A Modern Formal Logic by Milton Fisk

By Milton Fisk

This publication 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 test to characterize the present opinion of
logicians on the common concerns with which it bargains. In truth, it was
written in the conviction that one other view of those issues is extra adequate.
The cost paid for this shift is the ensuing lack of easy mechanical tests
for the correctness of ideas of the good judgment of sentences and of monadic
predicates. The deductive procedure of facts resorted to for developing these
principles demanding situations ingenuity with no being so tricky as to discourage it.

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Q p ~ q, q ~ r :. p ~ r p~q :. (q~r) ~ (p~r) jJ~ (q~r) :. (p·q) ~, p ~ q :. (p · r) ~ (q · r) p, q :. p. q p. q :. _;p :. _;q :. (p. _;p. _;q :. _;p u q p ~ q : : (p ~ q) . /p p · (q · r) : : (p · q) · r p U ( q U r) : : (p U q) U r p U ( q · r) : : (p U q) · (p U r) Tautology Condition Disjunction Bicondi tionali ty Transposition Commutation Commutation Double Negation Association Association Distribution (Taut) (CD) (Bicon) (Trans) (Com) (Com) (DN) (Assoc) (Assoc) (Dist) Nonsymbolic versions of some of these principles are already familiar from Chapter 1.

On this view formal validity is the only genuine kind. Yet this "formalist" view of validity is unconvincing for the following reason. To claim that (8), for example, is not really valid is to say that its premiss is an insufficient basis for validly inferring its conclusion. How is it insufficient? Could the premiss be true and the conclusion false? Clearly not, for red-but-not-colored is like circular-but-square. Is the premiss irrelevant to the conclusion? Certainly not, for in fixing a genus within which a species is 22 Validity [Chap.

Not-C. :. Not both D and E, (b) A only if unless B not both C and D. Although E, A. :. B provided that C and D, (c) It is the case both that A and B and that C. :. A and both B and C, (d) A and Band C. If A and B then either C or else D or E. Neither C nor E. :. D. 2. Rewrite as unabbreviated and, as far as possible, idiomatic English sentences: (a) A U (B U C), (d) (A·B) ~ (C~ (D U E)), (b) A~(B~C), (e) ((A~B) U (C~D)) U E, (c) A U (B · C), (f) (A ~ B) ~ C. §9 System S We shall describe system S by means of three things, a list of basic principles, a list of basic rules, and a definition of proof.

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