PHIL 110 Lecture Notes - Lecture 13: Propositional Calculus, First-Order Logic, Metalogic
31 Oct 2017
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Document Summary
A system of logic is complete if and only if everything that can be shown valid semantically in that system can be shown valid syntactically: every tautology is a theorem. Its corresponding conditional is a theorem: every theorem is a tautology. How would sentential logic handle this: all men are mortal, socrates is a man. In sentential logic, this appears to be invalid: that is because sentential logic deals with only atomic sentences or compound sentences created by the use of logical connectives. Predicate logic allows us to display the interior structure of sentences, both compound and atomic. Property constants: properties are, basically, ways things can be, examples: Is taller than (we can still use these capital letters as sentential sentence constants, as the difference will be clear. ) Individual constants: we use lowercase letters up to and including (cid:862)t(cid:863) to denote individuals, examples, my dog zada, socrates, sfu, the world"s tallest building d s f b.
