after their explanations: i) Men grow with eating and drinking. ii) A large man is taller than a small one by a head. iii) Ten is more than eight because two is added. All of these examples attempt to explain things through addition; in the first example, as he says, 'food adds flesh to flesh and bones to bones' (96d 1-2). We can see the same in other examples: the addition of a head in the second and of a number in the third. Actually he argues about addition after these examples: I will not even allow myself to say that where one is added to one either the one to which it is added or the one that is added becomes two, or that the one added and the one to which it is added becomes two because of the addition of the one to the other. (96e7-97a1) II Socrates speaks implicitly about two reasons of rejecting such explanations. Their first problem, in my view, is that they are not Real explanations. He wonders because it is obvious for him that coming close to each other cannot be the true cause of two ones’ becoming two: I wonder that when each of them is separated from the other, each of them is one, nor are they then two, but that, when they come near one another, this is the cause of their becoming two, the coming together and being placed closer to one another. (97a2-5) The second problem arises when we use the opposite things as the cause of the same thing: Nor can I any longer be persuaded that when one thing is divided, this division is the cause of its becoming two, for just now the cause of becoming two was the opposite. At that time it was their coming close together and one was added to the other, but now it is because one is taken and separated from the other. (97a5-b3) Corresponding the addition, or growing, to generation, division to destruction and twoness or oneness to being, it will be obvious how these examples are appropriate to Socrates’ expectation from natural scientists, namely the explanation of coming to be, destruction, and being. But they not only failed in giving one explanation for everything, but they did vice versa: they used the opposite explanations for the same thing. Two opposite things are at the extreme points of two-ness or, in other words, there are not two things that are more than two opposites two. If we sum up these two problems of explanation, namely, not being a real explanation and not being one, Socrates’ main problem with what is called 'physical explanation' will be obvious. Calling it a “requirement” of explanation, Politis (2010:70) formulates Socrates’ problem as such: “if same explanandum, then same explanans” or conversely: “if same explanans, then same explanandum”. Socrates’ reliance on traditional explanation, Politis thinks, was lost because he thought that “such explanations do not satisfy certain fundamental requirements of explanation” (ibid: 65). Bostoc’s formulation of the case is nearly the same: “Two opposite causes cannot have the same effect” and “the same causes cannot have opposite effects” (1986: 138). He calls them “two conditions which Socrates thinks any acceptable reasons or causes must satisfy”. (ibid) These are obviously some formulas that can be correctly said about Plato’s requirements or conditions of explanation but reducing the problem to this is misleading. His disappointment with them, I think, is due to the fact that they could not understand the necessity of One Real Explanation for all things. One Real Explanation is an explanation that can explain all the related matters in a unified and real way. Only in such a way we can understand the explanation and follow the argument. This is exactly what Plato has in mind when, in Sophist, gets the visitor to say that those philosophers 'have simply been talking their way through their explanations without paying any attention to whether we were following them or we were left behind' (243a7-b1). What is Socrates’ final decision about their explanation? Does he reject them completely? Does he think that they cannot be explanations at all or accept them as a low-level kind of explanation that, however, has some problems? Politis (2010:112) thinks that physical explanations 'cannot themselves be explanations' in Plato’s view but they can only be 'an element' in the explanation and 'can thus be accommodated within explanations' (ibid: 111). He thinks that Socrates’ disillusionment with them must be understood as resulting not in his throwing them out, but in his settling them to one side, for the sake of first examining what an explanation really is (ibid:112). David Hillel Ruben, on the other hand, thinks that Plato could not think about those explanations even as an element. '[He] did not find them less than fully adequate, and in need of supplementation', he says, 'but rather entirely unacceptable' and Socrates knows that he does not want to follow this alleged method of explanation at all (2004:47). For this last comment he refers to 97b3-7 where we have Socrates saying: I do not any longer persuade myself that I know why a unit or anything else comes to be, or perishes or exits by the old method of investigation, and I do not accept it, but I have a confused method of my own. We have already noted that Plato’s objection to natural scientists’ explanation was that they failed to suggest One Real Explanation. Having been disappointed with all those different incomprehensible explanations, the only thing that could make him hopeful again was One Real Explanation which he heard had been suggested by Anaxagoras’ theory of Mind (νοῦς). It was One explanation