In science and engineering one routinely builds descriptive models of a
product and perhaps its operation and attempts to derive conclusions about
whether, or how, it will work. Theoretically the conclusions are observable,
but in practice this may not be feasible. Deriving conclusions uses logic,
formal or not. Further applied disciplines generally have well developed
procedures for how the descriptive models are to be interpreted, e.g., what
constitutes a valid interpretation of a widget when the model contains a
widget description. If one comes to some derived conclusion one may well be
asked, possibly in a court of law, to justify the reasoning and explain how
the interpretation works. Of course this follows a standard logic based
paradigm of deduction and model theory. These descriptive models are
logical theories about the real and sometimes virtual worlds. Their model
theory in the logician's sense is critical. The questions of interest there
are details of what kind of logic can be justified and how exactly
interpretations are to be specified. The precision in many of the applied
communities do pretty well with ruling out the vagaries and ambiguities of
natural language. Often what reasoning is acceptable and how interpretations
are done, are negotiated extensively before a product is built. (01)
I keep wondering if this forum has anything useful to offer the science and
engineering community. Perhaps, I am missing something. (02)
Henson (03)
-----Original Message-----
From: Obrst, Leo J.
Sent: Monday, October 12, 2015 7:31 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] A Question About Logic (04)
I agree with the impetus, but not with your final clause, i.e., on the
inadequacy of formal logic, etc. Rather, I feel it is our major hope (at
least, to this point) for expressing what we intend, since otherwise we
contend with the vagaries and ambiguities of natural language, and spin our
wheels as philosophers and others have done for generations, mincing words.
However, we don't have to import some presuppositions of that formal logic,
and can consider it just as a technical tool. (05)
Thanks,
Leo (06)
>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>bounces@xxxxxxxxxxxxxxxx] On Behalf Of Paul Tyson
>Sent: Monday, October 12, 2015 8:06 PM
>To: [ontolog-forum] <ontolog-forum@xxxxxxxxxxxxxxxx>
>Subject: Re: [ontolog-forum] A Question About Logic
>
>On Mon, 2015-10-12 at 23:06 +0000, Obrst, Leo J. wrote:
>> I agree, Ed. This is why some of us view ontologies as not just
>> logical theories, but as logical theories about the real world.
>
>Including, presumably, Aristotle and those who find no just cause for
>abrogating his prior and posterior analytics.
>
>For one view on the inadequacy of mathematical logic for reasoning about
>the real world, see Veatch, "Intentional Logic: a logic based on
>philosophical realism".
>
>http://www.worldcat.org/oclc/1742427
>
>Regards,
>--Paul
>
>>
>>
>>
>> Thanks,
>>
>> Leo
>>
>>
>>
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Edward
>> Barkmeyer
>> Sent: Monday, October 12, 2015 6:58 PM
>> To: Thomas Johnston <tmj44p@xxxxxxx>; [ontolog-forum]
>> <ontolog-forum@xxxxxxxxxxxxxxxx>
>> Subject: Re: [ontolog-forum] A Question About Logic
>>
>>
>>
>>
>> Thomas,
>>
>>
>>
>> I do not claim to be an expert in this area, but I will make what I
>> believe is an important observation.
>>
>>
>>
>> I was taught formal logic as a mathematical discipline, not a
>> philosophical discipline. I do not believe that mathematics has any
>> interest in ontological commitment. It deals with conceptual spaces
>> that have certain properties, and whether those spaces have any
>> metaphysical counterpart is irrelevant. A mathematician does not have
>> a problem considering “six impossible things before breakfast”.
>>
>>
>>
>> To be useful any logical axiom is part of (perhaps all of) a theory.
>> So your Dog Theory may contain:
>>
>> - A1: All dogs are renates.
>>
>> - A2: Some dogs are friendly.
>>
>> as axioms.
>>
>>
>>
>> Consider then that “Some dogs are friendly” has the mathematical
>> representation:
>>
>> There is a thing in the universe of discourse that is a dog and that
>> is friendly.
>>
>>
>>
>> This actually asserts something rather more than the English
>> assertion, in that it requires the existence of a friendly dog in any
>> world of interest that constitutes the ‘universe of discourse’. That
>> is to say: any ‘universe’ or ‘model’ that satisfies the Dog Theory
>> contains at least one thing that satisfies Dog(x). No universe that
>> has no dog can satisfy the Dog Theory. But whether that universe
>> corresponds to any ontological notion of reality is a separate issue.
>> It may be that the Dog Theory is a *false* theory for the behavior of
>> the “real world”. But any ‘model’ for the Dog Theory necessarily
>> contains a thing that satisfies Dog(x).
>>
>>
>>
>> And we have examples of useful mathematical theories that are not
>> clearly grounded in reality. The base of the complex number system,
>> for example, is meaningless, but if you assume that it exists, you get
>> a powerful mathematics that can be used to predict physical behaviors.
>>
>>
>>
>> No one disputes that mathematical logic has value to philosophy, or
>> even that mathematical logic has its roots in philosophy. But, as a
>> domain of study, it has been formally separated from epistemology and
>> ontology for at least 50 years. Your question may be philosophically
>> significant, but ontological commitment is not intrinsic to
>> existential quantification.
