On Feb 18, 5:43 am, Jason Resch <jasonre...@gmail.com> wrote:
> On Thu, Feb 17, 2011 at 7:49 PM, Stephen Paul King
> > Hi All,
> > Question: Why must Platonia exist?
> How many ways are there to arrange 4 people in a line? If you think the
> answer 24 is true, regardless of any assumptions of axioms or set theory,
> etc. then truth has an objective, eternal, causeless existence of its own.
> These truths and falsehoods define or depend on the existence of other
> abstract objects, propositions, theoreticals, etc.
That mathematical truth is eternal, fixed etc, does not mean it ha
any existence at all, and can be explained by mathematics being non-
Platonism gets its force from noting the robustness and fixity of
mathematical truths, which are often described as "eternal". The
reasoning seems to be that if the truth of a statement is fixed, it
must be fixed by something external to itself. In other words,
mathematical truths msut be discovered, because if they were made they
could have be made differently, and so would not be fixed and eternal.
But there is no reason to think that these two metaphors
--"discovering" and "making"-- are the only options. Perhaps the modus
operandi of mathematics is unique; perhaps it combines the fixed
objectivity of discovering a physical fact about the external world
whilst being nonetheless an internal, non-empirical activity. The
Platonic thesis seems more obvious than it should because of an
ambiguity in the word "objective". Objective truths may be defined
ontologically as truths about real-world objects. Objective truths may
also be defined epistemically as truths that do not depend on the
whims or preferences of the speaker (unlike statements about the best
movie of flavour of ice-cream). Statements that are objective in the
ontological sense tend to be objective in the epistemic sense, but
that does not mean that all statements that are objective in the
epistemic sense need be objective in the ontological sense. They may
fail to depend on individual whims and preferences without depending
on anything external to the mind.
We are able to answer questions about mathematical objects in a clear
and unambiguous way, but that does not mean mathematical objects are
clear and unambiguous things. Being able to answer questions is
essentially epistemic. It doesn't imply any ontology in itself. The
epistemic fact that we can , in principle, answer questions about real
people may be explained by the existence and perceptual accessibility
of real people: but our ability to answer questions about mathematical
objects is explained by the existence of clear definitions and rules
doen't need to posit of existing immaterial numbers (plus some mode of
quasi-perceptual access to them).
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