because it was saying that “it is Mind that directs and is the cause of everything” (ὡς ἄρα νοῦς ἐστιν ὁ διακοσμῶν τε καὶ πάντων αἴτιος)' (97c1-2 cf. DK, Fr.15.8-9, 11-12, 12-14). That Socrates was searching for one explanation for all things can be proved even from what he has been expecting from natural philosophers. The case is, nonetheless, more clearly asserted when he speaks about Anaxagoras’ theory. In addition to διακοσμῶν τε καὶ πάντων αἴτιος of 97c2 mentioned above, we have τὸ τὸν νοῦν εἶναι πάντων αἴτιον (c3-4) and τόν γε νοῦν κοσμοῦντα πάντα κοσμεῖν (c4-5) all emphasizing the cause of all things (πάντα) which can clearly prove that one of the reasons which caused Socrates to embrace it delightfully was its claim to provide the cause of all things by One thing. But it was also a Real explanation because it was something specific: Mind. We pointed out that the cause of his dissatisfaction with the explanation of becoming two out of coming together was that it could not be a Real cause. Why Mind, in difference with those unreal causes, can be a Real cause? Because there is not, it seems at least at first, anything in the world more suitable than Mind to be the basis of explanation. The essential relation of knowledge and virtue or good and knowledge might help us understand the specific character of Mind. Trying to solve the problem of teachability of virtue, Socrates says that it can be teachable only if it is a kind of knowledge because nothing can be taught to human beings but knowledge (ἐπιστήμην) (Meno 87c2). The dilemma will be, then, whether virtue is knowledge or not (c11-12) and since virtue is good, we can change the question to: whether is there anything good separate from knowledge (εἰ μέν τί ἐστιν ἀγαθὸν καὶ ἄλλο χωριζόμενον ἐπιστήμης) (d4-5). Therefore, the conclusion will be that if there is nothing good which knowledge does not encompass, virtue can be nothing but knowledge (d6-8). Anaxagoras’ Mind, at least in Socrates’ view, was attempting to explain everything by the concept of the Good. This connection between Mind and the Good belongs more to the essential relation they have in Socrates’ thinking than Anaxagoras’ own theory because there are almost nothing about such a relation in Anaxagoras. The reason for Socrates’ reading can be that Mind is substantially compatible with Socrates’ idea of the relation between good and knowledge. Both the thesis 'no one does wrong willingly' and the theory of virtue as knowledge are evidences of this essential relation. Nobody who knows that something is bad can choose or do it as bad. The reason, when it is reason, that means when it is as it should be, when it is wise or when it knows, works only based on good-choosing. In this context, when Socrates hears that Mind is considered as the cause of everything, it sounds to him like this: Good should be regarded as the basis of the explanation of all things. We see him, thus, passing from the former to the latter without any proof. This is done in the second sentence after introducing Mind: I thought that if this were so, the arranging Mind would arrange all things and put each thing in the way that was Best (ὅπῃ ἂν βέλτιστα ἔχῃ). If one then wished to find the cause of each thing by which it either perishes or exists, one needs to find what is the best way (βέλτιστον αὐτῷ ἐστιν) for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is the most excellent (ἄριστον) and best (βέλτιστον). The same man must inevitably also know what is worse (χεῖρον), for that is part of the same knowledge. (97c4-d5) This passage is a good evidence of Socrates’ leap from Anaxagoras’ Mind to his own concept of the Good that can explain why Socrates found Anaxagoras theory after his own heart (97d7). Mind is welcomed because of its capability for explanation on the basis of good to 'explain why it is so of necessity, saying which is better (ἄμεινον), and that it was better (ἄμεινον) to be so' (97e1-3). On this basis, Anaxagoras could explain everything- that earth is flat or round, in the up or down or middle and if any of them, he would go on to show that it was better for it to be so. On the basis of his need for One Real Explanation, I think, we can elaborate why Anaxagoras’ Mind was so attractive for young Socrates. He emphasizes precisely on this point saying (98a1-b3): If he showed me those things I should be prepared never to desire any other kind of cause. I was ready to find out in the same way (οὕτω … ὡσαύτως) about the sun and the moon and …., how it is best (πῇ ποτε ταῦτ᾽ ἄμεινόν ἐστιν) that each should act or be acted upon. I never thought that Anaxagoras, who said that those things were directed by Mind, would bring any other cause for them than that it was best for them as they are (βέλτιστον αὐτὰ οὕτως ἔχειν ἐστὶν ὥσπερ ἔχει). Once he had given the best for each (ἑκάστῳ βέλτιστον) as the cause for each and the general cause of all, I thought he would go on to explain the common good for all (τὸ κοινὸν πᾶσιν ἐπεκδιηγήσεσθαι ἀγαθόν). What Socrates thought he had found in Anaxagoras can indicate what he had been expecting from natural scientists before. Socrates could not be satisfied with their explanations because they were unable to explain how it is the best for everything to be as it is. It can probably be said, then, that it was the lack of the unifying Good in their explanation that had disappointed him. Politis, conversely, thinks it is not true to say Socrates introduced this new method of explanation because of the fact that they were not good-based. 