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Aristotle

Logic

Assos and Macedonia

Natural Philosophy

There are some areas in which Aristotle's influence is often called into question. In biology, where he made some of his greatest contributions, he was ultimately superseded and is now read only for historical reasons. In politics his ideas continue to be debated, but, still, even they are most useful in a historical context. Thus one might argue that his greatest contribution to Western thought was the creation of logic. That a single mind could essentially invent such a vast field might be difficult to grasp, but Aristotle almost single-handedly reinvented other fields as well, whether or not they fall into the category of areas in which he has been superseded.

Aristotle placed all learning into three categories–theoretical, practical, and productive–and logic did not fall into any of these. Rather, Aristotle saw logic as a tool that underlay knowledge of all kinds, and he undertook its study because he believed it to be a necessary first step for learning. Logic enables one to recognize when a judgment requires proof and to verify the validity of such proof. Two preliminary works provided the foundation for Aristotle's work in logic: Categories and On Interpretation. In the former, he defined and analyzed the following list of categories (each followed by an example):

  • Substance: man
  • Quantity: two cubits long
  • Quality: white
  • Relation: double
  • Place: in the Lyceum
  • Date: yesterday
  • Posture: is sitting
  • Possession: is wearing shoes
  • Action: cuts
  • Passivity: is cut

This list does not attempt to be exhaustive, and Aristotle himself did not always use it consistently. The purpose of these categories is to show how these predicates (categoria means predicate) can describe a subject. This foundational work therefore sets the boundaries for terms and the types of distinctions that are possible.

In On Interpretation Aristotle turns from terms to propositions, which are sentences that contain either truth or falsity. Propositions assert judgments about concepts; for Aristotle, concepts are the likenesses of things, as experienced by a given person, in contrast to objective reality. A proposition attempts to combine or separate concepts, and it is to be considered true when its combination or separation corresponds to a combination or separation of the things it represents. This recognition of language as a signifier therefore provides the basis for an understanding of what truth and falsity mean.

With Prior Analytics Aristotle made his most important contribution to logic: the syllogism. A syllogism consists of certain assumptions or premises from which a conclusion can be deduced. Aristotle referred to the terms as the "extremes" and the "middle." The middle term is the conclusion that links the two extremes. A traditional example runs as follows:

  • All men are mortal.
  • All Athenians are men.
  • Therefore all Athenians are mortal.

Aristotle goes on to characterize the possible forms of the syllogism and the conclusions it can generate. For example, each extreme, what we'd call a premise, must be affirmative or negative and have a scope, either universal or particular.

In Posterior Analytics, Aristotle attempted to show how his logical theory could apply to scientific knowledge. He argues that a science must be based on axioms (self-evident truths), from which one can draw definitions and hypotheses. Euclidean geometry provides an example of a system built on this kind of logical model. One starts with a small number of axioms and extrapolates from them various hypotheses or postulates.

Aristotle's contribution to logic has also been undervalued, for the syllogism makes up only a small part of modern studies. Philosopher and mathematician Bertrand Russell dismissed nearly all of Aristotle's points as false, excepting only the syllogism, which he deemed unimportant. Aristotle's thought had clear limitations, but his accomplishments are usually acknowledged with more admiration, regardless of their direct relevance today. His contribution to logic is thus generally considered to be his greatest achievement.

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