False True/False Dichotomy - NISHIO Hirokazu's Scrapbox (Auto-translated from Japanese)

False True/False Dichotomy

Special case of [False dichotomy

Falsely assuming that a statement is "either true or false" for a given statement.

Example: The

Let f(x) = y. Is "f(x) is greater than 0" true? False?

explanation

True if "f(x) is greater than 0 for some x

False if "f(x) is greater than 0 for all x

f(x) is greater than 0", where the range of x is unclear, cannot be determined as either true or false.

Statements of the real world are often unclear

In this example, it's attributed to quantifier, but it's not limited to that.

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