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
--
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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