🚀 go-pugleaf

Matthew P. Wiener writes:
w>This could only show one particular infinite regression (or family of
w>such) was invalid.

True, but I think it establishes a burden of argument on someone who claims
that some other type of infinite regression is justifying.  After all, the
Pollock example has some nice attributes like deductive validity and
psychological nontransparency.  (By the latter, I mean that a person might
easily believe the premises without noticing that the conclusion follows.  
This would not be true of an argument of the form, "A&B, therefore A", for 
example.)

w>The example you give below does not bear upon the
w>one that I was discussing long ago: can self-reference lead to justified
w>belief?  Recall that I made this in analogy with Loeb's theorem, which
w>asserts that the number theoretic sentence that asserts "I am provable
w>within PA" is in fact true and provable within PA, despite the surface
w>appearances that it could go either way.

w>You then asserted that self-reference leads to infinite regress, ergo,
w>such a possibility is apriori untenable.  

I don't recall saying that -- you might be confusing me with some of the
Objectivists.  Anyway, the self-reference of your sentence above doesn't
require infinite regress to verify, so it seems importantly different
from, say, the English sentence "this sentence is true".  The latter 
sentence *does* require infinite regress to verify, and it seems 
objectionable (to me at least) for that reason.

w>[The Pollock example] reminds me of the infinite regression inside Lewis 
w>Carroll's Achilles and the tortoise story (-> binds tighter than &):
w>
w> Start              (q)  <--
w>   |             [   p , p->q ]  <--
w>   |          {      p , p->q , (p&p->q)->q }  <--
w>   V       <         p , p->q , (p&p->q)->q , p&p->q&(p&p->q)->q >  <--
w>  ... ( ...                                                    ... ) ...
w>
w>And so, by your reasoning, we should reject modus ponens.

But wait, there's less!  Since the first set of premises is *transparently*
implied by the Nth, anyone who accepts the Nth ought to accept the
first, without need to deduce that set of premises from anything else.
Hence, there's no need for the regress.  By contrast, in the Pollock example,
at any finite stage of the argument, there could be a point to appealing to 
the next set of premises.  E.g., someone might actually be convinced that q1
and that q1->p, if it is suggested to him that q2 and q2->q1 and q2->(q1->p).

One can consistently maintain that modus ponens is legitimate (i.e., that
q is justified by p & p->q, provided that p is already justified and so
is p->q) while maintaining that the above infinite regress fails to 
justify.  NOTE: "justify" is different from "validly deduce" (or at least,
the claim that they are the same needs to be argued for.)
--
"It only hurts when I laugh" --Marx
Paul Torek					torek@umix.cc.umich.edu