[FOM] comment on the video of the lecture by Voevodsky at IAS

[Calvin Ostrum]

On 05/18/2011 05:28 PM, Curtis Franks wrote:

> Parts of that explanation were very surprising. For example, one would
> expect the "third option" in the later slide to be something like "PA is
> for all we know inconsistent." That seems to be what follows from the
> denial of 1 and 2. But Voevodsky repeatedly suggests the stronger claim:
> We have here some evidence that PA is probably inconsistent --or -- the
> inconsistency of PA is the most likely explanation of Goedel's theorem.

Yes, I only listened to this once, while doing other things, so
perhaps I missed some explanation, but the three choices offered
seem at all not to be exhaustive.  I am surprised no one seems yet
to have commented on this.  Why couldn't PA be consistent, even
though we could not ever prove it?  That doesn't seem impossible
(in the vague "for all we know" interpretation of the modality)
although of course it has a Platonic feel to it that many would
not like.  Is an animosity toward that sort of thing hidden in
the claimed exhaustiveness of 1-2-3?

> Kuhn had a famous line: "When reading the works of an important thinker,
> look first for the apparent absurdities in the text and ask yourself how
> a sensible person could have written them. When you find an answer ...
> then you may find that more central passages, ones you previously
> thought you understood, have changed their meaning."

I guess this is supposed to refer to some cool new interpretation
of things that the "important thinker" has managed to think
up?  But couldn't a "sensible thinker" simply have done something
like written "knowledge" in 2 when he really meant something
like "truth" (so, something that we wish we could have knowledge
of)?  It doesn't seem all that likely, but one grasps at straws.

If that is the case then, 1-2-3 can easily be seen to be
exhaustive as required, but 2 should probably not be dismissed
as easily as he seems to have done.

I guess someone should just ask him. (Same with Ed Nelson, on
some similar matters of interpretation).