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In a system where numbers are not sets this statement is provably false.


No. It's nonsensical there. It not true or false.

Like "5 smells insanity" is nonsensical in natural language.

You can't even begin to consider if it's true or false because it's not a sentence (in sense of mathemathical logic).

https://en.m.wikipedia.org/wiki/Sentence_(mathematical_logic...


I can concede that it may depend on the precise formal system you are using, but I think you can easily imagine a logic where a predicate ∈ takes two variables (x, y) of any kind and returns "true" iff y is a set and x is in y. In a well-founded system where numbers are ur-elements ∈(5, 5) would be well-formed and equal to "false" as every other expression of the form ∈(x, x).

In this vein I would consider "5 smells insanity" nonsencial in the colloquial sense and at the same time false.




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