# We generally hold that a mathematical proposition such as "2 + 2 = 4" is necessarily true; it is difficult to imagine a possible world in which it is false. However, is it possible that "2 + 2 = 4" is not a statement that expresses a mathematical necessity (or an operation involving numeric values that must provide a certain result), but rather presents an inductive inference based on how people currently "define" the number "2", and the operator "+"? We could, for example, someday come to discover that "2" does not represent "2 things or ideas"; what we call 2 things may turn out to be 3 things, or 1 thing, etc. If this is possible then it would seem that "2 + 2 = 4" is an empirical, not a rational truth. Is this intelligible? I realize that this last statement, that we could discover 2 to refer to 3 things, etc., entails a theory of what a number is, i.e. a number "represents a quantity or amount of something". It seems, though, that in order to conclude that "2 + 2 = 4" is a necessary truth we must hold that a number is a "fixed" value; for example, a number is a (theoretical) quantity which is not grounded in any emprical relation (e.g. "2" represents a theoretical value that is "fixed"). Surely, though, the way we use numbers seems to indicate (as does applied mathematics) that we do not (always) mean that "2" is theoretical or rational; if this were true then we might (ironically) lose all meaning that mathematics provides in everday use. I realize there is more to this issue than what I present here; what, for example, does it mean for a number "to represent" to something or another. I think, however, there is enough here to make the question clear.

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