[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

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QUIPS.  Discussion Note 42

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JA = Jon Awbrey
JW = Jim Willgoose

Re: QUIPS-DIS 40.  http://stderr.org/pipermail/inquiry/2005-May/002730.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

JW: You say:

JA: Now, some people get bent out of shape if I enumerate a collection
    of k-tuples as the extension of a relative concept, but it remains
    a plain fact that Peirce used these sorts of concrete exemplitudes
    to analyze such concepts in the most effective and exacting detail.

JW: I do not and I agree.  Yet the existence of abstract objects for
    Peirce is quite another question.  A mere chapter title given for
    a book prospectus hardly counts as evidence of Platonism.  (The
    prospective book was the "The Principles of Mathematics" c. 1893,
    the chapter was titled "Plato's World:  An Elucidation of the Modern
    Ideas of Mathematics")  This could be construed as a rhetorical move
    to influence the conservative prejudices of the publisher.  Far more
    relevant is the discussion of "existence" in the usual expression
    common to mathematicians of the day;  "there is an x such that ..."
    One passage in particular comes to mind in which Peirce dismisses the
    expression as non-literal with respect to objects (such as k-tuples).
    I will try to find it in CP.  There are  plenty of other passages that
    could lead one to conclude he is a fictionalist (much like a poet whose
    ideas may or may not bear much resemblance to the world of existence)
    On the other hand, the algebra of logic has for its objects the "true"
    and the "false".  That bears a striking resemblance to Frege.  Go figure.

Jim,

The plain fact is that practicing mathematicians are all in their
waking and sleeping life platonic realists of the most naive sort.
It is simply not possible to keep up the fiction that numbers are
fictions and not go bonkers.  The distinction between numbers as
objects and numerals as symbols is critical to understanding the
subject -- it begins with numbers and comes round to your soul,
as Pythagoras eternally suspected.  The only non-literal thing
about the quantifier "for some", when read as "there exists",
is the illusion that it's some kind of 'fiat lux', but this
delusion of grandeur is far more prevalent among logicists
than mathematicians.

Jon Awbrey

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