Discussion of the Aristotelian syllogistic over the last sixty years has arguably centered on the question whether syllogisms are inferences or implications. But the significance of this debate at times has been taken to concern whether the syllogistic is a logic or a theory, and how it ought to be represented by modern systems. Largely missing from this discussion has been a study of the few passages in the Prior Analytics where Aristotle provides explicit guidance on how to individuate syllogisms. (...) I argue that syllogisms are individuated by unordered premise pairs and so may be fruitfully thought of as multi-succedent sequents. I conclude by drawing a few consequences for the representation of the syllogistic. (shrink)

Empty individual expressions are needed to reconstruct the actual use of scientific language as well as to make logic free from existence assumptions. According to Quine, a language must be extensional to be adequate for the purposes of science. By means of Lambert's non-extensionality argument it can be demonstrated that a language containing empty individual expressions cannot be extensional as long as truth-values are the extensions of sentences. This book investigates the soundness of Lambert's argument and examines the question of (...) whether and how extensionality of a language for free logic can be secured. To achieve these aims, the notion of extensionality is thoroughly analyzed and two new semantic approaches to free logic are developed in which states of affairs, but not truth-values, are the extensions of sentences. These two semantic approaches are defended against the slingshot argument. In this way, two possible solutions to the problem of extensionality arise which use non-existent objects in two different ways: whereas in dual domain semantics non-existent objects serve as referents of empty singular terms, in single domain semantics they serve as hole marker objects that mark the holes in states of affairs where an object is missing due to an irreferental individual expression. (shrink)

An investigation of Proclus' logic of the syllogistic and of negations in the Elements of Theology, On the Parmenides, and Platonic Theology. It is shown that Proclus employs interpretations over a linear semantic structure with operators for scalar negations (hypemegationlalpha-intensivum and privative negation). A natural deduction system for scalar negations and the classical syllogistic (as reconstructed by Corcoran and Smiley) is shown to be sound and complete for the non-Boolean linear structures. It is explained how Proclus' syllogistic presupposes converting the (...) tree of genera and species from Plato's diairesis into the Neoplatonic linear hierarchy of Being by use of scalar hyper and privative negations. (shrink)

The paper is a study of the logic of existence, negation, and order in the Neoplatonic tradition. The central idea is that Neoplatonists assume a logic in which the existence predicate is a comparative adjective and in which monadic predicates function as scalar adjectives that nest the background order. Various scalar predicate negations are then identifiable with various Neoplatonic negations, including a privative negation appropriate for the lower orders of reality and a hyper-negation appropriate for the higher. Reversion to the (...) One can then be explained as the logical inference of hyper-negations from mundane knowledge. Part I develops the relevant linguistic and logical theory, and Part II defends Wolfson and the scalar interpretation against the more traditional Aristotelian understanding of Whittaker and others of reversion as intensional abstraction. (shrink)

John Corcoran’s natural deduction system for Aristotle’s syllogistic is reconsidered.Though Corcoran is no doubt right in interpreting Aristotle as viewing syllogisms as arguments and in rejecting Lukasiewicz’s treatment in terms of conditional sentences, it is argued that Corcoran is wrong in thinking that the only alternative is to construe Barbara and Celarent as deduction rules in a natural deduction system.An alternative is presented that is technically more elegant and equally compatible with the texts.The abstract role assigned by tradition and Lukasiewicz (...) to Barbara and Celarent is retained.The two ‘ perfect syllogisms’ serve as ‘basic elements’ in the construction of an inductively defined set of valid syllogisms.The proposal departs from Lukasiewicz, and follows Corcoran, however, in construing the construction as one in natural deduction.The result is a sequent system with fewer rules and in which Barbara and Celarent serve as basic deductions.To compare the theory to Corcoran’s, his original is reformulated in current terms and generalized.It is shown to be equivalent to the proposed sequent system, and several variations are discussed.For all systems mentioned, a method of Henkin‐style completeness proofs is given that is more direct and intuitive than Corcoran’s original. (shrink)

This thesis aims to develop a psychologically plausible account of concepts by integrating key insights from philosophy (on the metaphysical basis for concept possession) and psychology (on the mechanisms underlying concept acquisition). I adopt an approach known as informational atomism, developed by Jerry Fodor. Informational atomism is the conjunction of two theses: (i) informational semantics, according to which conceptual content is constituted exhaustively by nomological mind–world relations; and (ii) conceptual atomism, according to which (lexical) concepts have no internal structure. I (...) argue that informational semantics needs to be supplemented by allowing content-constitutive rules of inference (“meaning postulates”). This is because the content of one important class of concepts, the logical terms, is not plausibly informational. And since, it is argued, no principled distinction can be drawn between logical concepts and the rest, the problem that this raises is a general one. An immediate difficulty is that Quine’s classic arguments against the analytic/synthetic distinction suggest that there can be no principled basis for distinguishing content-constitutive rules from the rest. I show that this concern can be overcome by taking a psychological approach: there is a fact of the matter as to whether or not a particular inference is governed by a mentally-represented inference rule, albeit one that analytic philosophy does not have the resources to determine. I then consider the implications of this approach for concept acquisition. One mechanism underlying concept acquisition is the development of perceptual detectors for the objects that we encounter. I investigate how this might work, by drawing on recent ideas in ethology on ‘learning instincts’, and recent insights into the neurological basis for perceptual learning. What emerges is a view of concept acquisition as involving a complex interplay between innate constraints and environmental input. This supports Fodor’s recent move away from radical concept nativism: concept acquisition requires innate mechanisms, but does not require that concepts themselves be innate. (shrink)