Comments on: Two Bootstrapping Problems

By: Alexey Romanov

Alexey Romanov — Wed, 26 Aug 2009 21:25:28 +0000

I clearly don’t understand something. So far as I can see, the problem starts by the time you get to 3a!

Consider someone whose colour vision is unreliable. In fact, let him be unable to distinguish between red and green (both appear to be green to him). When looking at a copy of Contexts, his colour vision tells him it’s green. Then why wouldn’t he reason as follows:
(1a’) That appears to be green (by introspection).
(2a’) That is green (by colour vision).
(3a’) So appearances match reality on this occasion.
?

By: Mike Titelbaum

Mike Titelbaum — Sat, 01 Aug 2009 05:24:12 +0000

The reliable/anti-reliable example is original to me, but as you note it’s a tidy version of a general class of cases in which a method’s providing one right answer implies that it is reliable. (Hence the immediate deductive step to that conclusion.) It’s an interesting question whether anyone has written up the fact that bootstrapping can be done without induction. I couldn’t find the point on a quick scan of the articles I have to hand, but perhaps someone with a deeper knowledge of the literature can chime in here?

By: Brian Weatherson

Brian Weatherson — Sat, 25 Jul 2009 21:56:56 +0000

Mike,

That’s a nice version of the problem. I guess any case where the subject knows in advance that if they are right on some cases, they are right on all cases, will get the puzzle going without an inductive step?

Do you know if anyone has written that up?

By: Mike Titelbaum

Mike Titelbaum — Thu, 23 Jul 2009 01:45:32 +0000

I can’t tell if your worry is a general one about principles that get one to 5, or in particular a worry about inductive principles that get one to 5. Many people are now of the opinion that one can do bootstrapping without any inductive step at all. For instance, suppose we add to your example that you know in the background that your color vision is either reliable or anti-reliable (in which case it goes wrong every time). Then you can skip from 3a immediately to 5 via a deduction. Of course, whatever objections one has to an inductive principle that gets from 4 to 5 might also be raised about the deductive principle that would be needed to get from 3a (plus your background knowledge) to 5. But the problem doesn’t look to me like it’s about induction per se.

By: Brian Weatherson

Brian Weatherson — Tue, 21 Jul 2009 15:54:40 +0000

Thanks Ezra. I had forgotten that the distinction is made that early.

By: Ezra Cook

Ezra Cook — Mon, 20 Jul 2009 00:53:30 +0000

In A Contextualist Solution to the Problem of Easy Knowledge, Ram Neta (Grazer, 2005) provides some ampliative closure schemas in an attempt to distinguish moves such as that between (4) and (5) that are acceptable from those that are not.

By: Brian Weatherson

Brian Weatherson — Sun, 19 Jul 2009 19:59:05 +0000

Thanks Aidan. I’d forgotten the details of Roger’s discussion, but I’ll look back at that.

By: Aidan McGlynn

Aidan McGlynn — Sun, 19 Jul 2009 16:21:46 +0000

Isn’t there’s some relevant discussion in Roger White’s anti-dogmatism paper? There White argues that one can infer a claim he labels NO FAULTS, which is more or less 4, if I’,m remembering correctly. This is supposed to be problematic since it’s hard to explain why NO FAULTS is true without appealing to something like 5.

(This perhaps isn’t quite what you’re after, since it’s more a way of responding to those who think the step from 4 to 5 is resistable, rather than an argument that reaching 4 is bad independently of whether we can move from 4 to 5. But it was one of the considerations Cohen mentioned at the conference, and it seemed relevant enough to be worth mentioning.)