Milton Fisk's A Modern Formal Logic PDF

By Milton Fisk

This e-book was once written for the newbie. It is no longer, despite the fact that, a survey of
modern formal common sense, for it does no longer try out to symbolize the present opinion of
logicians on the ordinary issues with which it offers. In truth, it was
written in the conviction that one other view of those concerns is extra adequate.
The fee paid for this shift is the ensuing lack of basic mechanical tests
for the correctness of rules of the good judgment of sentences and of monadic
predicates. The deductive procedure of evidence resorted to for developing these
principles demanding situations ingenuity with out being so tricky as to discourage it.

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Example text

Thus, since the original arguments were valid, the ones without the analytic premisses will be valid. The principle ' ( (p · q) ----7 p) ----7 r :. r' will then be correct. This reasoning is successful as regards the present example, but, as we shall soon see, it cannot be extended to all cases. We turn now to defining analyticity. For this purpose, we introduce the notion of conditionalized form. ' by a '----7'. The conditionalized form of MP is, then, '((p ----7 q) ·p) ----7 q'. It will, however, be helpful to treat each ': :' principle as having three conditionalized forms.

Taken together (i)-(iv) provide a definition of analyticity. With analyticity defined, we can specify a second sufficient condition for proof: II A sequence of formulas is a proof of a principle P if the last formula of the sequence is the conclusion-formula of P and each formula of the sequence either is a premiss-formula of P or follows immediately from one or more preceding formulas of the sequence or is an analytic formula. According to II, /2/ is a proof of'((p·q) ~ p) ~r :. r', since the first formula is a premiss-formula, the second is an analytic formula, the third follows imn1ediately from the first and second, and the last is the conclusion formula.

Since sentence variables are the only variables appearing in principles studied in the logic of sentences, the logical constants appearing in these principles will belong to a restricted class. Such logical constants must fit together with sentence variables to form patterns exemplified by well-formed sentences. The logical constants of this class are to be called sentence connectives. Most of them serve to connect into compound sentences either several sentences or several clauses which would become sentences under slight modification.

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A Modern Formal Logic by Milton Fisk

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