🚀 go-pugleaf

In article <9981@mimsy.UUCP>, flink@mimsy (Paul V Torek) writes:
>To support my claim that an infinite regress is not sufficient justification
>for believing something, I present Pollock's proof that ANY proposition may
>be "justified" using an infinite regress.

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

You then asserted that self-reference leads to infinite regress, ergo,
such a possibility is apriori untenable.  The jump from "some IRs are bad"
to "all IRs are bad" is an unforgivable quantifier switch.  Your example
is noteworthy, but I'm still convinced that most times I hear objections
to "infinite regress", I'm actually hearing ancient bugaboos.

Note that I don't actually yet have an opinion about IRs and bootstrapped
justifications, just that I find the possibility intriguing and not at all
obvious one way or another.

>Let "<--" stand for "is justified by", and let "->" stand for the material
>conditional.  Consider any proposition p, and any propositions q[i].

>	p <--
>	q1 , q1 -> p  <--
>	q2 , q2 -> q1 , q2 -> (q1 -> p)  <--
>	q3 , q3 -> q2 , q3 -> (q2 -> q1) , q3 -> (q2 -> (q1 -> p))  <--
>	etc.			[Pollock example]

And this reminds me of the infinite regression inside Lewis Carroll's
Achilles and the tortoise story (-> binds tighter than &):

 Start              (q)  <--
   |             [   p , p->q ]  <--
   |          {      p , p->q , (p&p->q)->q }  <--
   V       <         p , p->q , (p&p->q)->q , p&p->q&(p&p->q)->q >  <--
  ... ( ...                                                           ... ) ...

And so, by your reasoning, we should reject modus ponens.

How now brown cow?  (And is there anyone else who's always been bugged
by Carroll's example?)

Most curiously, about a month ago I came across an article about 2-3
years old in _The British Journal for the Philosophy of Science_ which
argued that Descartes' "cogito, ergo sum" can be justified as a Cantor
diagonalization!  I only skimmed the article--with neither belief nor
disbelief nor realization that I had argued similarly, just astonish-
ment--and filed it away mentally for later reference; perhaps someone
else would like to look at it.  [I unfortunately am busy.]

ucbvax!garnet!weemba	    Matthew P Wiener/Brahms Gang/Berkeley CA 94720
...those infected with the superstring syndrome have to believe in miracles:
not the minor ones like the parting of the Red Sea, but major ones in which
six of the ten space-time dimensions become compactified to the Planck scale.