>>
>>
>>
>> -Ed
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> From:ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Thomas
>> Johnston
>> Sent: Monday, October 12, 2015 5:01 PM
>> To: [ontolog-forum]
>> Subject: [ontolog-forum] A Question About Logic
>>
>>
>>
>>
>> Oct 10, 2015. A Question About Logic.
>>
>>
>>
>>
>>
>> I have a question about logic, which I hope the logicians in this
>> group can help me with.
>>
>>
>>
>>
>>
>> In predicate logic, universal quantification does not involve
>> ontological commitment, whereas existential quantification (as the
>> name suggests) does. To illustrate:
>>
>>
>>
>>
>>
>> "All dogs are renates" is formalized as "If anything is a dog, it is a
>> renate".
>>
>>
>> In notation: Ux(Dx --> Rx)
>>
>>
>>
>>
>>
>> "Some dogs are friendly" doesn't require translation, and in notation
>> is: Ex(Dx & Fx).
>>
>>
>>
>>
>>
>> (I use "U" for the universal quantifier, "E" for the existential
>> quantifier, "-->" for material implication, "~" for not, "&" for
>> conjunction, and "<--->" for the metalogical operator of being
>> equivalent to.)
>>
>>
>>
>>
>>
>> So Ex(Dx & Fx) says: "There exists a dog such that it is friendly."
>> "There exists"; in other words, an ontological commitment to the
>> existence of at least one dog.
>>
>>
>>
>>
>>
>> But Ux(Dx --> Rx) says: "If anything is a dog, it is a renate". No
>> ontological commitment here.
>>
>>
>>
>>
>>
>> This is all very familiar, of course. But here's a question: why, in
>> the formalization of predicate logic, was it decided that "Some X"
>> would carry ontological commitment whereas "All X" would not? (I think
>> the question has been asked and answered before, but I don't recall
>> what the answer is.)
>>
>>
>>
>>
>>
>> Now let's move on to the deMorgan's equivalences, in which the
>> negation of a universal quantification is an existential one, and vice
>> versa. In notation:
>>
>>
>>
>>
>>
>> ~Ux(Dx --> Rx) <---> Ex(Dx & ~Rx)
>>
>>
>> ~Ex(Dx & Fx) <---> Ux(Dx --> ~Fx)
>>
>>
>>
>>
>>
>> In English: "It is not the case that if something is a dog, then it is
>> a renate" is equivalent to "There exists something that is a dog and
>> is not a renate". And: "It is not the case that there exists a dog
>> which is friendly" is equivalent to "If something is a dog, then it is
>> not friendly".
>>
>>
>>
>>
>>
>> I've worked with deMorgan equivalences for so long that they seem
>> intuitively right to me. But now notice something: negation creates
>> and removes ontological commitment. And this seems really strange. Why
>> should negation do this? My being ontologically committed to something
>> doesn't have anything to do with negation; it's simply the expression
>> of my belief that the world contains something, of such-and-such a
>> type.
>>
>>
>>
>>
>>
>> Note, too, that Aristotle's square of opposition didn't have this
>> strange feature. The negation of "All dogs are renates" is simply
>> "Some dog is not a renate", and the negation of "Some dogs are
>> friendly" is simply "No dogs are friendly".
>>
>>
>>
>>
>>
>> I suspect that this strange feature, of negation having ontological
>> import, has something to do with Frege's meta-logical interpretation
>> of properties (predicates) as sets, i.e. as purely extensional
>> objects. But I don't know, and that's what I asking about.
>>
>>
>>
>>
>>
>> I'd also like to know if there are formal logics which do not impute
>> this extravagant power of ontological commitment / de-commitment to
>> the negation operator in predicate logics.
>>
>>
>>
>>
>>
>> As recent earlier comments have indicated, I'm currently on the track
>> of semantics, primarily of the cognitive variety, and definitely
>> including the diachronic variety. And so this question is well-off
>> that track. It came up as I was (re-)reading a book which, although it
>> is 25 years old, I highly recommend:
>>
>>
>>
>>
>>
>> Meaning and Grammar: an Introduction to Semantics(MIT, 1990), by
>> Gennaro Chierchia and Sally McConnell-Ginet
>>
>>
>>
>>
>>
>> What dates this book is that it is heavily influenced by Chomsky who,
>> at the time of the book's publication, had left behind (i)
>> transformational-generative grammar, (ii) extended
>> transformational-generative grammar (the result of the "linguistics
>> wars"), and was in either his (iii) principles and parameters
>> incarnation, or (iv) his X-bar theory incarnation, or somewhere
>> between the two.
>>
>>
>>
>>
>>
>> But the book is at least as deeply indebted to "west coast" semantics,
>> i.e. the Montague program, and, as it seems to me, the Chomskyean
>> associations do not run deep enough to tie this work to any of
>> Chomsky's later repudiated positions.
>>
>>
>>
>>
>>
>> Thanks,
>>
>>
>>
>>
>>
>> Tom
>>
>>
>>
>>
>>
>>
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