[FOM] Consistency of Robinson arithmetic

Richard Heck rgheck at brown.edu
Thu May 19 07:40:59 EDT 2011

On 05/19/2011 01:07 AM, Keith Brian Johnson wrote:
> Richard Heck wrote:
>> Perhaps the most intriguing possibility, to me, however, lies in work on
>> what people call "transmission failure". These are cases where one knows
>> that P, has a good (logical) argument from P to Q, and yet it seems as
>> if one can't (come to?) know Q on that basis. A classic sort of
>> (putative) example is: I know that that thing in the cage over there is
>> a zebra; if it's a zebra, then it isn't a cleverly disguised mule; so I
>> know that it isn't a cleverly disguised mule. Here, it seems as if one's
>> belief (even knowledge) can't support the claim that the thing isn't a
>> cleverly disguised mule. It's as if there's a sort of epistemic circularity.
> While I have not yet published my account of this, I have given it some 
> thought.  It seems to me (to put this very briefly) that there is no real 
> problem here if one speaks carefully; the problem comes if one speaks sloppily 
> in a way that obscures the possibility of error, so that paradoxical examples 
> exploiting that very possibility can be created.  There are two sources of 
> error:  First, our ordinary metaphysical and epistemic assumptions (such as that 
> our basic thought processes are reasonably reliable, that what feel like 
> memories of mental phenomena previously experienced really are, and that [for 
> empirical claims] there really is an objectively existing reality of which our 
> senses give us reasonably reliable information); second, our fallibility even 
> given those basic assumptions.  (Let's conjoin those metaphysical and epistemic 
> assumptions and call them "T.")  Because of this fallibility, we should usually 
> say not that we are (fully) justified in believing that p, but that we are 
> (fully) justified in believing that probably-p (or, alternatively, not that we 
> are fully justified in believing that p but that we are only partially justified 
> in believing that p, with some degree of epistemic likelihood); so, normally, we 
> should say not "S knows that p" but rather "Given T, S knows that probably-p."  
> Thus, when we say that S is justified in believing (read "knows") that that 
> animal is a zebra, then should also say that S is justified in believing (read 
> "knows") that that animal isn't a cleverly-disguised mule, for the simple reason 
> that what we really mean--or *should* really mean--is that given T, S is 
> justified in believing (read "knows") that that animal is probably a zebra, so 
> that given T, S is justified in believing (read "knows") that that animal is 
> probably not a cleverly-disguised mule.  The former epistemic likelihood 
> ("probability") can hardly be high if the latter isn't.
It is an important questions whether we should adopt a probabilist
account of belief, instead of or in addition to the more traditional
on-off conception. But I do not know anyone who has published on this
who thinks transmission-failure (of which there are perfectly ordinary
examples) has anything specific to do with probabilism.

Second, there are scope issues here that I do not know how you intend to
resolve. What is naturally suggested by the account is that S know that,
if T, then probably p, or something of the sort, whereas what you say
reads as: Assuming T, S knows that probably p, which just seems wrong.
But if the former is the correct view, then it appears as if you are
suggesting we should conditionalize all our beliefs on broadly
"metaphysical and epistemic assumptions". That simply doesn't appear a
plausible account of the ordinary examples (e.g., Wright's soccer game).

Finally, I personally find it difficult to distinguish this sort of
proposal from skepticism.

> Therefore, I don't think that anyone "worried about some kind of circularity in 
> consistency proofs," as Heck puts it, should appeal to the transmission failure 
> problem above.
I think if you read Timothy Chow's most recent contribution to this
thread, you will see echoes of that very idea.

Richard Heck

Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University

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