Logic

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1. In the Sophist and following Protagoras, Plato analyzes speech into two parts, i.e., a noun and a verb. A verb is a sign of actions, while a noun is a sign of agents of the actions. A sentence, he insists, must consist of at least one noun and at least one verb: two nouns in succession, or two verbs in succession, will never make a sentence. This distinction becomes the foundation of Aristotles logical analysis of argument.2. A is a discourse in which from certain things laid down something different follows of necessity (1.1. 24b18).3. A proposition (protasis) is, roughly speaking, a sentence considered in respect of its logical features.a. Propositions such as Every man is mortal and No Greeks are horses are universal propositions (katholou). The former is a universal affirmative (kataphatikos), while the latter is a universal negative (apophatikos).b. There are particular propositions (en merei) such as Some Greeks are bearded (a particular affirmative) or Some Greeks are not bearded (a particular negative).4. In propositions of all these kinds, Aristotle says, something is predicated of something else. The presence or absence of a negative sign determine whether these predications are affirmations or negations respectively (1.1. 24b17).5. The items that enter into predications in propositions are called by Aristotle terms (horoi). Terms can either figure as predicates themselves or have other terms predicated of them.a. Major term is the predicate of the conclusion.b. Minor term is the term of which the major is predicated in the conclusion.c. Middle term is the term that appears in each of the premisses.i. Aristotles use of these terms in the Prior Analytics is not consistent. But the above account is accepted as canonical since antiquity (see W.C. Kneale and M. Kneale, The Development of Logic (Oxford: Clarendon Press, 1962), 69-71).6. Aristotle uses schematic letters to bring out the patterns of the argument: If A belongs to every B, and B belongs to every C, A belongs to every C.a. Aristotles exposition of syllogisms follows the pattern If p and q, then necessarily r rather than p, q therefore r.