[Inquiry] Models and Morphisms

Jon Awbrey jawbrey at att.net
Wed Aug 1 21:00:09 CDT 2007


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M&M.  Note 4

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JA = Jon Awbrey
JS = John Sowa

JS: http://ontolog.cim3.net/forum/ontolog-forum/2007-07/msg00083.html

JA: This is all true, well enough, but it always helps me to realize
    that some people I know (logicians, model theorists) use "model"
    to mean anything that satisfies a theory, whether it be a formal
    construct that we make out of sticks and strings or another sort
    of thing in the world, while other people I know (engineers and
    applied mathematicians) use "model" to mean an analogue model
    or the target of a morphism, in semiotic terms, an icon of
    the object being modeled.  These senses of the word are
    not the same but they are perfectly compatible.

JA: Taking all that into account, it still makes sense to say that
    a theory is "true of" the syntactic constructs that the model
    theorist constructs and also "true of" other sorts of things
    in the world.  The theory picks out only those properties
    that the object and its icon share, which sharing is
    just what makes the icon an icon of its object.

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