'Socrates’ complaint against traditional explanation', he says, 'is independent of and prior to his becoming hopeful about good–based ones.' (2010, 99) If we have to accept that what he means by ‘good-based’ explanation is the same with what Socrates had in mind about Anaxagoras’ theory, Politis is misleading here. Socrates’ hope for Anaxagoras’ theory was, I believe, owing to the fact that he had been disappointed with natural philosophers’ explanations which justifies the suggestion to take that which is included in this new theory as the same with what was absent before. It is also misleading, I think, to call Socrates' theory teleological if we mean by this some kind of explanation that must be considered besides other kinds of explanation as, for example, Taylor thinks (1998, 11). If we behold the essential relation between the Good and the knowledge and observe the fact that the good is here considered as the basis of explanation, we cannot be satisfied with putting it besides other kinds of explanations only as one kind. It must be insisted that we are discussing what Socrates thought Anaxagoras’ theory of Mind should have been, not about Anaxagoras’ actual way of using Mind. Phaedo 97c-98b, is not about what Socrates found in Anaxagoras but what he thought he could find in it. On the contrary, it should also be noted that it was not this that was dashed at 98b, but Anaxagoras’ actual way of using Mind. It was Anaxagoras’ fault not to find out how to use such an excellent thesis (98b8-c2, cf. 98e-99b). He 'made no use of Mind nor gave it any responsibility for the management of the things, but mentioned as causes air and either and water and many other strange things'. (98b8-c2) Socrates’ complaint against Anaxagoras, as it is obvious in the text above, is not against Anaxagoras as the creator of Mind, but is against Anaxagoras as a natural scientist who turned back to their method of explanation. Socrates’ example of the explanation of his staying at prison, 98e-99b, confirms it. He says when we make a mistake like what Anaxagoras had made and paid attention to many causes, it is the ignorance of 'true causes' (ἀληθῶς αἰτίας) (98e1). Socrates says that 'to call those things causes is too absurd' (99a4-5) and by those things he means all things that, though are necessary for its being as it is, they are not the causes of its being as it is. Though they are necessary, but are not the Real causes. We can clearly see his main concern about a cause in 99b2-4: Imagine not being able to distinguish the real cause (αἴτιον τῷ ὄντι) (99b2) from that without which the cause cannot be able to act as a cause (ἐκεῖνο ἄνευ οὗ τὸ αἴτιον οὐκ ἄν ποτ᾽ εἴη αἴτιον). (99b3-4) We cannot call them causes and this name does not belong to them. They cannot be causes and explanations since they cannot explain the Good in what they want to explain. Socrates gives an example to show how not believing in 'good' as the basis of explanation makes people be wanderers between different unreal explanations of a thing. His words δέον συνδεῖν (binding that binds together) as a description for the Good shows that he want it to have a unifying role: They do not believe that the truly good and binding binds and holds them together (ὡς ἀληθῶς τὸ ἀγαθὸν καὶ δέον συνδεῖν καὶ συνέχειν οὐδὲν οἴονται). (99c5-6) At the end of discussing what he would like to be the explanation but became disappointed, he is still hopeful to find someone to teach him the workings of that kind of cause (99c6-8) which definitely shows he was not thoroughly disappointed of finding the way of using good in explanation. It is on this basis that we say One Real Explanation is the highest degree of explanation for him. What he suggests later on as the explanation by Forms is only a 'second voyage' (δεύτερον πλοῦν) (99c9-d1). Whatever this ‘second’ might mean, as Hackforth (1955, 137) notes, it must include some kind of ‘inferiority to πρῶτος πλοῦς’. His following use of the method of hypothesis after he finds that that wonderful One Real Explanation cannot be discovered easily -either by himself or by anyone else telling him its working- based on which he will make his new theory of explanation by Forms, can definitely show that the basis of explanation for him is still the Good even if he has to search for other theories of explanation. Having in mind Plato’s well-known analogy of the sun and the Good at Republic 508-509, we can dare to say that his warning of the danger of seeing the truth directly like one watching an eclipse of the sun in Phaedo (99d-e) is more about the difficulty of so-called good-based explanation than its insufficiency, a difficulty precisely confirmed in Republic (504e-505a, 506d-e). What is said in Republic is totally compatible with Phaedo 99d–e and the metaphor of watching an eclipse of the sun. In spite of the fact that we do not have adequate knowledge of the Idea of the Good, it is necessary for every kind of knowledge: 'If we do not know it, even if we know all other things, it is of no benefit to us without it' (505a6-7). The problem of our not having sufficient knowledge of the Idea of Good is tried to be solved by the same method of Phaedo 99d-e, that is to say, by looking at what is like instead of looking at thing itself (506d8-e4). It is this solution that leads to the comparison of the Good with sun in the allegory of Sun (508b12-13). What the Good is in the intelligible realm corresponds to what the sun is in the visible realm; as sun is not sight, but is its cause and is seen by it (b9-10), the Good