On Aug 5, 2011, at 9:58 AM, John F. Sowa wrote:
> I accidentally hit "send" before I finished. And upon rereading
> what I had written, I realize that Matthew had written "modal realism"
> but I had read it as "model realism".
>
> But that's a useful Freudian slip. If we could do a global change
> of "possible world" to "model", we would use a term that is familiar
> to engineers, and it would eliminate a huge amount of metaphysical
> confusion.
>
> In fact, Hintikka had used the term 'model set' to specify what
> Kripke called a possible world. (01)
Not really. Hintikka's model sets are sets of sentences. In a model *system*
-- basically, a set of model sets -- the model sets *correspond* to the
"worlds" of a corresponding Kripke model, but they are not the same; the worlds
of a Kripke model are featureless points. But it is easy to construct a Kripke
model from a Hintikka model system and v.v. And by the by, in "The Modes of
Modality" (which was published in the same 1963 issue of Acta Philosophical
Fennica as Kripke's "Semantical Considerations on Modal Logic"), Hintikka
appeals to the possible world metaphor a lot more than Kripke does. I'm getting
pretty tired of you making Kripke out to be some sort of villain and possible
world semantics as vaguely (or explicitly) sinister. (02)
> Kripke made some important
> contributions beyond Hintikka. But if he had used the term 'model'
> instead of 'possible world', he would have saved a lot of dead trees. (03)
It just isn't so. To anyone who is capable of reading Kripke's work on the
model theory of modal logic it is *perfectly* clear that his "possible worlds"
are nothing more than indices on, essentially, models for classical
propositional or (as the case may be) first-order logic. In fact, in that work
Kripke refers first and foremost to *model structures* and *models* and only
briefly appeals to the metaphor of possible worlds to provide a simple
intuitive gloss on the formal structures. But it is absolutely clear that there
is no philosophical baggage to the model theory; formally speaking, once again,
the set of "possible worlds" in a model structure is (as far as the models tell
us) a set of featureless points and the "accessibility" relation is nothing but
an arbitrary binary relation (with perhaps some stipulated formal properties
like reflexivity) over those points. *Nobody* who understands this material is
confused about this. Controversy -- of a strictly philosophical nature --
arises only when one goes *beyond* the formal mathematics and posits (or proves
from more basic philosophical principles) the existence of metaphysical
entities that are purported to be honest to goodness possible worlds and
develops a philosophical theory of them to explain or otherwise clarify our
intuitions about modality. Doing so turned out to be a very natural
philosophical outgrowth of the work of Hintikka, Kripke et al. and would have
arisen even if they hadn't used the possible world metaphor. (04)
-chris (05)
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