On 7/29/2010 4:03 PM, Mark Buda wrote:
Agreed, but I would point out that the answer to the question of the existence of numbers is the truth value of a logical proposition about the ideas we call "number" and "existence".


What logical proposition would that be? A proposition like "Every number has a successor" or "2+2=4" don't say tell us anything about whether numbers exist. Truth values in logic are just arbitrary assignments of T to some propositions (axioms) and F to others (contradictions). The are not evidence of existence.

And if you bring a definition of number in terms of other ideas such as "successor", then you are simply restating the logical propositions in terms of other ideas.

Most logical propositions about what we usually call reality are meaningless. Those that are meaningful are those that have to do, ultimately, with your present perceptions and set of beliefs about the universe.

But those aren't specifically *logical* propositions. The kind of truth value that attaches to them is epistemological. In fact you'll notice that if you ask a scientist whether some statement about the world is true he's likely to give you a litany of evidence with qualifications, rather than a 'yes' or 'no'.

As such, their truth value depends on who you are and what you choose to do.

I don't know what you mean by that, but I would agree that knowledge and meaning propositions is ultimately grounded in actions or at least potential actions.

Brent

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Mark Buda <her...@acm.org <mailto:her...@acm.org>>
I get my monkeys for nothing and my chimps for free.


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On Jul 29, 2010 6:36 PM, Brent Meeker <meeke...@dslextreme.com> wrote:
I don't think the existence of some number of distinct things is the same as the "existence" of numbers. Numbers are defined by order and successor - neither of which are present or implicit in a mere collection of atoms or anything else.

Brent
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