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RE: Tautology - A Tale Of Two Tales

in #cryptogee-musings7 years ago

The term "tautology" comes to us from logic, so if you have not had any experience in logic it can be very difficult. Logic has to do with the structure of arguments, not the content. So if you said something like "I am tired and hungry" and later said, "That couch is red and soft", those statments would both have the same logical structure: "A and B." In the first instance, 'A' stood for 'I am tired' and B stood for 'I am hungry'; in the second instance, 'A' stood for 'The couch is red' and B stood for 'The couch is soft.' We can break many English sentences into these logical forms.

Tautologies refer to logical forms which can never be false. Let's take the second example: "The couch is red and soft." If the couch were actually blue, then the statement "The couch is red and soft" would be false. So "A and B" is not a tautology - if either 'A' or 'B' is false (whatever they may stand for), then "A and B" is false. But let's look at another example: "The couch is red or not red". In formal logic, this is represented as 'A or not A'. If the couch is red, then "The couch is red or not red" is true. But if the couch is blue, then it's not red, so "The couch is red or not red" is still true. In fact this is true of any statement of the form "A or not A" - If A is true, "A or not A" is true, but if A is false, then not A is true, so "A or not A" is still true. Therefore, there is no way for "A or not A" to be false. Because of this, we call "A or not A" a tautology.

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