RE: SUO: On the (existence of the) supreme supertype
John and Pat,
Thanks very much for your comments on "contexts".
Incidentally, in addition to the references in John's survey of work on
contexts, here is another paper I'd like to mention:
Dinsmore, John (1987) "Mental spaces from a functional perspective".
Cognitive Science, 11, pp. 1-21.
Cheers,
Phil
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John Sowa wrote:
>
> Pat and Phil,
>
> This topic is getting very close to issues that I discuss in my
> paper on contexts (of which the last three sections are still
> incomplete):
>
> http://www.bestweb.net/~sowa/ontology/contexts.htm
>
> The first four sections are a revised, updated version of what
> I wrote in two earlier papers (much of which has gone into
> Chapter 5 of my KR book). Section 6 presents a version
> of what I call "Modular Models", which generalize Tarski's
> "flat" models, Kripke's models of possible worlds, and models
> with hierarchical namespaces. Then in the final Section 7,
> I (plan to) show how any nested or modular model can be
> converted to a "flat" Tarski-style model in which every
> individual has a unique segmented name (somewhat like the
> URL's on the WWW).
>
> Basic point: The modules let you use abbreviated names, which
> might not be globally unique and some of which might correspond
> to "possibilia" or fictional entities. But the ability to
> translate any modular model to a flat Tarski-style model
> means that the fundamental underlying logic and proof theory
> is equivalent to conventional FOL.
>
> Some comments on your comments:
Just to be clear, all the ">>" comments below are Pat's, in response to a
previous message from me.
All the ">" comments below are John's, in response to Pat.
>
> >.... There is a potential
> >mismatch between 'exists' meaning actual existence in the real world
> >and 'exists' used as a quantifier in the logic. If we want our logic
> >to be able to reason about circumstances which might never actually
> >obtain (as is often done in planning. by considering alternative
> >possible futures, then deciding to perform actions which make some of
> >them impossible; and as is also done in counterfactual reasoning),
> >then we have to allow into the domain of quantification things which
> >do not in fact exist in the first sense, and also be able to
> >contemplate things which do exist having properties which they never
> >in fact have.
>
> I agree. That is why we need a formalism that allows us to
> have modules, or contexts, or worlds, or whatever you want to
> call them. Within any context, the global domain of discourse
> is restricted to a smaller subset (which might consist of
> "real things" or possible just name-like surrogates for eitehr
> "real" things or some kind of possibilia). But the formalism,
> whether nested or flattened, is always pure FOL in style.
>
> >A common strategy is to introduce 'imaginary entities' or
> >'possibilia' as a distinct category in the classification heirarchy,
> >but I would argue that this is a mistake, on several grounds.
>
> Instead of 'imaginary entities', I would propose set-theoretical
> constructs, which mathemticians are happy with, and leave the
> issue of whether any particular such construct corresponds to
> something in the real world to the people who worry about
> philosophy of science, theory of evidence, human perception,
> and other such issues (which I don't want to minimize -- I just
> want to make a clear distinction between the formalism and the
> issues of what exists in the real world).
>
> >... (Quine in a famous passage points out the error in
> >going from 'it is possible that someone could have been standing in
> >the empty doorway' to 'there is a possible person standing in the
> >empty doorway', by asking *how many* possible but non-actual people
> >every empty doorway has to contain?)
>
> Yes, I quote this passage in Section 3 of my context paper.
>
> >.... I would suggest that any nonreal thing
> >needs to be thought of as enclosed within a non-real causal bubble
> >which is large enough to provide a causal 'horizon' insulating any
> >effects of the unreal thing from influencing any events in the real
> >world, or vice versa. The safest such bubble would be an entire
> >possible world, but we might allow somewhat smaller sets of
> >circumstances or 4-d enclosing space-times to play the same role.
>
> Precisely what Peirce did. In fact, his bubbles are actually
> oval in shape. I use rectangles because they are easier to
> draw. But my point is that you can flatten those bubbles
> to a conventional Tarski-style model by prefixing every
> reference with a fully qualified name that indicates exactly
> which nest of bubbles it is located in. So you can have
> your bubbles and eat them too.
>
> >Then the way to introduce 'possibilia' into the ontology is to
> >introduce these 'bubbles', and allow 'IsReal' as a predicate on them
> >(which asserts that that set of circumstances does in fact obtain in
> >the real world somewhere/when).
>
> I would put "real" or the subscript 0 in the identifier on
> some privileged bubble that is intended to represent whatever
> is presumed to be the real world. But of course, that qualifier
> does not have any significant effect on the logic.
>
> > Then a possible-but-not-real person
> >(eg my imaginary brother) is simply a normal person who has the
> >misfortune to only be enclosed inside nonreal bubbles. This overall
> >picture has no need for a special category of 'possibilia',
> >therefore, and it is meaningless to even talk about
> >possible-but-unreal things inside real worlds.
>
> In the formalism, everything is just a set-theoretical
> construct. To avoid arguments about what Tarski actually
> intended, I will allow anyone to think or claim that the
> items with "real" or subscript 0 in their fully qualified
> names are "actually" present in the privileged bubble.
>
> John