is so regarding knowledge. It has, then, the same role for knowledge that the sun has for sight. Socrates draws our attention to the function of sun in our seeing. The eyes can see everything only in the light of the day being unable to see the same things in the gloom of night (508c4-6). Without the sun, our eyes are dimmed and blind as if they do not have clear vision any longer (c6-7). That the Good must have the same role about knowledge based on the analogy means that it must be considered as a required condition of any kind of knowledge: The soul, then, thinks (νόει) in the same way: whenever it focuses on what is shined upon by truth and being, understands (ἐνόησέν), knows (ἔγνω) and apparently possesses understanding (νοῦν ἔχειν). (508d4-6) Socrates does not use agathon in this paragraph and substitutes it with both aletheia and to on. He links them with the Idea of the Good when he is to assert the conclusion of the analogy: That which gives truth to the objects of knowledge and the power of knowing to the knower, you must say, is the Idea of the Good: being the cause of knowledge and truth (αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας) so far as it is known (ὡς γιγνωσκομένης μὲν διανοοῦ). (508e1-4) Knowledge and truth are called goodlike (ἀγαθοειδῆ) since they are not the same as the Good but more honoured (508e6-509a5). What had been implicitly contemplated and searched in Phaedo, is now explicitly being asserted in Republic. The Form of the Good in Republic, of which Santas speaks as 'the centerpiece of the canonical Platonism of the middle dialogues, the centerpiece of Plato’s metaphysics, epistemology, ethics and …' (1983, 256) much more can be said. Plato’s Cave allegory in Book VIII dedicates a similar role to the Idea of the Good. The Idea of the Good is there as the last thing to be seen in the knowable realm, something so important that its seeing equals to understanding the fact that it is the cause of all that is correct and beautiful (517b). Producing both light and its source in visible realm, it controls and provides truth and understanding in the intelligible realm (517c). The same point is asserted in a more explicit way in the Republic, where the Good is considered not only as a condition for the knowledge of X, but also as what binds all the objects of knowledge and also the soul in its knowing them. At Republic VI, 508e1-3, when Socrates says that the Form of the Good 'gives truth to the things known and the power to know to the knower (τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν)' , he wants to set the Good at the highest point of his epistemological structure by which all the elements of this structure are bound. This point is emphasized at 509b6-7: 'the objects of knowledge owe their being known to the good' (τοῖς γιγνωσκομένοις … τὸ γιγνώσκεσθαι … ὑπὸ τοῦ ἀγαθοῦ παρεῖναι). Good is the cause of knowledge (αἴτιαν δ᾽ ἐπιστήμης) (508e3), and the Form of the good, as is said in book VII, is the basis of knowing and its meaning since you cannot know anything without finding it: Unless someone can distinguish in an account the form of the good from everything else, cannot survive all refutation (ὃς ἂν μὴ ἔχῃ διορίσασθαι τῷ λόγῳ ἀπὸ τῶν ἄλλων πάντων ἀφελὼν τὴν τοῦ ἀγαθοῦ ἰδέαν). (534b8-c1) This binding aspect of the Good is by no means a simple binding of all knowledge or all the objects of knowledge, but the most complicated kind of binding as it is expected from the author of the Republic. The kind of unity the Good gives to the different knowledge of different things is comparable with the unity which each Form gives to its participants in Republic: as all the participants of a Form are united by referring to the ideas, all different kinds of knowledge are united by referring to the Good. If we observe Aristotle's assertion that for Plato and the believers of Forms, the causative relation of the One with the Forms is the same as that of the Forms with particulars (e.g. Metaphysics 988a10-11, 988b4), that is to say the One is the essence (e.g., ibid, 988a10-11: τοῦ τί ἐστὶν, 988b4-6: τὸ τί ἢν εἶναί) of the Forms besides his statement that for them One is the Good (e.g. ibid, 988b11-13) the relation between the Good and unity may become more apparent. Since the quiddity of the Good (τί ποτ᾽ ἐστὶ τἀγαθὸν) is more than discussion (506d8-e2), we cannot await Socrates to tell us how this binding role is played. All we can expect is to hear from him an analogy by which this unifying role is envisaged, the sun. The kind of unity that the Good gives to the knowledge and its objects in the intelligible realm is comparable to the unity that the sun gives to the sight and its objects in the visible realm (508b-c). The allegory of Line (Republic VI, 509d-511), like that of the Sun, tries to bind all various kinds of knowledge. The hierarchical model of the Line which encompasses all kinds of knowledge from imagination to understanding can clearly be considered as Plato’s effort to bind all kinds of knowledge by a certain unhypothetical principle. The method of hypothesis starts, in the first subsection of the intelligible realm, with a hypothesis that is not directed firstly to a principle but a conclusion (510b4-6). It proceeds, in the other subsection, to a 'principle which is not a hypothesis' (b7) and is called the 'unhypothetical principle of all things' (ἀνυποθέτου ἐπὶ τὴν τοῦ παντὸς ἀρχὴν) (511b6-7). This παντὸς must refer not only to the objects of the intelligible realm but to the sensible objects as well. Plato does