david petry wrote: > > herbzet wrote: > > david petry wrote: > > > > > > > [...] > > > > > > > > 2) Godel's Theorem (loosely, no consistent formalism can prove its own > > > consistency) Informally, our skeptic claims, a proof is a compelling > > > argument. It seems clear to our skeptic that if we are to believe that > > > the formal theorems in our formalism should be accepted as compelling > > > arguments, then at the very least it must be the case that we already > > > believe that our formalism is consistent, and hence, no possible formal > > > proof within that formalism could be considered to be the evidence that > > > compels us to believe that the formalism is consistent. > > > > This last sentence is well-written. I strongly agree with it, > > though it's possible that I might consider such a proof to be > > in the nature of corroborating evidence. > > > > > And our skeptic > > > asks, is that not already the essential content of Godel's theorem? > > > > No. > > The pretense of this article is that a skeptic who has read popular > books on mathematics is asking the question. She believes that > mathematics must be justified by helping us understand the observable > world in which we live. Your answer is rather unsatisfying to her.
1) From the tone of your original post, I would think think your skeptic would be more unsatisfied with a "yes" answer. I should think she would be relieved to hear that the answer is "no".
2) I think a better word than "pretense" would be "conceit". But that's a matter of taste.
'Even the crows on the roofs caw about the nature of conditionals.'