Online research in philosophy

This paper is concerned with a natural deduction system for First Degree Entailment (FDE). First, we exhibit a brief history of FDE and of combined systems whose underlying idea is used in developing the natural deduction system. Then, after presenting the language and a semantics of FDE, we develop a natural deduction system for FDE. We then prove soundness and completeness of the system with respect to the semantics. The system neatly represents the four-valued semantics for FDE.

Quine, in an influential passage, characterizes a certain kind of metaphysical view as "Aristotelian essentialism." Recent work on Aristotle suggests that he may not have been an essentialist in Quine's sense. This paper examines the question whether, and to what extent, Aristotle is committed to the kind of essentialism Quine discusses. Various promising areas of Aristotle's thought (alteration vs. coming-to-be and passing-away, kath' hauto predication) are examined and found wanting as sources of essentialism. Instead, Aristotle is found to be committed to essentialism in the hylomorphic conception of substance featured in the late books of the Metaphysics, despite the superficially anti-essentialistic appearance of the conception of matter as the ultimate subject of predication. Essentialism is part and parcel of Aristotle's conception of substances as the basic individuals.

A predicate logic typically has a heterogeneous semantic theory. Subject terms and predicates have distinct semantic roles: subject terms refer; predicates characterize. And a sentence expresses a truth if the object to which the subject term refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subject terms and predicates refer; a sentence is true if the subject term and predicate name one and the same thing. There is evidence that Aristotle holds that subject terms and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle’s core semantic notion is not identity but the weaker relation of constitution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle’s view, just in case the mereological sum of humans is a part of the mereological sum of mortals.

This book takes up the central themes of Aristotle's metaphysical theory and the various transformations they undergo prior to their full expression in the Metaphysics. Aristotle's metaphysics is bedevilled by classic puzzles involving such notions as form, predication, universal, and substance, which result from his attempt to adapt the various requirements on primary substance developed in his earlier works so that they fit the very different metaphysical picture in his later work. Professor Lewis argues that Aristotle is himself aware of most if not all of these difficulties and in the Metaphysics works hard to ensure the coherence of his theory. He presents Aristotle's views as a formal theory complete with axioms, definitions, and theorems.

Aristotle and the sea battle, by G. E. M. Anscombe.--Aristotle's different possibilities, by K. J. J. Hintikka.--On Aristotle's square of opposition, by M. Thompson.--Categories in Aristotle and in Kant, by J. C. Wilson.--Aristotle's Categories, chapters I-V: translation and notes, by J. L. Ackrill.--Aristotle's theory of categories, by J. M. E. Moravcsik.--Essence and accident, by I. M. Copi.--Tithenai ta phainomena, by G. E. L. Owen.--Matter and predication in Aristotle, by J. Owens.--Problems in Metaphysics Z, chapter 13, by M. J. Woods.--The meaning of agathon in the Ethics of Aristotle, by H. A. Prichard.--Agathon and eudaimonia in the Ethics of Aristotle, by J. L. Austin.--The final good in Aristotle's Ethics, by W. F. R. Hardie.--Aristotle on pleasure, by J. O. Urmson.--Bibliography (p. 335-341).

Diotima criticizes, but does not refute, Aristophanes’ thesis that love is desire for completeness. Her argument incorporates that thesis within a more complextheory: eros is desire for the permanent possession of the good, and hence also desire for immortality. Aristophanes cannot account for the aspirations entailed in the desire for fame or in the desire for knowledge. Such aspirations can be understood only with reference to the good. However, the paper shows how time plays a fundamental role in the original pursuit of wholeness at the center of Aristophanes’ myth of the two halves. Diotima appropriates his thesis when she describes the urge to leave behind something similar to what one has been. The desire for immortality is nothing but a desire for completeness pursued by mortal nature against the never-ending destruction of time.

Aristotle and the sea battle, by G. E. M. Anscombe.--Aristotle's different possibilities, by K. J. J. Hintikka.--On Aristotle's square of opposition, by M. Thompson.--Categories in Aristotle and in Kant, by J. C. Wilson.--Aristotle's Categories, chapters I-V: translation and notes, by J. L. Ackrill--Aristotle's theory of categories, by J. M. E. Moravcsik.--Essence and accident, by I. M. Copi.--Tithenai ta phainomena, by G. E. L. Owen.--Matter and predication in Aristotle, by J. Owens.--Problems in Metaphysics Z, chapter 13, by M. J. Woods.--The meaning of agathon in the Ethics of Aristotle, by H. A. Prichard.--Agathon and eudaimonia in the Ethics of Aristotle, by J. L. Austin.--The final good in Aristotle's Ethics, by W. F. R. Hardie.--Aristotle on pleasure, by J. O. Urmson.--Bibliography (p. 335-41).

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.

This book claims that Aristotle followed an aspect theory of predication.

Three distinctly different interpretations of Aristotle?s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle?s remarkable degree of metalogical sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ?sullogimos? to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle?s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction.