By Milton Fisk
This booklet was once written for the newbie. It is no longer, although, a survey of
modern formal common sense, for it does no longer test to symbolize the present opinion of
logicians on the hassle-free issues with which it offers. In truth, it was
written in the conviction that one other view of those issues 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 process of evidence resorted to for developing these
principles demanding situations ingenuity with no being so tricky as to discourage it.
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Extra info for A Modern Formal Logic
A principle tells us that any argument with, say, the pattern Si, S2 :. Sa is valid and, hence, that Sa follows from S1 and S2 • To prove that Sa follows from S 1 and S2 we can give either a nonhypothetical proof with this as its conclusion or a proof of Sa from the hypotheses S1 and ,$2 • The latter course is by far the simpler, and we thus adopt it for proving principles. Now Si, S2, and Sa are variables for formulas and formulas do not literally follow from formulas. Thus the terminology of the last paragraph needs explaining.
Therefore' has been replaced by a pyramid of three dots, and periods after have given way to commas between premiss-£ormulas. When ' :. ' is used, we shall mean by a premiss1ormula any one of the separately written formulas appearing to the left of the ' :. '. The formula to the right of the ' :. ' is to be called the conclusion1ormula of the pattern or of the principle. The context will always make it clear whether a quoted pattern stands for a pattern or abbreviates a principle. A further economy can be realized by abbreviating a conjunction of two principles such as : if p then q :.
But such a use cannot be justified if we set out in building a system either with what can easily be recognized as an incorrect principle or with a set of principles from ,vhich an obviously incorrect principle is derivable. Since the pattern quoted in any principle of validity serves to distinguish it from other principles of validity in which patterns are quoted, it will be convenient to abbreviate a principle of validity by a pattern. Thus instead of writing: Any argument made with a sequence of sentences having the pattern 'if p then q.
A Modern Formal Logic by Milton Fisk