🚀 go-pugleaf

_The Liar: An Essay in Truth and Circularity_, by Jon Barwise and
John Etchemendy, Oxford University Press, 1987.  It only costs $20;
its ISBN is 0-19-505072-X.  Buy this book.

	Okay, alright already, I will.

In article <8307@agate.BERKELEY.EDU> weemba@garnet.berkeley.edu (Obnoxious Math Grad Student) writes:

>Kripke first made concrete part of this feeling with the following example:

> (A)	Most of Nixon's assertions about Watergate are false.
> (B)	Everything Jones says about Watergate is true.

>Pretty harmless looking, no?  But what if A is Jones' *only* assertion
>about Watergate, and B was asserted by Nixon, who also said, coinciden-
>tally, 2k other things about Watergate, k of them clearly true, and k
>of them just as clearly false?  As Kripke said, "there can be no syn-
>tactic or semantic `sieve' that will winnow out the `bad' cases while
>preserving the `good' ones."

I would accept Kripke's statement, on the grounds that he knows much
more about these things than I do.  (A true reducible statement :-)).
However I do not see that this is a good example.  If we eliminate the
2k statements as window dressing, we are left with, in schematic
form

(A)	'B' is false
(B)	'A' is true

Now I am content to say that neither (A) nor (B) are true or false,
that they are not, despite appearances, statements having truth value.
But that is beside the point -- what I do not see is that this example
justifies or illuminates Kripke's assertion "there can be no ...".

Perhaps there cannot be such a sieve.  But in this instance we have
no problem in separating the sheep from the goats.  Now I would expect
that the problem of deciding whether statements are reducible or irreducible
is undecidable, i.e. there is no decision procedure.  I don't know this,
but it sounds like the sort of thing that is undecidable.

What this example does show that is that statements cannot be classified
one by one.  And it follows simply enough that there are infinite sets
of statements that can't be classified in a finite procedure.
-- 

In the fields of Hell where the grass grows high
Are the graves of dreams allowed to die.
	Richard Harter, SMDS  Inc.