posit, therefore, an epistemological principle for all things, a principle that all things are, epistemologically, bound and, thus, unified by. III To pass over that theory of explanation by the Good to attach a new theory in Phaedo, Socrates needs a new method, the method of hypothesis. This method is used to represent an image of what the real explanation is, enabling us to look at the real one. He describes this method as such: However, I started in this manner: taking as my hypothesis in each case the theory that seemed to me the most compelling. I would consider as true, about cause and everything else, whatever agreed with this, and as untrue whatever did not so agree. (100a3-7) It is through this method that he comes to the kind of cause he has always been concerned about (100b2-3). Though his new kind of explanation is emphasized to be what he has never stopped talking about, I am not to agree with Bluck (2014, 14) that in this coming to the theory of explanation by Forms, there is a transition from ‘purely Socratic thought to Plato’s own development of it’ because the theory of good-based explanation in neither less Platonic than the theory of Forms nor is in a lower rank. However, Socrates knows that this theory can be used only when the existence of Forms has been accepted (100b7-9). If we accept the existence of forms, there will be no better way to explain a thing unless by its form: I think that, if there is anything beautiful besides the Beautiful itself, it is beautiful for no other reason that it shares in that Beautiful, and I say so with everything. (100c4-6) He calls this theory simple, naïve, and foolish and emphasizes that it is not the way of the relation between things and their Form that is important for this kind of explanation but this very theory of Form as explanation (100d). He also calls this answer to the question of explanation the safest answer and impossible to fall into error. It is not an answer which makes us surprised, but the most predictable one. He mentions the problem of the same explanations for the opposites again adding another problem which is the problem of explanation by the opposites: Bigger is bigger by a head which is small and this would be strange, namely, that someone is made bigger by something small. (101b1-2) Bostock (1986: 137) interprets this as the third condition of explanation and formulates it as such: “A cause cannot be the opposite of the effect it has”. We can also see this theory, for instance, in Timaeus 29b5-9. The theory of explanation by Forms is the most possible consistent theory with this kind of thinking. The Forms are the only things that can be the aitia of things: You would loudly exclaim that you do not know how else each thing can come to be except by sharing in the particular reality in which it shares, and in these cases you do not know of any other cause of becoming two except by sharing in Two-ness, and that the things that are to be two must share in this… (101c2-6) Let us return to the method of hypothesis on which he based his theory of explanation by Forms. He told us that in this method we should take the most compelling theory as our hypothesis and then analyze everything on its basis: Whatever agrees with it will be considered as true and whatever not, as false. The theory of Form as explanation is his first hypothesis here. It is obvious that the theory was the most compelling theory for him. Now he says that before examining the consequence of this theory, you should not examine the hypothesis itself; and continues: 'When you must give an account of your hypothesis itself, you will proceed in the same way: you will assume another hypothesis, the one which seems to you the best of the higher ones until you come to something acceptable.' (101d5-e1) Now we know that we should examine the consequences of our theory and be careful not to jumble the consequences and the hypothesis at once. What is the consequence of the theory of Form as explanation? It might have happened that one thing has two opposite Forms. Let’s see his example: If you say these things are so, when you then say that Simmias is taller than Socrates but shorter than Phaedo, do not you mean that there is in Simmias both tallness and shortness? (102b3-6) Thus, it is obvious that it cannot be an explanation of something just by referring to its Form because it can share many Forms and it cannot be meaningful to say something is so and so because it shares a Form and it is such and such because it shares another Form, the opposite to the first one. It is noteworthy that this is not the same with what we have discussed as a problem in physical explanation (the opposite things as the cause of the same things) but something different: the opposite things as the cause of opposite characters of the same thing. In the former case, for example, addition and division were the causes of the same thing, two-ness, while here tallness and shortness are the causes of two opposite characters, being taller than Socrates and being shorter than Phaedo, in the same person, Simmias. While the first problem forced Socrates to look for one explanation for all things, this problem will make him distinguish between what is the thing itself and what it happened to have: It is not, surely, the nature of Simmias to be taller than Socrates because he is Simmias but because of the tallness he happened to have (τῷ μεγέθει ὃ τυγχάνει ἔχων). Nor is he taller than Socrates because Socrates is Socrates, but because Socrates has smallness compared with the tallness