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Logical Transformation Rules
Although he did so in a humorous and somewhat ironical manner, C. S. "Jack" Lewis trashed the lack of logic in today's thinking (read the part in "The Lion, the Witch, and the Wardrobe" where the professor tells Peter and Susan that Lucy's story about meeting Mr. Tumnus is probably true). Although now almost completely neglected in education it's impossible to understand religious arguments like those put forward by Thomas Anselm and Descartes without a rudimentary knowledge of the transformation rules of the first order predicate calculus. But rather than just simply give a reference of a typically incoherent textbook, what is given below should be enough to follow the unimaginable wisdom in CooperToons' logical argument.
T = T
F = F
T = F
F = F
T = T
F = F
T = T
F = T
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T = F |
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F = T |
Although it's not proper grammar in modern English to use doublenegatives, that is a purely pedantic and arbitrary rule. Early English is pepperred with double and triple negatives as are other languages. Logic also does not prohibit any number of negatives although they usually are reduced to one or no negatives to make the meaning clear.
T
= F
= T
T
= F
= T
= F
Finally, an important rule is that an "if-then" statement is equivalent to an "not - or" statement. In other words if you see P Q, then you can substitue a P V Q and it means the same thing.
Oh, yes. For those having a really slow day, "T" means "True" and "F" means "False".
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