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Re: [ontolog-forum] A Question About Logic

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Wed, 28 Oct 2015 09:52:26 -0400
Message-id: <5630D31A.1010602@xxxxxxxxxxx>
On 10/28/2015 3:57 AM, rrovetto@xxxxxxxxxxx wrote:
> You wrote: (c) (p implies q) cannot be observed, as Hume discussed
> at length... some logicians would explicitly say implication has
> nothing to do with causation, but rather is a relation between
> statements, propositions, or arguments and is related to validity, etc.
> They would say that material implication, for example, is not the
> causation relation.    (01)

I admit that I should have added a few more words of clarification:    (02)

  1. Hume was emphasizing issues of causation, which is an important
     use, but only one of many uses for if-then statements.    (03)

  2. Material implication, as it is used in first-order logic, does
     not depend on causation.  More generally, FOL is a purely
     mathematical theory that relates highly stylized sentences
     to formal, set-theoretical models.  No observation of anything
     (other than diagrams of those models) is required to justify FOL.    (04)

  3. But I would add that most (perhaps all) applications of if-then
     statements to observable phenomena involve some assumption about
     a law-like connection between the antecedent and consequent.    (05)

  4. Those law-like connections cannot be observed in the phenomena.
     They follow from some previous assumptions about nature (i.e.,
     physical laws) or about human behavior (i.e., deontic laws).    (06)

  5. In support of point #4, note that explanations of the use
     of if-then often involve the word 'because', which suggests
     the similarities between law-like interpretations of social
     phenomena and physical phenomena.    (07)

  6. The law-like nature of if-then sentences in ordinary language
     are related to modal words like 'must' and 'should', which are
     also used in explanations of if-then sentences.  In modal logics,
     those words are represented by operators that express necessity
     or obligation -- both of which depend on laws of some kind.    (08)

For an analysis of the relationships between laws and modality,
see http://www.jfsowa.com/pubs/worlds.pdf    (09)

John    (010)

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