[MaFLa] reminder: invitation to a talk on `Truth and Possibility` - 10 November, 4.30 PM
Biberk at ceu.hu
Wed Nov 4 10:13:21 CET 2009
The CEU Philosophy Department cordially invites you to a talk
(as part of its Departmental Colloquium series)
Jan Wolenski (Jagiellonian University))
Truth and Possibility
Tuesday, 10 November 2009, 4.30 PM, Zrinyi 14, Room 412
We have an obvious assertion
(1) A Þ àA.
If we apply T-scheme to A , it results in
(2) TA Þ àA.
Thus, what is true, is possibile as well. Although truth and
possibility are treated here as monadic sentential (propositional)
operators, a similar argument holds for predicates „is true” and „is
possible”. Hence, I will use I both readings as equivalent.
We can also apply T-scheme to àA and obtain
(3) TA Þ T(àA).
This means that truth of a sentence implies that it is true, that the
sentence in question is true too. If we agree that „is true” should be
interpreted as „is true In a model M”, A and àA are true in the same
Since (1) cannot be converted to àA Þ A, àA is weaker than A. In
particular, àA can be false, but A. Assume that A is consistent and
false. This means, on the base of Gödel-Malcev completeness theorem,
that it has a model in which is true. On the other hand, this model
must be different than the model in which A is true. Denote this model
by M’. Semantics of possibile worlds has no problem with that. It is
enough to distinguish a model M* as the actual world and say that other
are accessible from it. Thus, A can be false in M*, but true in M’.
This, however, contradicts our earlier assumption that A and àA are true
in the same model. Logically speaking, introducing M* and M does not
matter, because models are abstract algebraic structures. The situation
changes when we pass to ontology, because the basic intuition points out
that the actual world exists in the fundamental sense, but other merely
What can we do in order to resolve the issue? One way is to take a
Platonic stance and treat all possible worlds as abstract objects. This
is at odds with ordinary intuitions. Thus, we should find a solution
respecting that M* is distinguished not only for logical, but also for
ontological reasons. Possible worlds as logical constructs can be
identified with models of maximally consistent sets of propositions. On
this level, M* can be arbitrarily chosen. If we add the ontological
factor, M* becomes a representation of the world in which we live. This
open a possibility for naturalism.
E-mail: biberk at ceu.hu
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