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Is there an example where a mathematical theorem is proven by demonstrating the necessity of a proof, without actually providing the proof?

زكريا حسناوي
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    There is no such example. Even if you successfully prove "$T$ has a proof", a proof of "$T$ has a proof" does not count as a proof of $T$, for somewhat subtle logical reasons. I explained this e.g. here in the context of a closely related (albeit slightly different) question. (preemptive admin note: I won't turn this comment into an answer as it'd essentially be a dupe) – Z. A. K. Jan 24 '24 at 09:43
  • Regardless of whether this is considered evidence or not, is there any example at all that shows a particular case has evidence without providing the evidence? – زكريا حسناوي Jan 24 '24 at 10:48
  • I understand, you mean that the statement would be self-referential and therefore an invalid circular inference – زكريا حسناوي Jan 25 '24 at 20:21
  • @Z.A.K. You are correct; I misremembered the theorem, and my comment was completely erroneous. – Mark Saving Jan 26 '24 at 06:45
  • @MarkSaving: No worries, glad we're on the same page. – Z. A. K. Jan 26 '24 at 07:51

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