of the other? (102c1-4) These are what happened for them to have and they do not have them because they are themselves as if these characters make their nature. This is only tallness that has tallness as its nature and only shortness that has shortness as its nature. Thus: Not only tallness itself is never willing to be tall and short at the same time, but also that the tallness in us will never admit the shortness or be overcome. (102d6-8) He concludes that the opposites themselves (not what have them by accidence) cannot accept each other while they are themselves. This leads us to a crucial point: only what that shares in a Form by its nature, refuses its opposite or cannot have it while it is itself. It means we can explain a thing by a Form it shares in only when it shares in it essentially. He says: It is true then about some of these things that not only the Form itself deserves its own name for all time, but there is something else- that is not the Form but has its character whenever it exists. (103e2-5) Every tall thing shares in the Form of tallness because it is tall, but only what has tallness in its nature can deserve the name of the Form essentially. What we have used as our example here, tallness, is his previous example and is not suitable to show what he wants to show us because there is not or at least we are not aware of a special thing which has tallness by its nature except the Form of tallness itself. Socrates’ own examples are ‘fire’ and ‘snow’ which have hotness and coldness by their nature and cannot accept the opposite. We have, thereupon, three classes of things: Forms (hot itself); what shares in or has the Form by its nature (fire); and what shares in Form by accidence (every hot thing). It is only the second or what shares in Form by nature that refuses its opposite. It is in this way that Socrates solves the problem of explanation by Form, the explanation of two opposite characters of a thing by two opposite Forms. Everything that shares in a Form by nature is always called with that Form and can never be called by the opposite: It cannot 'admit that Form which is opposite to that which it is' (104b9-10). He uses the examples of odd and even: Consider three: do you not think that it must always be called both by its own name and by that of the Odd, which is not the same as three? That is the nature of three, and of five, and of half of all the numbers; each of them is odd, but it is not the Odd. (104a5-b1) By this method, he reaches to a necessary opposition between things which are not the opposites: Five does not admit the Form of the Even, nor will ten, its double, admit the Form of the Odd. The double itself is an opposite of something else, yet it will not admit the Form of the Odd. (105a6-b1) Now he can extend his previous safe and foolish theory of explanation by Forms (by resolving that problem of the explanation of opposite Forms in the same thing) and pass to another not foolish but still safe theory of explanation. (105b6-c6) Let us review what we have discussed above and summarize them: 1. Plato cannot be satisfied with the natural scientists’ explanations since they have ignored to introduce One Real Explanation. 2. That One Real Explanation, for Plato, is a theory that i) can explain all things by a unitary way of explanation, and ii) can do this with showing how it is good or best for them to be as they are. Plato was disappointed with Anaxagoras’ Mind because he did not show how Mind could satisfy the conditions mentioned above (Anaxagoras used many other causes and did not use Mind to show how it was best for everything to be as it was). In spite of the fact that Anaxagoras made him disappointed, Plato did not leave the above conditions as the necessary conditions for an explanation. He had to come to other theories of explanation as 'second best' ones because neither he himself nor anyone else could show "the workings" of such an explanation. 3. He represents the theory of explanation by Form as his own confused theory of explanation as the safest, but foolish. Having encountered with the problem of the two opposite Forms as explanations of two opposites in one thing, he used the leading point of the method of hypothesis that when you reach to a problem and want to examine the hypothesis itself, you should assume another hypothesis; and he came to distinguish between what a thing is by its nature and what it is by accidence. The result was a new theory of explanation based on the previous theory through making limitations on it: the theory of explanation only by those Forms to which a thing shares by its nature. He still preserves this crucial point that explanation should refer to the Forms. What is added to this point here is that he restricts and limits that theory to the Forms which refer to the nature of what is going to be explained. IV Finally we should ask again what is Plato’s theory of explanation? Does he have one unitary theory of explanation? Taylor thinks that we cannot find a 'single principle' of explanation in Phaedo. Annas (1995, 25) thinks that Plato’s argument in Phaedo is a mixed one because he could not distinguish between different meanings of the explanation which Aristotle did. She says that Phaedo is ‘a classic case of what Aristotle regards as confusion arising from failure to note that a philosophically important term is being used as though it had a single sense, whereas in fact it is crucially ambiguous’. She thinks that Plato is 'confusedly treating together different kinds of explanation' and