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LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy)
Continuing with the review of this text and my learning more symbolic logic.
Philosopher Langer, explains that symbolic logic contains certain principles of logical reasoning. (210). Although her teaching has its complexities, the reader should take comfort that principles of logical reasoning are also contained within the academic disciplines of philosophy, philosophy of religion and theology. If these disciplines are done correctly!
In symbolic logic, the method by which all propositions in a system are produced rests on 'general canons of logic procedure'. (210) These are 'universally known, though seldom explicitly stated'. (210). This lack of the explicit contributes to the complexity and philosophical challenge of symbolic logic.
Principles
Principle of substitution
It is assumed that whenever two terms are identical, and are the names for the same element, either symbol may be used in the place of the other. (210). Langer explains that if a = b then a x c could also be written as b x c (210), as example.
Principle of application
This is the assumption that a statement about to any element applies to each element. (210). Therefore quote:
'(a, b) . a + b = b + a' (210)
If this is true of r and m then r + m = m + r
Principle of inference
It has been recognized in academic literature (in regard to symbolic logic, my add), that if a proposition many be granted (known as true), if another proposition us implied, that second proposition may also be accepted and asserted. (210-211). Langer's explanation below. Since the first propositions means the same as (⊃) the second proposition, both can be logically asserted within symbolic logic.
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