🚀 go-pugleaf

Matthew P. Wiener writes:
w> And not just an infinite regression, but transfinite 
w> regressions.  I've seen people say things to the effect
w> that, "0# is harmless, and why not, 0## will be too (which
w> justifies 0# by the by), and hey, so will 0###, (which 
w> justifies 0##) and so on by transfinite induction of thin-air
w> assumptions.  But this Pollock-like reasoning, while
w> plausible--to some people at least--is generally considered
w> too suspicious or embarrassing even, so one rethinks the
w> issue and discovers a single higher principle that covers
w> all the 0##...##..##...s.

Sounds like plain old scientific-style generalization to me.  
These people have all these intuitions about the O#'s, and ask
themselves "what do all these have in common that makes them so
appealing?"  Whereupon they discover the single higher principle
you refer to.  Kinda like, "why do all these fruits (banana, apple,
cherry ...) taste sweet?"  "Ah, sugar."  Perhaps the implicatory
relations among the O#'s are incidental to their appeal? 

t>	     Anyway, the self-reference of your sentence above doesn't
t> require infinite regress to verify, so it seems importantly 
t> different from, say, the English sentence "this sentence is
t> true".  The LATTER sentence *does* require ...

w> Ah, but the mathematical sentence "this sentence is provable"
w> does not require an infinite regress to verify! 

I just said that myself (capitalized emphasis added).

w> [much deleted...]
w> But as for ordinary language, ordinary beliefs?  I don't think
w> anyone can claim to know.

Well sure we can!  Psychologists have studied this.  Dan Osherson,
for one, tested what inferences people would draw from each of
many sets of premises.  100% of his subjects used modus ponens.
(Most of them drew inferences by affirming the consequent, too;
and in some experiments, they fail to use modus tollens.)
--
       "The philosopher's dictionary defines `outSmarting
        the opposition' as accepting the conclusions of their
        reductio ad absurdum arguments" --Jerry Fodor
Paul Torek					torek@umix.cc.umich.edu