Dear Brian,

"can be defined ..." implies the necessary existence of something or process or whatever that does the act of defining the set. Truth values do not do this, btw. Sets are collections defined in terms of functions, but numbers in-themselves are not those functions.. Unless you are considering some other ideas of what sets are... If we are going to think of set as having ontological primacy we have to have a notion of a set that does not need a membership function.

On 9/6/2012 10:28 AM, Brian Tenneson wrote:
All numbers can be defined in terms of sets.  The question becomes this:
do sets have ontological primacy relative to mankind or are sets invented or created by mankind?

On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough < <>> wrote:

    Hi Stephen P. King
    Yes, of course, but I wanted a more obvious, dramatic example.
    The philosophy of mathematics says something like the numbers
    belong to a static or eternal world, change itself  is a property
    of geometry.
    Numbers and geometry thus belong to the platonic world,
    which is forbidden or at least not consistent with the philosophy
    of materialism, IMHO.
    If numbers are platonic, I wonder what the  presumably materialist
    Steven Hawkings has to say about their origin in his recent
    book on numbers.
    Roger Clough, <>
    Leibniz would say, "If there's no God, we'd have to invent him
    so that everything could function."

        ----- Receiving the following content -----
        *From:* Stephen P. King <>
        *Receiver:* everything-list
        *Time:* 2012-09-06, 07:53:18
        *Subject:* Re: Could we have invented the prime numbers ?

        Dear Roger,

            Could the mere possibility of being a number (without the
        specificity of which one) be considered to be "there from the



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