🚀 go-pugleaf

In article <8224@agate.BERKELEY.EDU> weemba@garnet.berkeley.edu (Obnoxious Math Grad Student) writes:
>I've just come across what looks like an extremely fascinating book.
>_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.

	I will put it on my buy list... Sounds very interesting.

Re the example of claire and the three of clubs.  It sounds at
first hearing that the difference between the Austinian version
and the Russellian version is that the Russellian version reduces
to the Austinian version if we add terms that make statements about
context, i.e. "Claire has the three of clubs and this person is Claire
and this person holds this card and this card is the three of clubs."
This does not sound so interesting.  However I have my doubts about
this "adding terms that make statements about context"; I shall be
interested in seeing what is actually done.

Re the liars paradox.  The following (in loose form) seems satisfactory
to me:  We make a distinction between statements and data.  Statments
about data are either true or false.  We can also make statements about
statements.  Statements about statements do not have to be either true
or false.  However we can classify statements as reducible (founded)
or irreducible (unfounded).  Reducible statements can be resolved in
terms of true and false.  True and false do not directly apply to
irreducible statements; instead the relevant question is "Can truth
or falsity be consistently assigned to the statement".  There are
four possibilities (both T and F, T only, F only, and neither.)

The reducible statements satisfy a two valued logic; the irreducible
ones a four valued logic.  Moreover, truth of a reducible statement
is not the same thing as 'T only' for an irreducible statement.  The
latter says that you can consistently treat it as being true, but not
as false; it has no 'truth' value per se.

An immediate corollary is that it is not permissable to quantify over
irreducible statements in the usual form of truth and falsity, because
true and false are not correct categories for irreducible statements.

Whether this in fact works, is quite another matter.  But, if it does,
it seems satisfactory to me.  I rather suspect it doesn't -- it all
sounds too simple minded not to have been analyzed and shown wanting
a long time ago.
-- 

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