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, Goldbach's Conjecture, the Twin Prime Conjecture) or "proved general theorems" (e.g.
What they disagree about is the status of an ordinary mathematical conjecture, such as Goldbach's Conjecture.
In particular, Wittgenstein asserts that uncontroversial mathematical conjectures, such as Goldbach's Conjecture (hereafter 'GC') and the erstwhile conjecture "Fermat's Last Theorem" (hereafter 'FLT'), have no sense (or, perhaps, no determinate sense) and that the unsystematic proof of such a conjecture gives it a sense that it didn't previously have (PG 374) because "it's unintelligible that I should admit, when I've got the proof, that it's a proof of precisely this proposition, or of the induction meant by this proposition" (PR �155).
Together, Wittgenstein's finitism and his criterion of algorithmic decidability shed considerable light on his highly controversial remarks about putatively meaningful conjectures such as FLT and GC.
GC is not a mathematical proposition because we do not know how to decide it, and if someone like G.
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