Polarity and Inseparability: The Foundation of the Apodictic Portion of Aristotle's Modal Logic
TL;DR: In this paper, a system based on Aristotle's tests for things that can never combine (polarity) and things that cannot separate (inseparability) is presented. But it does not make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy.
Abstract: Modern logicians have sought to unlock the modal secrets of Aristotle's Syllogistic by assuming a version of essentialism and treating it as a primitive within the semantics. These attempts ultimately distort Aristotle's ontology. None of these approaches make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy. I base a system on Aristotle's tests for things that can never combine (polarity) and things that can never separate (inseparability). The resulting system not only reproduces Aristotle's recorded results for the apodictic syllogistic in the Prior Analytics but it also generates rather than assumes Aristotle's distinctions among ‘necessary’, ‘essential’ and ‘accidental’. By developing a system around tests that are in Aristotle and basic to ancient Greek philosophy, the system is linked to a history of practices, providing a platform for future work on the origins of logic.
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TL;DR: 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 as mentioned in this paper. And now, we will not let you run out any more to get this book.
Abstract: 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.
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TL;DR: In Prior Analytics 1.15, a modal syllogism of the form XQM is established as mentioned in this paper, and the proofs are valid given a small number of plausible assumptions, although they are in tension with some claims found elsewhere in the modal system.
Abstract: 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.
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Book•
01 Jan 1962
TL;DR: The primary purpose of this book has not been to recount all that past scholars have said about the science, but rather to record the first appearances of those ideas which seem most important in the logic of our own day as discussed by the authors.
Abstract: The primary purpose of this book has not been to recount all that past scholars have said about the science, but rather to record the first appearances of those ideas which seem most important in the logic of our own day.
1,141 citations
Book•
01 Dec 1957
387 citations
Book•
01 Jul 1987
258 citations
Book•
31 Dec 1949
192 citations
"Polarity and Inseparability: The Fo..." refers background in this paper
...While the prevailing view today is that the modal syllogistic contains ambiguities, inconsistencies, and errors (e.g. Becker 1933, Ross 1949, Bochénski 1956, 1957, Łukasiewicz 1957, Kneale 1962, Kneale and Kneale 1962, McCall 1963, Rescher 1964, Wieland 1966,Hintikka 1973, van Rijen 1989, Striker…...
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