Question

explain how aristotle's natural philosophy led to the development of logic specifically his categorical, syllogistic logic?

Answer 1

Aristotle’s logical works contain the earliest formal study of logic that we have. It is therefore all the more remarkable that together they comprise a highly developed logical theory, one that was able to command immense respect for many centuries: Kant, who was ten times more distant from Aristotle than we are from him, even held that nothing significant had been added to Aristotle’s views in the intervening two millennia.

In the last century, Aristotle’s reputation as a logician has undergone two remarkable reversals. The rise of modern formal logic following the work of Frege and Russell brought with it a recognition of the many serious limitations of Aristotle’s logic; today, very few would try to maintain that it is adequate as a basis for understanding science, mathematics, or even everyday reasoning. At the same time, scholars trained in modern formal techniques have come to view Aristotle with new respect, not so much for the correctness of his results as for the remarkable similarity in spirit between much of his work and modern logic. As Jonathan Lear has put it, “Aristotle shares with modern logicians a fundamental interest in metatheory”: his primary goal is not to offer a practical guide to argumentation but to study the properties of inferential systems themselves.

Aristotle’s Logical Works: The Organon

The ancient commentators grouped together several of Aristotle’s treatises under the title Organon (“Instrument”) and regarded them as comprising his logical works:

1. Categories
2. On Interpretation
3. Prior Analytics
4. Posterior Analytics
5. Topics
6. On Sophistical Refutations

In fact, the title Organon reflects a much later controversy about whether logic is a part of philosophy (as the Stoics maintained) or merely a tool used by philosophy (as the later Peripatetics thought); calling the logical works “The Instrument” is a way of taking sides on this point. Aristotle himself never uses this term, nor does he give much indication that these particular treatises form some kind of group, though there are frequent cross-references between the Topics and the Analytics. On the other hand, Aristotle treats the Prior and Posterior Analytics as one work, and On Sophistical Refutations is a final section, or an appendix, to the Topics). To these works should be added the Rhetoric, which explicitly declares its reliance on the Topics.

The Syllogistic

Aristotle’s most famous achievement as logician is his theory of inference, traditionally called the syllogistic (though not by Aristotle). That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises. Aristotle calls the term shared by the premises the middle term (meson) and each of the other two terms in the premises an extreme (akron). The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises. Aristotle refers to these term arrangements as figures(schêmata)

	First Figure	Second Figure	Third Figure
	Predicate	Subject	Predicate	Subject	Predicate	Subject
Premise	aa	bb	aa	bb	aa	cc
Premise	bb	cc	aa	cc	bb	cc
Conclusion	aa	cc	bb	cc	aa	bb

Aristotle calls the term which is the predicate of the conclusion the major term and the term which is the subject of the conclusion the minor term. The premise containing the major term is the major premise, and the premise containing the minor term is the minor premise.

Aristotle then systematically investigates all possible combinations of two premises in each of the three figures. For each combination, he either demonstrates that some conclusion necessarily follows or demonstrates that no conclusion follows. The results he states are correct.