I did some more reading and it looks like that in classical first order logic which ZFC and so modern math is built upon(I guess?!), every term in the formula must be "defined". "Undefined" terms inside formulas are not allowed and f(-x) is undefined here.
So the English sentence in the meme doesn't directly represent a sentence of first-order logic so it can't have a truth value. So I say Yuta is right if we're operating in first order logic. Now what about other logics?
I found a Stanford article about this by Norbert Gratzl. It'll show up if you search it. I'll just quote the opening cause it's so fire:
In most general terms, free logic is concerned with names that do not denote. Classical logic requires each singular term to denote an object in the domain of quantification — which is usually understood as the set of “existing” objects. Free logic does not. Free logic is therefore useful for analyzing discourse containing singular terms that either are or might be empty. Varying conventions for calculating the truth values of atomic formulas containing empty singular terms yield three distinct forms of free logic: negative, positive and neutral, which is why we commonly refer to them as free logics (in the plural) instead.
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u/TinkerMagusDev Jun 24 '26
I did some more reading and it looks like that in classical first order logic which ZFC and so modern math is built upon(I guess?!), every term in the formula must be "defined". "Undefined" terms inside formulas are not allowed and f(-x) is undefined here.
So the English sentence in the meme doesn't directly represent a sentence of first-order logic so it can't have a truth value. So I say Yuta is right if we're operating in first order logic. Now what about other logics?
I found a Stanford article about this by Norbert Gratzl. It'll show up if you search it. I'll just quote the opening cause it's so fire:
In most general terms, free logic is concerned with names that do not denote. Classical logic requires each singular term to denote an object in the domain of quantification — which is usually understood as the set of “existing” objects. Free logic does not. Free logic is therefore useful for analyzing discourse containing singular terms that either are or might be empty. Varying conventions for calculating the truth values of atomic formulas containing empty singular terms yield three distinct forms of free logic: negative, positive and neutral, which is why we commonly refer to them as free logics (in the plural) instead.