[FOM] Possible worlds
Neil Tennant
neilt at mercutio.cohums.ohio-state.edu
Wed Dec 20 09:17:21 EST 2006
On Tue, 19 Dec 2006, Ignacio Nattochdag wrote:
> The trivalent calculus is a calculus of propositions with three
> different values: true, false, and possible.
> ...
> In the trivalent calculus if the proposition A is true, then the
> proposition "A is possible" is also true; if the proposition B is
> false, then the proposition "B is possible" is also false; this works
> quite nice both with our intuitions and our calculating methods.
No, it does not. The proposition
Grass is purple
is false, but it is possible that grass might have been purple (rather
than green).
Modal logic has always striven to characterize a notion of possibility on
which contingent falsehoods, though false, are nevertheless possible.
Moreover, if (as you claim) the third truth-value of Lukasiewicz's
calculus is to bear the interpretation "possible", and if (as you claim)
that interpretation accords with our modal intuitions, then one is at a
loss to understand why Tarski should have gone to the alleged length
(which you endorsed earlier) of offering CNpp as a "definition" of Mp in
this trivalent calculus.
Another problem is this: you say that the third truth-value is "possible";
and you also talk about the truth and/or falsity of claims of the form "A
is possible". How is the *truth-value* called "possible" connected to the
*metalinguistic predicate* "... is possible"? Do you simply use a Slupecki
operator, which you have omitted to mention?
Neil Tennant
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