SUO: Re: single vs. multiple ontology standard
>> > 4. No one has yet shown that there are two truly incompatible and equally
>> > valid theories that we need to include. I realize that Pat might
>> > reasonably disagree with this, but we simply haven't reached the
>> > of our discussion on 3d vs 4d. Each of us takes a different view on who
>> > has the burden of proof naturally.
>>The number of incompatible systems in the world is overwhelming,
>>and every one of them, if axiomatized, would be inconsistent with
>>every other one.
>That's the key, and the reason which I believe we can find an
>axiomatization that supports nominally 3d and 4d views without
>contradiction (as Cyc does).
Cyc does it by adopting the mapping of the endurantist ontolgy into
the perdurantist one whichI sketched in my email to you (in which(
R(a, b) true in I ) maps to R(a duringI, b during I) ). This is not
'supporting' both views: it is adopting one of them and providing a
mapping from the other. (In an endurantist ontology, 'a during I'
would be a sort error if a was a continuant, so this translation
would be syntactically ill-formed, never mind contradictory.) Also,
it isn't in fact obvious that Cyc is entirely consistent here, since
it has only a rather weak ontology of property change, and attempts
to extend it have given rise to some problems (the one I recall was
that the death of a spouse was inferred by Cyc to be a kind of
Let me say that I think that the Cyc compromise is in fact quite
reasonable, and probably about the best approach one could take in a
monolithic ontology. But it is *not* in accordance with both views.
> We don't have to create all possible axioms that accord with the
>world. We can make reasonable engineering choices that result in
>one set of axioms.
>>In many cases, the incompatibilities are at a low
>>level, and there exists a common compatible subset (which can be
>>found as the common supertype in the lattice). Pat is not basing
>>his argument on just the 3D vs. 4D issue, but on an enormous number
>>of examples that anyone working in the area runs into constantly.
>However, until actually formalized, I believe these issues appear
>worse than they are.
I wonder if its even worth saying this, but Adam, might it not have
occurred to you that I found all the problems that worry me most
directly, when trying to formalize knowledge? That formalizing
things, and worrying about the problems that arise from doing that
formalizing, has been my business for most of my career?
The perdurantist/endurantist issue comes up directly *when
formalizing*. The rival axiomatisations of time (density or not,
continuity or not, what kind of continuum, splitting endpoints, etc.)
all arise directly when writing axioms: they weren't even noticed
until people tried to formalize their intuitions. The 'heap paradox'
arises because *the formalizations of* concepts like 'large' allow
one to use mathematical induction . The (still open) issues of how
best to express notions of granularity and approximation all arise
*when formalizing*. The distinctions between 'promiscuous' and
'sparse' ontologies are distinctions between styles of formalizing.
And so on.
>>One reason why Pat has dropped his subscription to SUO is that
>>he is incredulous and disgusted at the idea that anyone could
>>even claim that "No one has yet shown that there are two truly
>>incompatible and equally valid theories that we need to include."
>>I also find such a claim outrageous, but I no longer find anything
>>outrageous unbelievable. I have not yet dropped my subscription
>>because I have somewhat more patience than Pat has.
>If it's so outrageous, it should be easy to find some concrete
>examples and express them as axioms, showing a logical
>contradiction. Then we have something concrete to discuss.
>Otherwise it's just intuition and conjecture.
I have done this now in many email messages to you regarding the
perdurantist/endurantist distinction, and my 'catalog' of temporal
theories does it at length, with model-theoretic exmples showing
where the contradictions arise. I wish, Adam, that you would not
constantly repeat this 'challenge' to make things concrete for you,
when it has already been answered, but you are apparently too busy,
or something, to actually read the documents. I recognize the
rhetorical strategy: it is a way of implying that you are the man
concerned with practical, down-to-earth matters of real axioms, in
contrast to the airhead philosophers and theoreticians who blow
things all out of proportion. In fact, however, all you are doing is
advertising your inability to understand the technical literature of
your own profession.
>I realize that if Pat is reading this smoke must be exploding out
>his ears but seriously, try to think of me as a reasonable person
>making these statements with a smile.
I wish I could. Unfortunately, to think of you as reasonable is now
beyond my powers of imagination.
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