continues: A grasp of Aristotle’s point in physics II3 would have enabled Plato to transform his confused discussion into an unconfused discussion of three distinct kinds of explanation; but Plato shows no sign of any such grasp. (ibid) Vlastos recognizes three kinds of explanation in Plato to show how he anticipates Aristotle’s doctrine: Plato has not only distinguished here mechanical from teleological causes…. but has also come within sight of the still more radical distinction between both of these and the logical aitia of classification and entailment. (1971: 166) He thinks that Plato’s use of that ‘safe’ explanation was in order to 'explode pseudo–problems which arise when the categorical difference between logical and physical aitia is ignored' (ibid). Politis, on the other side, thinks that Plato defends a 'unitary account of explanation, i.e. an account that is supposed to be true of each and every explanation without distinction' (2010: 98). For him, this unitary account is nothing but essence. He says that Plato cannot distinguish between the teleological and formal explanations 'for he thinks that all explanations are formal and essence-based' (ibid: 99). What Plato distinguishes, he thinks, is between those essence–based explanations appealing to the essence of the good and those that do not appeal to it and believes that 'good-based explanations depend on essence–based ones' (ibid: 101) because it is necessary for good–based explanations if they are to satisfy what he calls the requirements of explanation, to depend on essence–based explanations (ibid: 101-102). He even says that 'good–based explanations are a kind of essence–based explanations' (ibid: 102). What I think is that we have a unitary theory of explanation we called One Real Explanation which is good-based. Based on this ground, even if explanation by Forms appealing to essence may be a second ranked explanation, it must be regarded on the same principle (good-based explanation) and under his unitary theory of One Real Explanation. As White (1989, 166) points out, ‘the second voyage will be directed toward’ the Good because otherwise Socrates appeal to what is “best” would be misleading. This becomes more apparent if we pay attention to the relation of Good and Forms as is construed in Republic or reported by Aristotle. Consequently, if we have Republic in mind, where the Good plays the causal role it were to play in Phaedo and is explicitly taken as aitia (cf. Herrmann 2007), the good-based unitary theory comes more apparent. If not, maybe we will not have such a single principle between One Real Explanation and explanation by Form and essence. In spite of the fact that we agree with Politis that Plato defends a unitary account of explanation, we have to disagree with his reduction of explanation to essence since we must consider the theory of explanation by essence either as a theory that is a second theory lower than One Real Explanation or as a theory that will finally come along with it based on the relation between Forms and the Form of the Good in Republic. In this way, we should accept that One Real Explanation is an explanation which seems inaccessible in Phaedo but achieved in Republic. If so, his overall theory of explanation is that there should be one explanation for all things and this explanation explains the presence of good in them. In this interpretation, we must consider the theories of 'explanation by Form' and 'explanation by Form appealing to essence' as the steps that cannot reach the One Real Explanation. Neither is the theory of explanation by Forms nor the theory of explanation by Forms appealing to essence are thus complete. They are some steps toward that One Real Explanation, but necessarily uncompleted steps that cannot reach it at least in Phaedo. If we add the Form of the Good as the highest Form which all other Forms share in, as it is said in Republic, and continue the method of hypothesis as it is drawn out in Phaedo, we will have, then, a complete theory of explanation by the Form of the Good and need only one more step: taking good as the essence of all the Forms or what all of them share in. Such being the case, our theories of explanation by Form and explanation by Form that appeals to the essence will be completed with the theory of good as the essence of all explanations and thus can be included in One Real Explanation. If this can be done, it, however, will show that we have a unitary theory of explanation in Plato’s philosophy. Notes

In this article, it's tried to study Aristotle's narrative of pre-Socratics on the base of Aristotle's texts and mainly using metaphysics, physics, genesis and decadence books. It is also tried to show how Aristotle has interpreted all the pre-Socratics in one way and on the base of his own philosophy framework. He interprets pre-Socratic Arche as an element that means comprehensive matter which is nothing itself, but everything is combination of it and even considers that as substance and the other things as accident. He interprets the distinction of Arche and other things on the basis of this contrast in his philosophy. Aristotle, also analyzes pre-Socratics' viewpoint to change on the base of his distinction among change, genesis and corruption. All these cases show that Aristotle has interpreted the pre-Socratics on the basis of his thought, as Aristotelians. On this basis, since Aristotle's thoughts are the first and the most important sources of pre-Socratic philosophy, Aristotle's role should be considered in studies.

