Aristotle’s Syllogistic: From the Standpoint of Modern Formal Logic

This inspiring book becomes one that is very booming. After published, this book can steal the market and book lovers to always run out of this book. And now, we will not let you run out any more to get this book. Why should be aristotle on meaning and essence? As a book lover, you must know that enjoying the book to read should be relevant to how you exactly need now. If they are not too much relevance, you can take the way of the inspirations to create for new inspirations.

Aristotle on meaning and essence

Aristotle’s De Interpretatione: Contradiction and Dialectic

Aristotle’s views on abstraction explain how he can hold that parts of animals are both secondary substances and relata . The wing of a bird, qua being a part, is a relatum ; that wing, per se, is a secondary substance. Aristotle’s views on motion and change make clear his position on parts of animals. Motion and change are relations. Strictly speaking then, motion and change hold between relata . Such relata are accidents of subjects: their ultimate subjects are the substances; yet their proximate subjects may be its accidents taken as subjects in their own right, like surfaces and numbers. When the subjects themselves are in the category of relation , the change is instantaneous; otherwise it can be gradual. As parts of animals can undergo gradual change, they are not relata ; rather they are substances. Still these substances qua parts are relata . For a part of a woman like a hand to be a part of her, it must function as a hand. When it does not function it is a hand in name only. A non-functioning hand is still a substance with a history of its own but is not a fully actualized part of the substance the human being. Aristotle also allows for parts that are not actual but potential in various degrees.

Parts of Animals

In his discussion of the four causes, Aristotle claims that ‘the hypotheses are material causes of the conclusion’ (Physics 2.3, Metaphysics Δ 2). This claim has puzzled commentators since antiquity. It is usually taken to mean that the premises of any deduction are material causes of the conclusion. By contrast, I argue that the claim does not apply to deductions in general but only to scientific demonstrations. In Aristotle’s view, the theorems of a given science are composites composed of the indemonstrable premises from which they are demonstrated. Accordingly, these premises are elements, and hence material causes, of the theorems. Given this, Aristotle’s claim can be shown to be well-motivated and illuminating. 1. Hypotheses are material causes of the conclusion In Physics 2.3 and its doublet in Metaphysics Δ 2, Aristotle distinguishes the so-called four causes. The first of them is characterized as ‘that from which as a constituent something comes to be’. Since antiquity, this type of cause is known as the ‘material cause’. Aristotle illustrates it by a series of examples as follows: 1 τὸ ἐξ οὗ γίγνεταί τι ἐνυπάρχοντος, Phys. 2.3 194b24 (= Metaph. Δ 2 1013a24–5). 2 The ancient commentators refer to it as ὑλικὸν αἴτιον (Alex. Aphr. in Metaph. 349.2, 351.5, 353.20, Philop. in Phys. 243.21, 243.30, 246.25–247.11, 249.6, Simpl. in Phys. 314.27, 319.20, 320.13, Asclep. in Metaph. 305.22–4, 306.9–14). Moravcsik argues that this type of cause should rather be called ‘constitutive

Aristotle on Principles as Elements

A method of modal proof in Aristotle

In Prior Analytics 1.15 Aristotle undertakes to establish certain modal syllogisms of the form XQM. Although these syllogisms are central to his modal system, the proofs he offers for them are problematic. The precise structure of these proofs is disputed, and it is often thought that they are invalid. We propose an interpretation which resolves the main difficulties with them: the proofs are valid given a small number of intrinsically plausible assumptions, although they are in tension with some claims found elsewhere in Aristotle’s modal syllogistic. The proofs make use of a rule of propositional modal logic which we call the possibility rule. We investigate how this rule interacts and coheres with the core elements of the modal syllogistic.

Proof by assumption of the possible in prior analytics 1.15

This paper illustrates how Aristotle’s topological theses about change in Physics 5-6 can help address metaphysical issues. Two distinctions from Physics 5. 1 are discussed: changing per se versus changing per aliud; motion versus change. Change from white to black is motion and alteration, whereas change from white to not white is neither. But is not every change from white to black identical with a change from white to not white? Theses from Physics 6 refute the identity. Is change from white to black at least accompanied by change from white to not white? Perhaps, but given further theses from Physics 6, this supposition yields unwelcome consequences. Most likely, when something changes from white to black it changes merely per aliud, not per se, from white to not white. Genuine change between white and not white is found elsewhere; its admission has bearing on Aristotle’s theory of perception.

Jacob Rosen

Papers

A method of modal proof in Aristotle

Proof by assumption of the possible in prior analytics 1.15

Motion and Change in Aristotle’s Physics 5. 1