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There is a law of logic called:

The law of excluded middle: either X is true, or not-X is true.

There is no middle ground here.

Mathematicians and philosophers have occasionally attacked the idea that excluded middle is a logically valid law.

We can't hope to settle the debate here, but our ability to reason about alternative possibilities even in everyday life, would be almost completely paralyzed were we to be denied the use of the law of excluded middle.
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More to explore:

Logical puzzle that essentially uses the law of excluded middle

Another tool that we need to use
 

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Never heard of this law before and read about it and it makes no sense to me. I'm no expert on logic or philosophy, but isn't the "middle" what we are trying to figure out most of the time when using logic?

Too many high level threads in a day
 

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Never heard of this law before and read about it and it makes no sense to me. I'm no expert on logic or philosophy, but isn't the "middle" what we are trying to figure out most of the time when using logic?

Too many high level threads in a day
Do not take the word middle too literally. Logic doesn't care about meaning :)
 

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I remember being introduced to some different types of logic from Robert Anton Wilson's works. He mentioned the mathematician Von Neumann who had the three-valued logic: true, false, and maybe. Then there was Anatol Rapoport with his four-valued logic of true, false, indeterminate, and meaningless.

Wilson himself had a different variation, saying “All phenomena are real in some sense, unreal in some sense, meaningless in some sense, real and meaningless in some sense, unreal and meaningless in some sense, and real and unreal and meaningless in some sense.” And then there's the logic of Alfred Korzybski, who had a many-valued logic with probabilities in which there is perhaps more than one truth value (he attacked Aristotle's "is" of identity, which later was used in his development of general semantics). These are a few cases of non-Aristotelian logic where people have tried to devise ways that go beyond the black/white binary.
 
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How exactly is this the essential tool for the INTP? Oh and I hope you are aware that this kind of thinking is not a "tool".
 

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Yup. Makes sense.

An observed thing cannot be on fire and not on fire at the same time.

All adjectives that operate on some kind of graduated scale can be simplified into the brightline when a thing can be truthfully described as x, regardless of the degree of x. Once this binary is determined, the law of the excluded middle applies.
 
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Wherein is the problem?

A statement is either true or untrue.
 
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