[FOM] A question about dialetheism and sorites (Joao Marcos)
SandyHodges at attbi.com
Thu Nov 21 17:11:21 EST 2002
SH: For myself I would no more care to assert:
This sentence is not true.
than I would:
The moon is made of blue cheese.
Joao Marcos: Do you intend to say that both sentences should receive
the value "false"? Do you see this as a reasonable solution in the case
of the first "Liar sentence"?
I think the first of my example sentences is of the intermediate truth
status (I don't see that it matters much whether this status is called
"Neither true nor false", or "Both true and false", or "fails to
correspond to a proposition" or "fails to terminate when considered as a
sub-routine" or any of the dozens of other proposals.)
What I do think is that the language we use to make assertions, can call
the statements in that same language "strongly true". Strongly true
means that if "a" designates a statement that has the intermediate truth
status, then "a is strongly true" is false, rather than being itself
intermediate. "a is strongly true" is in the same language as the
statement "a" designates, and not in a meta-language.
Priest does not have a "strongly true" predicate in his object language,
and he can't. He is committed to:
T: true(a) => A
His "true(a)" holds when a is either strongly true or intermediate.
Now in the case of "a" designating A, a strongly true or strongly false
statement, T should hold of course. What is questionable is whether T
should hold when "a" designates a statement of intermediate truth
I think that a language unable to call its own statements strongly true,
would not be practical for a set of individuals, with different
knowledge (and objectives), who need to talk to each other. I do not
see the requirement that a language be usable by multiple individuals,
as having anything to do with "natural language" or vagueness.
Certain formal systems would lead to practical problems which other
formal systems can correct, without the latter systems being any less
formal. For example FOL has the problem that it lacks a mechanism for
designating its own formulas; as an individual will sometimes want to
do, to talk about some other individual's utterance.
If a language has a strong-truth predicate, that has consequences due to
the paradoxes. The best systems, I think, have a mechanism for calling
a single utterance of a formula strongly true, without being committed
to calling all utterances of that same formula strongly true. Someone
who calls an utterance of a formula strongly true, would be committed to
not calling another utterance of the same formula strongly false. But
it would be no retraction to call an utterance intermediate, when you
have earlier called an utterance of the same formula strongly true.
Utterance 1. Utterance 2 is strongly true.
Utterance 2. Utterance 1 is either intermediate or strongly false.
Utterance 3. Utterances 1 and 2 are intermediate.
Utterance 4. Utterance 1 is intermediate.
Utterance 5. Utterance 1 is either intermediate or strongly false.
I call both utterances 1 and 2 intermediate. Utterance 3 states my
position and I call it strongly true, and I also call utterance 4
strongly true. I also call utterance 5 (which follows from 4)
strongly true. Thus I call 5 strongly true, but it is no retraction to
call utterance 2 intermediate, even though 2 and 5 are the same formula.
This position is called token-relativism. A non token-relativist will
call utterance 5 intermediate. Various means are available so that the
statement of one's position (utterance 3) does not lead to utterance 5
being strongly true. But all such mechanisms, it seems to me, lead to
problems if we are looking for a language that could be used by a set of
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Sandy Hodges / Alameda, California, USA
mail to SandyHodges at attbi.com will reach me.
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