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.