Rick, (01)
You have to distinguish nominalism as a mathematical exercise
from nominalism as metaphysics. (02)
For example, an extreme nominalism would say that the so-called
laws of nature are just statistical summaries of observations,
and there is no reason to expect them to be violated at the
next observation. (03)
But most physicists believe that a law like F=ma reflects some
reality that is independent of our existence or observation.
They readily admit that any particular statement of the law,
such as a Newtonian version, might be replaced by a more
general law, such as an Einsteinian version or a quantum
mechanical version or whatever. (04)
But they would still claim that the reality that supports F=ma
is still just as real as it ever was. The Newtonian version is
quite adequate for describing the kind of reality we encounter
while driving a car, even though it might require some adjustments
for extremely large or small cases. (05)
So in that case, even something as abstract as an equation
like F=ma corresponds to some kind of reality. (06)
On 9/22/2010 9:23 PM, Rick Murphy wrote:
> On Wed, 2010-09-22 at 08:59 -0400, John F. Sowa wrote:
>> > On 9/21/2010 10:32 PM, Rick Murphy wrote:
>>> > > Do you Doug, or others here, actually believe in the existence of
>>> > > objects that are not material? Do you believe that abstract objects
>>> > > exist? What about non-existent objects? There's no shortage of papers
>>> > > that make these claims. Here are two: [1], [2].
>> >
>> > Whenever anybody raises such issues, I recommend a short transcript
>> > of a lecture that Alonzo Church presented at Harvard -- specifically
>> > for the purpose of annoying Quine:
> Funny, I hope there were constructivists in the audience. (07)
First of all, the use of mathematical constructions is not
a criterion for distinguishing nominalists from other kinds
of metaphysicians. (08)
For example, sets are abstract objects, and the empty set is an
extremely non-intuitive kind of abstract object. (Anybody who has
taught introductory set theory knows how much confusion is caused
by the empty set.) (09)
But many constructivists are happy to construct so-called "distinct
individuals" represented by {}, {{}}, {{},{}}, {{{},{}},{{},{}}}, etc.
Anybody who lets existential quantifiers range over such things has
an ontology that only looks parsimonious. (010)
John (011)
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