Igor Martinjak

I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent is just one of 27 possible complete deductive systems with the two mutually non-derivable syllogistic rules. On top of that, given the fact that there are two combinations of mutually non-derivable conversion rules, I conclude that Prior Analytics hides in itself 54 complete deductive systems with a minimal number of mutually non-derivable rules. Finally, it is commented what might be the role of analysis; to what extent Aristotle could be aware of possibilities presented here; why he still prefers only one deductive system to many others with the same deductive power.

The possibility of formal representation of Aristotle’s discussion about singular predication in Categories 10, 13b27-35 is investigated through three symbolic idioms: the first-order language with identity, with and without definitive description, and through the languages of free logics. I show that such representations are not fully adequate. According to the first option, we are committing Aristotle with some (meta)logical implications he is not willing to accept. According to the second option, we are burdening Aristotle with Russell’s theory of names. Finally, the third option leaves us with the assumption that ‘exist(s)’ could be represented with a predicate. This assumption, however, Aristotle emphatically rejects.

According to the well–known argument, the traditional conception of existence and predication leads to the infamous paradox of non-existence. For instance, the sentence ‘Pegasus does not exist’ commits us to accept that there is something that does not exist. The easy way out is to analyze existence as a second–order concept expressing that there is at least one instance of some first–order concept. In this article, I argue that the traditional conception of existence and predication does not lead to the paradox of non-existence. Negative existentials are not subject-predicate sentences that select existing beings only to deny them the property of existence. Aristotle’s insistence that being is not a genus, i.e. that being is not a predicate of some subject, is pivotal. Furthermore, Aristotle does not have a uniform conception of existence and predication. According to Aristotle, to be is to be an item in the categorical scheme, and consequently, every predication of some being should be analysable as one of the most general types of predication according to the categorical scheme. However, in the conceptual framework of Aristotle’s philosophy, a different problem of non-existence arises. For instance, ‘Pegasus is thought-about’ might commits us to the claim that Pegasus is a being of some kind. I reconstruct Aristotle’s solution as being satisfactory in the light of his understanding of predication and existence. Moreover, I suggest that a similar puzzle leads many contemporary philosophers to an abandonment of the Quinean concept of existence and predication in favour of a more traditional approach.