Stan, list,
The main idea is not that of a long run. Instead the idea is that of
sufficient investigation. Call it 'sufficiently long' or 'sufficiently
far-reaching' or 'sufficiently deep' or 'sufficiently good' or
'sufficiently good for long enough', or the like, it's stlll the same
basic idea.
If in a given case you believe that you've reached the truth about a
given kind of phenomenon after five minutes of investigation, then you
believe that you have reached, after five minutes, the opinion that
anybody sufficiently investigating, over whatever length of time, would
reach about that kind of phenomenon. It's far from automatically
preposterous to believe that.
There is no absolute assurance that actual inquiry on a given question
will not go wrong for millions of years, remaining insufficient for
millions of years and leaving the actual inquirers not only ignorant but
also erroneous all along the way. But fallibilism implies not that the
objects or findings of inquiry are unreal and mere figments, but only
that they may be unreal and figments, insofar as the real does not
depend on what any actual inquirers think of it. On the other hand, do
you really believe that there are no cases where we've reached truths
about general characters of things, done good statistical studies on the
distributions of such characters, and so on?
The idea that we can succeed in inquiry does not drive us to the idea
that we can't fail in it. Peirce was both a fallibilist and, to coin a
word, a successibilist (he opposed radical skepticism and held that the
real is the cognizable). Peirce took these ideas as presuppositions to
reasoning in general and shaping scientific method. He regarded such
presuppositions as collectively taking on the aspect of hopes which, in
practice, we hardly can doubt. Really, one can reasonably believe that
sharks have a general character without knowing a great deal about
sharks. They would be like other kinds of things where investigation
revealed only over time certain definite characters common to members of
a kind, some of which characters also distinguish the kind, the
characters together parts of a complex character called the general
nature of the kind.
Best, Ben
On 9/20/2014 10:03 AM, Stanley N Salthe wrote:
Ben -- You asserted
>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.
Regarding suppositions about actual phenomena -- like, say, the nature
of sharks -- since 'the long run' is NOT now, how can we know which
version from different cultures is 'real'? This is the basic reason
one must be a nominalist.
STAN
On Fri, Sep 19, 2014 at 10:31 PM, Benjamin Udell wrote:
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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