[FOM] A question about dialetheism and sorites

Sandy Hodges SandyHodges at attbi.com
Thu Nov 14 02:18:00 EST 2002

> And this sentence is equivalent   (in da  Costa's   logic  C_{1},  for

>  example)  of asserting a "strong negation"  ~s Blue(saucer),
>  having all properties of classical negation. So  you'd be  removing
>  any inexactness about the blueness of the  saucer, and  assuring
>  your audience that it is definitely not the case that the saucer is
>  Walter Carnielli

I looked up one of da Costa's papers, but not apparently the right
one.   If you can say that a saucer is definitely blue, and say another
is blue and not blue, and say a third is definitely not blue, could
there be a saucer that was borderline in color between two of these
three states?   For example could a saucer that is borderline between
(definitely not blue) and (blue and not blue) be both?

Allen Hazen suggested I look at Graham Priest's Logic of Paradox.   The
primary claim made by this paper is:

Claim (1): Some sentences are both true and false.

But in his "Concluding self-referential postscript" he says (the
equivalent of):

It is not the case that some sentences are both true and false.

This contradiction is not a retraction, however: rather it is an example
of the very claim that (1) makes.    Thus, whatever Graham Priest may
say, he is in no way committed not to say the exact opposite in another
place.    No doubt there are some claims he has no intention on
contradicting, but there seems to be no mechanism for indicating which
these are.    In particular, if he wished to claim that a certain saucer
was definitely not blue, it would not help in his system to say:

The saucer is not blue and "The saucer is blue" is not true.

It would not help because he is using "weak" truth, so that if "The
saucer is blue" is both true and false, then "'The saucer is blue' is
not true" is both true and false.

At one point in his paper he makes use of the concepts "true only" and
"false only."  "true only" means true without also being false.    He
may perhaps wish these concepts to be "strong," so that

"'The saucer is blue' is true only"

will be false (and false only) if "The saucer is blue" is both true and
false.    He does not provide an analysis of sentences using "true only"
however.     Priest claims that the Tarskian bi-conditional:

True(a)  iff  A

[where "a" names a sentence, and "A" stands for the content of that
must be true (true only, I think he means) even is A is paradoxical.
This is a somewhat remarkable claim, since he doesn't think even modus
ponens is valid when the premises are paradoxical.    But the more
interesting claim would be that:

True-only(a)   iff   A

is true only (or even that it is true) for paradoxical A's.    I guess
that he would not claim this.

Priest compares his "both true and false" system with other "neither
true nor false" ones.    But if the comparison is to be made, then the
mapping between them should be

Priest           Belnap e.g.
true only <----> true
both true and false <-----> neither true nor false
false only <-----> false

with this mapping, the systems are not so different; the main difference
is that Priest is willing to assert paradoxical statements (since after
all they are true, even if they are also false).    For myself I would
no more care to assert:

This sentence is not true.

than I would:

The moon is made of blue cheese.

------- -- ---- - --- -- --------- -----
Sandy Hodges / Alameda,  California,   USA
mail to SandyHodges at attbi.com will reach me.

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