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> The actual source of non-constructibility is always the law of excluded middle I gotta ask, are there alternative formulations of LEM that are still useful b
by infogulch 4y ago
> The actual source of non-constructibility is always the law of excluded middle
I gotta ask, are there alternative formulations of LEM that are still useful but cause fewer problems for constructibility?
- loicd 4y agoThere are weaker forms, those accepted in intuitionistic logic. The law of excluded middle usually appears in mathematical proofs in the form of reasoning by contradiction: To prove A, assume not-A and reach a contradiction This is the non-constructible reasoning par excellence, but the following weaker form is constructible: To prove not-A, assume A and reach a contradiction Intuitionistic logic also allows so-called Ex Falso: To prove A, reach a contradiction (without assuming not-A) Now, if what you wanted is a form of LEM that is non-constructible but 'less' non-constructible than LEM, then I don't know.