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But definitions can and are proven false. I hate it, mind you, but I can’t ignore it. For example, the usage of “literally” as an intensifier, e.g. “I literally
by sgarland 1y ago
But definitions can and are proven false. I hate it, mind you, but I can’t ignore it. For example, the usage of “literally” as an intensifier, e.g. “I literally died of laughter.”
- Eisenstein 1y agoBut that is their whole point -- as much as you want to make the definition something else, you can't. And this is a perfect example of that.
- perching_aix 1y agoLogical statements can be proven true/false. Definitions are not logical statements, they do not have truth values, therefore cannot be proven neither true, nor false. These are mathematical logic basics.
- drdeca 1y agoYes. However, in some cases (though probably not the ones relevant here) a definition can be proven to be incoherent (or, to presuppose something false), which is vaguely similar to “being false”.
- thaumasiotes 1y agoIt would be difficult for a definition to make any presuppositions. You could have a definition that defines some set in which a contradiction is involved ("an integer is special if it is both prime and divisible by 4"), but then you'd say that the set so defined is empty, not that the definition is incoherent.
- drdeca 1y agoIt is quite common for a lemma to be needed to ensure that a definition is well-defined. The term “defi-lemma” exists for a reason. As a simple example, suppose X is a set and r is a relation on X. If I define Y := X/r , the set of equivalence relations with respect to r, this implicitly assumes that the relation r is an equivalence relation.