What are to be discussed in this article include two main points: i) some kind of a fixed structure can be found in all the chronologies that have been proposed from the last quarter of 19th century onward; a structure that is called here “standard” chronology, and ii) in spite of the fact that the appearance of this structure owes too much to the stylistic evidences, these evidences themselves do not confirm anything in the structure but the place of the so-called late dialogues. The standard chronology of Plato’s dialogues is inclined to consider Meno and Republic as dialogues that have been composed after so-called Socratic dialogues and before Parmenides and Theaetetus. This chronology also insists that the latter two dialogues must be dated after so-called middle dialogues and before dialogues like Sophist, Timaeus, Philebus and Laws. This papper is to illuminate the fact that except the similarities between the late dialogues and their probable lateness, the place of other dialogues, more importantly among them the so-called middle period dialogues, Theaetetus and Parmenides, cannot be approved by stylistic evidences.

در اين مقاله تلاش مي‌كنیم روايت ارسطو از پيش‌سقراطيان را بر اساس متون خود ارسطو و عمدتاً با استفاده از كتاب‌هاي متافيزيك، فيزيك و كون و فساد مورد بررسي قرار دهیم و نشان دهيم چگونه ارسطو همه پيش‌سقراطيان را به يك نحو و بر مبناي چهارچوب فلسفه خودتفسير مي‌كند. او آرخه پيش‌سقراطي را به معناي عنصر يعني امري بسيط كه خود از چيز ديگري نيست و همه چيز از آن تركيب شده است، تفسير مي كند و حتي آن را به عنوان جوهر و هر چيز ديگر را به عنوان عرض در نظرمي گيرد و تمايز آرخه و اشياء را بر مبناي اين تقابل در فلسفه خود مورد تفسير قرار مي‌دهد. ارسطو همچنين نگاه پیش سقراطیان به تغییر را بر مبناي تمايز خود ميان تغيير و كون و فساد تحليل مي‌كند. همه اين موارد نشانگر آن هستند که ارسطو پیش سقراطیان را ارسطوئی و بر مبنای اندیشه خود تفسیر کرده است. در اين صورت، با توجه به اينكه ارسطو از اولين و مهم ترين منابع انديشه هاي پيش سقراطيان است، در بررسي آنها همواره بايد نقش ارسطو را مد نظر قرار داد.

What this essay is to discuss is Plato''s theory of explanation in Phaedo. In this dialogue, we observe that Socrates criticizes both the natural scientists’ explanations and Anaxagoras’ theory of Mind since he thinks they could not explain all things, firstly, in a unitary and, secondary, in a real way. Thence, we are to call what Plato is seeking as his ideal explanation in Phaedo “One Real Explanation”. He talks at least about three kinds of explanation, two of which, the confused and foolish way of explanation by Forms and the explanation by Forms appealing to essence, are just "second best" and lower degrees of explanation. His ideal explanation is an explanation that can explain all things by one thing and in a real way. Though he cannot show, at least in Phaedo, how this One Real Explanation can work, we can see Plato completing his plan by the Form of the Good in Republic.

در اين جستار بر آنيم اصول وجود شناختي و معرفت شناختي افلاطون در محاورات اوليه و علي الخصوص لاخس، خارميدس، اوثيفرون، اوتيدموس و هيپياس بزرگ را بر مبناي سه عنصر آنچه «دور سقراطي» مي ناميم يعني پرسش سقراطي، ادعاي سقراطي انكار دانش و النخوس مورد بررسي قرار دهيم. حاصل اين بررسي شش اصل وجود - معرفت شناختي است: شناخت الف، معرفت‌شناسي دوقطبي، وجودشناسي دو‌قطبي، معرفت گسسته، وجود گسسته و معرفت وجود. اگرچه اين اصول عمدتاً جديد نبوده و پيشتر مورد بحث محققان قرار گرفته‌اند، آنچه مورد نظر اين جستار است در نظر گرفتن آين اصول در كنار يكديگر و تاكيد بر هماهنگي و مطلق بودن آنهاست. تناسب و هماهنگي ميان اصول معرفت شناختي و اصول وجودشناختي و همساني آنها در برخي ويژگي ها همچون مطلق بودن و گسستگي علاوه بر آنكه نشان دهنده سازگاري نظري محاورات اوليه است، مي تواند تاييدي بر نتايج اين تحقيق باشد.