Formal logic

Law of non-contradiction

For all propositions p, it is impossible for both p and not p to be true, or

Formal logic - law of non-contradiction

Law of excluded middle

Either p or not p must be true, or

Formal logic - law of excluded middle

There is no third or middle true proposition between them.

Principle of identity

A thing  is identical with itself, or

Formal logic - principle of identity

Criticisms of the laws of thought

L.E.J. Brouwer, a Dutch mathematical intuitionist, rejected the law of excluded middle in mathematical proofs that used infinities. Since an actual infinity does not exist in the real world and the argument for the existence of God relates to the real world, the law of excluded middle is valid for my purpose.

Jan Jukasiewicz of the Polish school of logic developed a propositional calculus that had a third truth-value of neither truth nor falsity to deal with future contingent events when the laws of non-contradiction and excluded middle both fail. Since the laws of non-contraction and excluded middle will be applied to past events and not future contingent events, they remain valid for my purpose.


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