Peter Simons

Common nouns enter into modern predicate logic only as parts of predicates, While in lesniewski's 'ontology' they are classified together with proper nouns as 'names'. A system of natural deduction rules is presented which sharply separates proper from common nouns, Within which lesniewski's calculus is contained as a logic solely of common nouns, Together with copula, Identity predicate, Definite article, And quantifiers 'any', 'every', 'some' and 'no'. The fragment developed is closer to the natural syntax of english than either frege's or lesniewski's languages, Enabling these to be seen as complementary rather than competing, As approximations to syntactically more complex languages

Occurrents are entities that exist in time and, with few or no exceptions, extend over time as well, that is, they have parts corresponding to the different times at which they exist. This makes it very easy to say what makes it true that they exist at the times at which they do. Singular existential propositions, being contingent, positive and arguably atomic, stand in need of truth-makers, entities in virtue of whose existence they are true. The obvious candidate for what makes it true that Tony Blair exists is the Right Honourable Member for Sedgefield himself: by virtue of his existing, it is true that he exists. Nothing could be more straightforward. However, things that exist in time, with few exceptions, exist at some times and not at others. So a proposition to the effect that a certain object exists at a certain time likewise stands in need of a truth-maker, one matching the requirements of the existential proposition in question in its temporal specificity. Take an occurrent such as a boxing match and suppose it is going on twenty minutes after starting: by virtue of what is this true? The obvious answer here is that it is by virtue of the existence of that temporal part or phase which extends just over the time in question. Other temporal parts of the same occurrent which do not extend over this time do not act as truth-maker for the temporally specific existential proposition, this one does. There is no problem because occurrents do have temporal parts which can do this job.

The debate between 3- and 4-dimensionalists is one of the most lively and pervasive in current metaphysics. At stake is a glittering prize: the correct metaphysical analysis of material things and other objects commonly thought to persist in time by enduring. Since we count ourselves among such objects the outcome of the debate is of more than merely academic interest to us. Obviously the ramifications of the debate, even of the points raised by Kit Fine, go far beyond what I can discuss here, so I shall simply select some salient issues and comment on them from my own somewhat heterodox point of view.

Following its welcome revival in the late twentieth century, metaphysics in the analytic tradition has succumbed to decadence, with an astonishing variety of outlandish and extreme positions or “metaphysical follies” being taken seriously. This has caused an inevitable backlash among more scientifically-minded philosophers and incurred the scorn of scientists. Much of the reason for this is the blithe ignoring of empirical science by armchair metaphysicians. The roles of empirical knowledge in good, scientific metaphysics are however unclear. In virtue of its maximal generality, metaphysics is remote from straightforward empirical checks. This article explores, with historical and contemporary examples, the ways in which empirical information may inform and be fed back into metaphysics, the disputed role of common sense, and the delicate balance to be maintained, within a fallibilist, scientific metaphysics, between speculative, categorial and empirical elements.

Frege's theory of real numbers has undeservedly received almost no attention, in part because what we have is only a fragment. Yet his theory is interesting for the light it throws on logicism, and it is quite different from standard modern approaches. Frege polemicizes vigorously against his contemporaries, sketches the main features of his own radical alternative, and begins the formal development. This paper summarizes and expounds what he has to say, and goes on to reconstruct the most important steps which he is likely to have subsequently taken. The various difficulties facing his theory in this reconstruction are outlined, and some surprising consequences drawn about the nature of his logicism

Among biological kinds, the most important are species. But species, however defined, have vague boundaries, both synchronically owing to hybridization and ongoing speciation, and diachronically owing to genetic drift and genealogical continuity despite speciation. It is argued that the solution to the problems of species and their vague boundaries is to adopt a thoroughgoing nominalism in regard to all biological taxa, from species to domains. The base entities are individual organisms: populations of these compose species and higher taxa. This accommodates all the important biological facts while avoiding the legacy problems of pre-evolutionary typological taxonomy, which saw species and other taxa as prior to their members. Species are however not individuals: they are spatiotemporally bounded collections, which are plural particulars.

Confounding earlier predictions of naysayers and sceptics, by the beginning of the twenty-first century, metaphysics had re-emerged for the first time in decades as a vital, progressive and exciting branch of philosophy. Although the most strident criticisms came from early analytic philosophers such as Carnap, it is analytical metaphysics that has led the way. But rather than trace the stages of the revival of metaphysics, we consider a spread of contemporary themes which have been especially fruitful in expanding the circle of metaphysical discussion from its modest beginnings at the hands of Strawson and Quine in mid-century. The topics are divided into four groups: Expanding the Toolbox; Ontological Speculations; Systematics; and Applications

Despite its lack of influence in analytical philosophy, and independently of its content as a process philosophy, Whitehead's system in Process and Reality affords a valuable lesson on how to pursue revisionary systematic metaphysics. This paper argues the case generally for metaphysical revision and system, describes the structure of Whitehead's categorial scheme, endorses his idea of an ultimate which is not an entity, and outlines an alternative, “digital” ultimate or basis composed of several analytical factors. [I]n the absence of a well-defined categoreal scheme of entities, issuing in a satisfactory metaphysical system, every premise in a philosophical argument is under suspicion.

