1002 Lecture Notes - Sentence Clause Structure, Propositional Calculus, Mathematical Induction
5 Feb 2013
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Besides proving that sd is sound, that is, that it will not allow us to derive sentences that are not t-f entailed by the assumptions they are derived from, we would also like to prove that. Sd is complete, that is, that if a sentence is t-f entailed by a set of sentences, there must be some way of deriving that sentence from a subset of those sentences. Completeness: if a sentence, p, of sl is truth functionally entailed by a set, , of sentences of sl, then there is some way of deriving p from a subset of the sentences in . Any student who has struggled with the derivations in chapters 5. 3 and 5. 4 will eagerly anticipate the proof of this theorem, hoping that its demonstration will at last reveal the secret method for effortlessly and faultlessly doing any derivation. Alas, all such hopes are bitterly disappointed by chapter 6. 4.
