[FOM] A question about dialetheism and sorites

Walter Carnielli carniell at cle.unicamp.br
Wed Nov 13 06:42:43 EST 2002

Sandy Hodges   asked:

>"Now suppose the saucer is definitely not blue, lacking any hint of
>blueness.   I say: "The saucer is not blue."  I wish to be as
>informative as possible about the blueness of the saucer.   However, as

>far as my audience can tell,  I may be simply failing to say "The
i>s blue."   For all they can tell, the saucer may be both blue and not
>blue and I am telling them only part of what I know about it.   My
>question is, is there any way, in a paraconsistent logic, for me to
>assert that the saucer is not blue, and also not in the state of being
>both blue and not blue?
>In particular, does

> ~ Blue(saucer) & ~ ( Blue(saucer) & ~ Blue(saucer) )

> have this meaning?"

It depends  upon which  paraconsistent  logic you have in mind.
Dialetheism is a very particular way of paraconsistency,  charged
with  strong  ontological assumptions, as the  existence  of
in the sense of  really true contradictions.
However, as your example tells, we do not need metaphysics to express
contradictory views about facts  of  the  world, where the
contradiction  is
just due to vagueness, misinformation, or other kinds of inexacteness.

In the  "logics of formal inconsistency",  for  example, which are
free of   dialetheist ideology (and which are a  kind
of "upgrade"  of the paraconsistent logics introduced by da Costa )
you can express  your  information precisely by the sentence
~ Blue(saucer) & ~ ( Blue(saucer) & ~ Blue(saucer) ), as you suggest.

And this sentence is equivalent   (in da  Costa's   logic  C_{1},  for
of asserting a "strong negation"  ~s Blue(saucer),  having all
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 blue.

Walter Carnielli
CLE-UNICAMP, Campinas, SP, Brazil
<carniell at cle.unicamp.br>
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