PHIL 110 Lecture Notes - Lecture 2: Propositional Calculus, Sentence Clause Structure, Logical Connective
31 Oct 2017
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Formal logic attempts to (cid:862)translate(cid:863) some of ordinary language and to provide rules for reasoning with those claims: specifically, it can be used to represent arguments. We can use sentential logic to represent some arguments: the sentences in question are declarative, atomic sentences have no parts that are themselves sentences, compound sentences have atomic sentences as parts. Capital letters stand for specific sentences (e. g. (cid:862)p(cid:863) stood for (cid:862)dr. mc is a baboon(cid:863). Let (cid:862)p(cid:863) and (cid:862)q(cid:863) be sentence variables (as opposed to sentence constants). Variables are place-holders, while constants stand for specific sentences. Our convention will be upper-case letters for constants and lower-case letters (beginning with (cid:862)p(cid:863)) for variables. Sentences containing variables do not -- they are sentence form. p q | p q. The symbol is called a (cid:862)dot(cid:863) and forms conjunction. A conjunction is true if and only if both its conjuncts are true. p | ~p.
