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Why study mathematics? One cannot deliberate about necessities, since practical things must admit of being otherwise than they are (DA 433a29–30). A sound demonstration shows what is necessary of an observed subject (AnPo.90b38–91a5). For example, “man” is not truly predicated of Callias’ hand. Fine, G. On Ideas. Though the audience seemingly “immediately” grasps the fact of birth without it being given in perception, the passage from the perception to the fact is inferential and depends on the background assumption of the suppressed premise. Consequently, a person who demands a demonstration of this principle is no better than a plant. Geometrical analysis is the method by which a mathematician works backwards from a desired result to find the elements that constitute that result. Though the imitation itself is a kind of technique or art, this pleasure is natural to human beings. Aristotle. 33, 1980. 2nd ed., Oxford: Clarendon Press, 1948. It was presumably during this period that he authored most of his surviving texts, which have the appearance of lecture transcripts edited so they could be read aloud in Aristotle’s absence. Cartwright, N. and J. Pemberton. Though all meaningful speech consists of combinations of these constituents, Aristotle limits logic to the consideration of statements, which assert or deny the presence of something in the past, present, or future (Int.17a20–24). The final cause of each kind corresponds to the reason that it continues to persist. Judged solely in terms of his philosophical influence, only Plato is his peer: Aristotle's works shaped centuries of philosophy from Late Antiquity through the Renaissance, and even today continue to be studied with keen, non-antiquarian interest. “Did Aristotle ‘Develop’? Sachs translates… More . Should the poet imitate things as they are, or as they should be? Since all sublunary bodies move in a rectilinear pattern, the heavenly bodies must be composed of a different body that naturally moves in a circle (DC 269a2–10, Meteor.340b6–15). The inductive form of rhetoric, reasoning from example, can be illustrated as follows. However, because people are by nature communal or political, in order to lead a complete life, one needs to form friendships with excellent people, and it is in living together with others that one comes to lead a happy life. The deductive form of rhetoric, enthymeme, is a dialectical syllogism in which the probable premise is suppressed so that one reasons directly from the necessary premise to the conclusion. As opposed to superlunary, eternal substances, sublunary living things cannot preserve themselves individually or, as Aristotle puts it, “in number.” Nevertheless, because living is better than not living (EN 1170b2–5), each individual has a natural drive to preserve itself “in kind.” Such a drive for self-preservation is the primary way in which living creatures participate in the divine (DA 415a25–b7). Teleological explanations are necessary conditionally; that is, they depend on the assumption that the biologist has correctly identified the end for the sake of which the organism behaves as it does. The pity and fear produced by imitative poetry are the source of a peculiar form of pleasure (Poet.1453b11–14). Although this is the best kind of political community, Aristotle does not say that the best life for an individual is necessarily the political life. The order of works in this table descends from Andronicus’ edition (1st. Regardless of whether one is asking what something is in a definition or why something is the way it is by giving its cause, it is only when the principles or starting points of a science are given that demonstration becomes possible. Aristotle’s ethics are thus part of his political philosophy.

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