Howard, lists,
Epistemologies are not claims about special concrete phenomena in the
sense that they and their deductively implied conclusions would be
directly testable for falsity by special concrete experiments or
experiences. That's also true of principles of statistics and of
statistical inference, yet such principles are not generally regarded as
requiring a leap of faith. Mathematics is also not directly testable by
special concrete experiments, yet mathematics, whether as theory or
language, is not generally regarded as requiring a leap of faith. What
mathematics requires is leaps of transformational imagination in
honoring agreements (hypothetical assumptions) as binding. Two dots in
the imagination are as good an example of two things as any two physical
objects - better, even, since more amenable for mathematical study. Some
sets of mathematical assumptions are nontrivial and lead inexorably,
deductively, to nontrivial conclusions which compel the reasoner. If you
think that mathematics is _/merely/_ symbols, still that's to admit that
mathematical symbols form structures that, by their transformabilities,
model possibilities.
Contrary to your claim, physical laws are not physical forces and do not
depend like forces on time and rates. Instead physical laws _/are/_
those dependences on time and rates and are expressed mathematically,
which is to say that some mathematics is instantiated in the actual,
although you think that mathematical limit ideas of absolute continuity
and absolute discreteness should be instantiated like photons, rocks,
trees, or Socrates in order for mathematics to be real. But "real" in a
Peircean context just means capable of being objectively investigated
such that various intelligences would converge sooner or later, but
still inevitably, on the same conclusions, rather than on some set of
mutually incompatible conclusions. You think that some sort of
dynamicism is a safer and more skeptical bet than realism about generals
and modalities. But the idea that varied intelligences will not tend
toward agreement about mathematical conclusions is no safe bet.
So the question is, again, do you think that numbers can be objectively
investigated as numbers? - such that (individually, biologically, etc.)
various intelligences, proceeding from the same assumptions, would reach
the same conclusions. If you do think so, then you are a nominalist or
anti-realist in name only.
*One man, two votes,
for Dominic Frontiere*
Rigid bodies, and incompletely but sufficiently rigid bodies, although
able to go through transformations that leave them, e.g., rotated 180
degrees, and so on, still cannot change their chirality or handedness in
that manner (except in an eldritch elder Outer Limits episode).
Opposite-handed but otherwise equivalent objects conform to the
mathematics of their mirror-style equivalence as inexorably as a dynamic
process follows dynamic laws. Phenomenologically, forces are like
sheriffs enforcing the physical laws. Yet there are mathematical rules
that physical phenomena respect without forces pushing one around when
one attempts to defy them, such as the lack of a non-deformative
continuous transformation into a chiral opposite. Sometimes mathematics
rules by 'smart power'.
The idea that mathematics' real end is to help physics, with which your
wording suggests agreement, was put forth by some positivists, one of
whom went so far as to say that mathematicians who thought themselves to
have some other or broader purpose should discount their subjective
feelings about it as merely illusory and due to their choice of profession.
I could go on, but the question is, do you think that numbers can be
objectively investigated as numbers? If so, then you are a nominalist or
anti-realist in name only, and a realist in the Peircean sense. If not,
then you do not believe that there is a reliable mathematical expression
of physical phenomena.
Best, Ben
On 9/18/2014 11:42 PM, Howard Pattee wrote:
At 10:39 AM 9/18/2014, Benjamin wrote:
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.
HP: I agree. These are all fields in which humans make models of their
experiences. They may agree on their models but still disagree on
different epistemologies, realism, nominalism, eliminative
materialism, and so on. These epistemologies are /interpretations / of
their models with respect to what they believe exists or what they
believe is real.
Epistemologies are not empirically decidable, e.g., not falsifiable.
True belief in any epistemology requires a leap of faith. There are
degrees of faith, skepticism being at the low end. In my own view as a
physicist, nominalism requires a much safer leap of faith than
realism. However, I often think realistically. I see no harm in it as
long as I don't see it as the one true belief.
BU: Being alive, instantiating life, is far from enough to do
biology. Instantiating mathematical structure is far from enough to
do mathematics.
HP: Again, I agree. That does not mean that "doing math" is the same
as "doing physics". Mathematics is the best /language/ that we use to
describe physical laws. There is an inexorability in physical laws
that does not exist in the great variety of mathematical concepts and
rules.
> [HP] No one has discovered a point or a triangle or a number,
the infinite or the infinitesimal, in Nature
BU: 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.
HP: Here I disagree. You are not distinguishing mathematical /rules/
from physical /laws/ . Mathematics provides the most exact /symbolic
language/ in which the laws are described. Symbolic rules are not like
physical material forces. Specifically, laws are inexorably time and
rate-dependent. Logic and mathematics do not involve time and rates.
That is why I say that "only humans do mathematics" (manipulate
symbols), which they do at their own rates. Humans cannot "do forces
and laws". Forces act at the lawful rates whether we like it or not.
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.
HP: I do not understand. What I call real depends only on my epistemic
assumptions, and I am not at all sure that defining "real" is
important to have a good model. What we need to understand is what
Wigner called the "unreasonable effectiveness" of our mathematics in
describing laws. There is no good reason for this effectiveness.
Wigner quotes** Peirce: " . . . and it is probable that there is some
secret here which remains to be discovered."
Peirce, as a chemist (1887) also agreed with Hertz's epistemology (1884):
“The result that the chemist /observes/ is brought about by/nature/
[Hertz: “the image of the consequents of nature”]; the result that the
mathematician observes is brought about by the associations of
the/mind/ . [Hertz: “consequents of images in the mind”] . . . the
power that connects the conditions of the mathematicians diagram with
the relations he /observes/ in it is just as occult and mysterious to
us as the power of Nature that brings about the results of the
chemical experiment." [W:6, 37, Letter to Noble on the Nature of
Reasoning, May 28, 1987. (1897)]
Hertz: "As a matter of fact, we do not know, nor have we any means of
knowing, whether our conception of things are in conformity with them
in any other than this /one/ fundamental respect [Peirce's "power that
connects"].
Howard
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