FOM: Truth for Sentence Tokens
SandyHodges at attbi.com
Tue Aug 20 09:13:25 EDT 2002
Thanks to Till Mossakowski for the reference to Beck's thesis, which I
did not know about, have just read, and found very interesting indeed.
His proposal agrees with mine on these points:
1. Sentence tokens that say the same thing can have different truth
2. The Tarskian bi-conditionals: True("a") <=> a do not necessarily
hold when "a" is self-referential.
3. Rule of excluded middle.
His proposal retains bivalence (every sentence is true or false). Mine
drops bivalence but keeps the "only if" side of the Tarskian
4. True("a") => a
5. False("a") => ~a
hold even for self-referential sentences. As a result, he considers
the Liar false, and the Truth-Teller true, while I consider them both
paradoxical. I think, but am not quite sure, that of these sentences:
The following sentence is not true.
The preceding sentence is not true.
he would consider them both true, where I consider them both
With regards to Charlie Silver's doubt: "the consequence that one
instance of 'This sentence is False' may be true while another instance
is false, is not acceptable, to my mind." I presume this refers to the
A. Sentence A is not true.
B. Sentence A is not true.
In Beck's system, A is not true and B is true, while in mine, A is
paradoxical and B is true. I like to think of this analogy to
self-reference: A child's computer game, where to win, the player has
to write a true description under pictures on the screen. But an evil
programmer has written the program so that if "horse" is written under
the picture of the horse, the picture changes to a donkey. And if
anything other than "horse" is written, the picture changes back to a
horse. We can suppose someone (Jones) has said:
What Charlie Silver is about to say is true.
Charlie wishes to say something about Jones's sentence, but he's in a
situation where what he (Charlie) says, changes the truth of what he is
talking about. This is not the ordinary situation where we all we
need to do to make a true statement is to find out the facts, and make
our sentence conform to them. It is this self-reference which is going
to make Charlie's statement paradoxical. But someone else talking
about Jones's sentence is not in this paradoxical situation. All that
person needs to do is make her sentence conform to the facts, without
worrying about those facts changing as a result of what she says.
Thus, even though she may end up saying the exact same words that
Charlie ends up saying, I see no reason to call her sentence token
paradoxical, just because Charlie's is.
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Sandy Hodges / Alameda, California, USA
mail to SandyHodges at attbi.com will reach me.
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