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Re: [ontolog-forum] A Question About Logic

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Wed, 14 Oct 2015 02:36:43 -0400
Message-id: <561DF7FB.9030609@xxxxxxxxxxx>
Pat and Tom,    (01)

Tom
>>> why, in the formalization of predicate logic, was it decided
>>> that "Some X" would carry ontological commitment    (02)

JFS
>> Nobody made that decision.  It's a fact of perception.    (03)

Pat
> I wish John had not mentioned perception here, as it muddies
> the discussion with irrelevant ideas. It is not a fact of
> perception. but a fact of the truth-conditions of the sentencesMy
> involved.    (04)

I agree.  The point I made about perception was part of an argument
in favor of adopting a logic with only two operators (existential
quantifier and conjunction or ex-con logic) as a useful subset of
logic.  In fact, that is the subset that is expressible in RDF.    (05)

If you add negation to RDF (or ex-con logic) and allow all possible
syntactic combinations, you get full FOL with the usual semantics
for both proof theory and model theory.    (06)

Tom
> I'll respond to you and the others as soon as I can -- but
> not before I think I may understand you.    (07)

OK.  But I'd like to add a few more points:    (08)

  1. I agree that Pat's examples show why it's awkward to assume
     a logic that requires every category to have at least one
     member.  That is equivalent to forbidding any sentence of
     the form ~(Ex)P(X).  That makes it impossible to state
     certain true sentences (e.g., "There are no unicorns").    (09)

  2. I think that the problematical issue is the phrase
     'ontological commitment'.  When you say (Ex)P(x), you're
     not just making an ontological commitment, you're making
     an assertion.  The commitment is not the result of the
     logic, it's the result of the assertion.    (010)

  3. When Aristotle assumed that every category had at least
     one element, he forced a type A sentence, such as
     'All Greeks are mortal' to assert the equivalent of
     (Ax)(Greek(x) -> Mortal(x)) & (Ey)Greek(y).    (011)

  4. That implies that Aristotle's logic made a stronger
     ontological commitment than modern FOL.  But is that
     a good idea?    (012)

  5. For example, the category PassengerPigeon once included
     millions of birds, but today they're extinct.  Does that
     mean that general assertions about passenger pigeons,
     which were formally acceptable, shall no longer be stated?    (013)

John    (014)

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