[lit-ideas] Witters's Superstition and Ambiguous Grammar

  • From: Jlsperanza@xxxxxxx
  • To: lit-ideas@xxxxxxxxxxxxx
  • Date: Sun, 16 Jun 2013 21:30:41 -0400 (EDT)

Modern discussion of the infinite is now regarded as part of set theory and 
 mathematics, unless you are a Griceian and regard it as part of the theory 
of  implicature ("As far as I _know_ -- not far, I think -- there are 
infinitely  infinite stars"). 
 
 
 
 
 This discussion is generally avoided by philosophers ("I have other  
infinite things to say" being the lame excuse) 
 
 
 
An exception was Wittgenstein, who made an impassioned attack upon  
axiomatic set theory, and upon the idea of the actual infinite, during his  
"middle 
period".

Witters writes in "Philosophical Remarks", ยง 14: 
 

"Does the relation  correlate the class of all numbers with one of  its 
subclasses?"
 
Typically, Witters goes on to answer his own question:

"No."
 
"It correlates any arbitrary number with another, and in that way we arrive 
 at infinitely many pairs of classes, of which one is correlated with the 
other,  but which are never related as class and subclass."
 
Witters goes on:
 
"Neither is this infinite process itself in some sense or other such a pair 
 of classes."
 
Witters, unlike Grice, concludes, typically, by blaming English (or German, 
 strictly) on this:
 
"In the superstition that  correlates a class with its subclass, we  merely 
have yet another case of ambiguous grammar."
 
Or not, of the course.
 
And YET, Popper thinks 'infinity' belongs in World 3.
 
Cheers,
 
Speranza
 
 
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