In the first part of my updating of Carnap, I noticed that his account fell prey to the same sort of criticism that Shalkowski offered for "ontologically-based" reductive accounts of modality -- specifically possible worlds as
concreta or
abstracta. Whereas it looks as though, if Shalkowski's paper finds purchase, there is a trouble with no real solution in sight for these metaphysical sort of reductions, I tried to sketch a way out of this sort of difficulty for
semantically- (or more generally
epistemically-) based approaches to the reductive account of modality of the sort that I think Carnap is aiming at. Basically, the idea was the following. Carnap's
state-descriptions are sets of sentences that, in terms of a formal language, describe the possible worlds of (say) Lewis. These state-descriptions are essentially sets of sentences that describe, to speak a bit in the manner Levine in his [1998], the distribution of properties across individuals. [[Of course, this is a bit misleading, because it seems that we must have some way to
carve-up the matter of our environment into individual objects before we can even begin to assign properties to those individuals -- so it seems that our system of concepts must be deployed before we can even begin marking out individual objects.]] But before we can even take something like these state-descriptions sets of sentences describing possible worlds (even if they only have conceptual ontological status), it seems we must have some way to delimit the class of these state-descriptions. We don't want every combination and permutation of properties across objects to be permissible -- in that case, we'd be left without any true
de dicto modal claims -- a triangle might lack the property of being a trilateral for instance. [[This is the equivalent of allowing
impossible worlds into the pluriverse.]] I believe the divide between world and how the world is described is important in helping resolve this issue.
The suggestion was to allow only those state-descriptions which corresponded to (imagined) worlds (or perhaps mini-worlds) in which concepts could be
coherently deployed in describing the environment of the world (or mini-world) by a cognizer who possessed those concepts. For example, if a cognizer possessed the concepts WATER and H
2O, then no state description in which there was an individual which was water but not H
2O would be permissible. I need to spell the suggestion out in more detail, but I believe the basic idea is that, with the help of "possible worlds" as useful metaphor, certain kinds of
de dicto modal claims can be addressed in terms of concept possession on a certain view of that. What I've come to realize, is that by the "addressed" of the previous sentence, I can't meant "completely explained" because it seems that the condition I've developed as a restriction on allowable possible worlds (via allowable state-descriptions) is only a
necessary one, rather than being
necessary and
sufficient one. As an illustration, it doesn't seem that my suggestion for delimiting the class of state-descriptions helps us out at all on the Goliath/Lumpl puzzle. (Maybe Ludwig's paper helps us out here.) And of course, the treatment I've offered of modality is not a reductive one, but rather only
semi-reductive --
de dicto modality (and eventually
de re modality) is reduced to concept possession and competence in referring to particulars. These respective notions do have a modal dimension, but the hope is that concept possession and competence with names in referring are easier to make sense of than full blown (prima facie mysterious)
de re and
de dicto modal claims.
But in any case, I think this shows that (again if Shalkowski's criticisms hit their mark -- I need to take a look at Ted Sider's 2003 "Reductive Theories of Modality" in the
Oxford Handbook of Metaphysics to see if he heads off Shalkowski's argument -- if so maybe I can head off the counter-argument) ontologically-based approaches to
de dicto modality suffer precisely becase there is no separation between (possible) world and language. Perhaps this difficulty will feature again in arguments for conventionalism and
de re modal claims. That is, we can't even secure reference to an individual in different possible worlds (we I say that, read "different imagined conceptually coherent scenarios") if we don't have some conceptual content associated with the names for those individuals -- and that requires some sort of separation between (possible) world (or individual) and language (or names for that individual).