In "meaning and modality" lewy claims the only ground for rejecting disjunctive syllogism as acceptable for entailment is rejection of bivalence. Examining lewis's 'proofs' of the paradoxes of strict implication he suggests the proof of 'if a then (b or not-B)' suppresses a premiss, Restoration of which blocks the paradox, Whereas the proof of 'if (a and not-A) then b' cannot be so blocked. But the paradoxes are dual, So he should have treated them dually by restoring a suppressed disjunct in the consequent of the second. When this is done, The second paradox is blocked and disjunctive syllogism fares no better than the principle lewy discarded

I consider the idea of a propositional logic of location based on the following semantic framework, derived from ideas of Prior. We have a collection L of locations and a collection S of statements such that a statement may be evaluated for truth at each location. Typically one and the same statement may be true at one location and false at another. Given this semantic framework we may proceed in two ways: introducing names for locations, predicates for the relations among them and an “at” preposition to express the value of statements at locations; or introduce statement operators which do not name locations but whose truth-conditional effect depends on the truth or falsity of embedded statements at various locations. The latter is akin to Prior’s approach to tense logic. In any logic of location there will be some basic operators which we can define. By ringing the changes on the topology of locations, different logical systems may be generated, and the challenge for the logician is then in each case to find operators, axioms and rules yielding a proof theory adequate to the semantics. The generality of the approach is illustrated with familiar and not so familiar examples from modal, tense and place logic, mathematics, and even the logic of games. To the memory of Ted Dawson, who introduced me to philosophy and the writings of Arthur Prior.

This is a broad survey of the chronology of the rift between continental and analytic philosophy, starting in 1899. Whereas at that time there was no discernible divide, as the twentieth century progresses we can see a gradual parting of the ways in which philosophy was done, culminating in a period of maximum separation in 1945-68, followed by some convergence. There is one substantial historical thesis proposed, and facts are adduced from the chronology to back it up: that the divide was never absolute, never purely geographical, and above all that it was not inevitable, but was largely the product of accidental historical circumstances, of which the most crucial was the flourishing of totalitarianism in Europe and the disruption caused by two world wars.

Suppose you hold the following opinions in the philosophy of logic. First-order predicate logic is expressively inadequate to regiment concepts of mathematic and natural language; logicism is plausible and attractive; set theory as an adjunct to logic is unnatural and ontologically extravagant; humanly usable languages are finite in lexicon and syntax; it is worth striving for a Tarskian semantics for mathematics; there are no Platonic abstract objects. Then you are probably already in cognitive distress. One way to decease your unhappiness, short for embracing Platonism, is to accept higher-order logic and look, as did Arthur Prior, for a plausible way to neutralize the ontological commitment to abstract entities that this acceptance appears to entail.

Here is a dilemma. By robust common sense, the sun exists. Yet the sun is a vague object, lacking exact identity conditions, and therefore by widely accepted standards of objecthood does not exist. What goes for it goes for almost all other material things. Standard solutions to the problem of vagueness for predicates fall flat for vague objects. This paper attempts a theory which accounts for our common beliefs about vague objects by taking them as well-founded phenomena, founded on collections of more exact objects. The key notions allowing us to assign sensible truth-values to propositions about vague objects are those of truth-value density and expected truth-value. These will be illustrated in use.

This paper assesses those features of Lesniewski's Ontology which make it difficult to understand for logicians accustomed to more orthodox systems of logic. It is seen that certain general features of presentation and content can, by selective acceptance or modification, be accommodated with a fairly orthodox viewpoint. The chief difficulty lies in the interpretation of Le?niewski's names, and the constant ???. Four interpretations are suggested in turn: Le?niewski's names as monadic predicates; as class terms; as common nouns; and as empty, singular or plural terms. This last and least orthodox interpretation is argued to be the most suitable, but it is shown how it can be made to live in harmony with either the common noun or the class interpretation

Gilbert Ryle wrote that "Meaning-theory expanded just when and just in so far as it was released from that 'Fido'-Fido box, the lid of which was never even lifted by Meinong". This paper sets out to relieve Ryle's oversimplification about Meinong and the role of meaning theory in his thought. One step away from canine simplicity about meaning is the recognition of a distinction between sense and reference, such as we find in Frege, Husserl, and the early Russell. In Über Möglichkeit und Wahrscheinlichkeit (1915) Meinong seems to corroborate Ryle when he writes, "Word-meanings are objects", but immediately after this, he qualifies it: "Word-meanings are very often auxiliary objects". The distinction between auxiliary and target objects in Meinong's later work allows us to attribute to him a theory of sense and reference which shows him to have indeed lifted the box-lid.