Thanks for your reply.
On Fri, Sep 7, 2012 at 11:19 PM, meekerdb <meeke...@verizon.net> wrote:
> On 9/7/2012 8:43 PM, Jason Resch wrote:
>> Platonism (or mathematical realism) is the majority viewpoint of modern
> In a survey of mathematicians I know it is an even division. Of course
> they are all methodological Platonists, but not necessarily philosophical
That is interesting. Among the non-platonists, what schools of thought did
you find most popular?
> Computationalism (or functionalism) is the majority viewpoint of
>> cognitive scientists and philosophers of mind. Thus the scientific
>> consensus is that infinite (mathematical) truth
> Except mathematical truth is just a marker, T, whose value is preserved by
> the rules of logic. Whether a proposition that has T corresponds with any
> fact is another question.
Functionalism maintains that so long as the same relations are preserved,
whether they be relations between neurons, silicon circuits, ping pong
balls, objects in other possible universes, objects in a mathematical
structure, or the integers themselves, the same brain state will result.
If one subscribes to Platonism, then there exist mathematical objects that
possess the same relations that exist in our brains, and if one subscribes
to functionalism, these platonic instances of our brains would not be
zombies but fully conscious.
> is the self-existent cause and reason for our existence.
> That is very far from a scientific consensus.
I agree, few realize it. Not many mathematicians are also philosophers of
mind, but does it not follow from platonism+functionalism?
> I'd say majority the opinion among scientists who are philosophically
> inclined is that mathematics and logic are languages in which we create
> models that represent what we think about reality.
Perhaps, but this wouldn't be platonism, Many scientists probably are
unaware that that formalism failed and that mathematical truth transcends
any description, which is why it is better to look at the consensus of
domain experts. A biologist probably isn't the best person to ask about
whether there is one universe or many.
> This explains why there can be contradictory mathematical models and even
> mutually inconsistent sets of axioms and rules of inference.
This is no different than the existence of contradictory and inconsistent
physical theories. We arrive at better axiomatic systems for explaining
truth about the numbers in the same way we arrive at better physical
theories for explaining truth of the natural world. Some turn out to be
more powerful, explain more, etc, and we stick with them until a better one
> Few people today have realized that this is inevitable conclusion of
>> these two commonly held beliefs.
> Not only that a few people have rejected it.
Sure, many people reject Bruno's UDA, but has anyone shown the error in its
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