Howard, Frederik, lists,
Howard, is your objection is to using the decidedly adjectival "real" to
describe something other than a concrete individual object, this man,
this horse? Would you allow an adverb? Then you could say that Earth and
Mars are really two planets, and their twoness has really-ness in
respect of planetness. But ordinary language makes little accommodation
for that kind of talk. We would still end up saying 'reality' to cover
the ideas of 'realness,' 'really-ness', etc.
You wrote,
> [HP] The evidence I know is that only human brains (and their
artifacts) actually do mathematics. I have no evidence that
inanimate nature does even simple mathematics.
Only humans (at least here on Earth) do sociology, psychology, biology,
chemistry, or physics. I have no evidence that elementary nature does
even simple physics, or even wears a lab coat.
Being alive, instantiating life, is far from enough to do biology.
Instantiating mathematical structure is far from enough to do mathematics.
> [HP] No one has discovered a point or a triangle or a number, the
infinite or the infinitesimal, in Nature
In your sense, nobody has discovered a physical law in nature either.
Rules, constraints, norms, distributions, etc., are not animals,
vegetables, minerals, or particles. Therefore by your standards they are
not real. By saying that X is "real," Peirce means that X is objectively
investigable as X. You won't use the word "real" in that way.
But do you think that numbers can be objectively investigated as numbers?
Best, Ben
On 9/18/2014 8:30 AM, Howard Pattee wrote:
At 12:07 PM 9/17/2014, Frederik wrote:
I think it follows from these observations [that MRI scans require
mathematics] that it is a preposterous claim to say that mathematics
is the study of neurological structures - or that mathematics could,
in any way, be reduced to neuropsychology.
HP: I agree that there are too many MRI papers, and that MRI images by
themselves explain nothing. But also logic by itself explains nothing.
I'll repeat my point that, like other primitive concepts,
/understanding mathematics requires complementary models./ What is
preposterous is to claim that any one view of the Foundations of
Mathematics <http://en.wikipedia.org/wiki/Foundations_of_mathematics>
is the only non-preposterous view. Preposterous views in physics are
common, but accepted only if supported by experimental evidence. The
evidence I know is that only human brains (and their artifacts)
actually do mathematics. I have no evidence that inanimate nature does
even simple mathematics.
Human math began with geometry and numbers. No one has discovered a
point or a triangle or a number, the infinite or the infinitesimal, in
Nature. >From Zeno and Aristotle (“That which moves does not move by
counting”) to Cantor and Dedekind, discreteness and continuity have
been impossible to combine in one logical model. Peirce spent many
years trying to describe precisely how points could form a continuous
line. Like Aristotle, he concluded that they couldn’t.
We now believe(from MRI images) that concepts of discrete objects,
like points, and concepts of continuous motions and structures, like
lines, are formed in different regions of the brain, or at least by
different neural codes. It all began 400 million years ago when the
earliest sensorimotor controls based on vision required brains to
distinguish discrete objects from their continuous motions.
Howard
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