Lukasiewicz's keywords


History of Logic


"The fundamental difference between Stoic and Aristotelian logic does not lie in the fact that hypothetical and disjunctive propositions occur in Stoic dialectic, while in Aristotelian Syllogistic only categorical propositions appear. Strictly speaking, hypothetical propositions can be found in Aristotle's syllogistic also, for each proper Aristotelian is an implication, and hence a hypothetical proposition. For example, 'If a belongs to all b and c belongs to alla a, then c belongs to all b'. The main difference between the two ancient systems of logic lies rather in the fact that in the Stoic syllogisms the variables are propositional variables, while in Aristotle's they are term variables. This crucial difference is completely oblitered, however, if we translate the above-mentioned Stoic syllogism as Prantl does"
("On the History of the Logic of Propositions" [1934], in Selected Works, North Holland, Amsterdam 1970, p. 199).

"Formalism, or better formalization, means the ideal of exactitude that each deductive system strives to attain. We say that a deductive axiomatically construed system is formalized when the correctness of the deductions on the system can be verified without having to refer back to the meaning of the expressions and symbols used in the deductions. They may be verified, that is, by anyone who understands the rules of inference of the system. In this sense the Stoics prepared the way for formalism and they cannot be credited highly enough for that. They held strictly to words and not to their meanings, which is the principal requirement of formalization an they even did so in conscious opposition to the Peripatetics".
("On the History of the Logic of Propositions" [1934], in Selected Works, North Holland, Amsterdam 1970, pp. 207-8).

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