Gary f. , list
De Tienne slide 23 starts with: "BECAUSE mathematics, in principle, is
not concerned with anything but itself. The world could stop existing,
but to pure mathematicians that would at most be an inconvenience."
This is clearly a blunder since if the world stopped existing, there
would no more exist mathematicians at all, neither pure nor applied.
It is repeated in slide 24 that you published today: "The significance
and truth-value of such constructs [those of mathematicians] depends
only on their *internal* inferential coherence, *not on the world of
experience*."
Writing such a definitive judgment is just ignoring the every day work
of mathematicians who pass their time in diverses *experiments* with
forms, abstracts figures, models, constructs, etc., not to speak of the
value of their underlying hypotheses.
The slide 23 blunder that you minimize as "a choice of language" is
certainly a good rhetorical trick to get the laughs on one's side. But
this is not a valid scientific argument. And since it will be repeated
in the following slide, it has an intended purpose: to show that pure
mathematics are internally coherent wild dreams cut off the world.
In fact I think that the human ancestors of mathematics were those
prehistoric people who managed to figure out on the walls of their caves
the drawings of savage animals.
I wish that at the end of this slow reading you will undertake the
phaneroscopic observations of mathematicians at work, without any
prejudice as Peirce suggested it.
Bernard Morand
Le 10/08/2021 à 16:09, g...@gnusystems.ca a écrit :
Bernard, thank you for a thoughtful post (and thanks to Jon S for an
equally thoughtful reply to it). I especially appreciate your tacit
acknowledgement of the emotional basis of your own response to De
Tienne’s choice of language at “the starting point in slide 23.” But
my own response will be limited to this part of your post:
BM: By pointing at the opposition egocentrism / world existence, De
Tienne is repeating the well known duality between abstract and
concrete, imaginary and existence. BTW Marty is entitled to see it as
excluding mathematics out of a scientific realm that will end confined
into the experimental sciences. I don't think that such a project can
be qualified as peircian.
GF: Of course Marty is entitled to carry on his crusade against a
putative attempt (by De Tienne and other scholars) to “exclude
mathematics” from science and from a Peircean understanding of it. He
is also “entitled” to attribute malicious intent to anyone who does
not sign on to his crusade, even to those who simply ignore it. But in
my opinion, the rest of us are no less entitled to ignore it as simply
irrelevant to what De Tienne is saying about phaneroscopy, and to
maintain a focus on the actual content of his slides.
After a few attempts to communicate with Robert on a reasonable basis,
which I soon realized were futile, I have simply turned my limited
attention elsewhere. Frankly, given a choice to spend my time reading
Marty or reading Peirce, I will choose Peirce every time. Robert is
entitled to carry on his crusade as long as he likes, and others are
entitled to give it the attention they think it deserves. As for me, I
have nothing to say about it that hasn’t been said already.
Turning back to the “slow read,” I might point out that it is about
/phaneroscopy/, including its non-reciprocal dependence on mathematics
for abstract principles. The fact that nearly all sciences call upon
mathematics for principles under which to organize their observations
is /taken for granted/ in De Tienne’s talk, as it is too obvious to be
made a focal point in a discussion of phaneroscopy. Robert and his
fellow crusaders naturally interpret this taking-for-granted as a
/denial/ of the importance of mathematics, and insist on reading this
denial into De Tienne’s explicit text, regardless of what it actually
says in its context. As we have seen, questioning this style of
interpretation only leads to more unfounded accusations of malicious
intent and various intellectual sins. Consequently I feel entitled to
say nothing further about the whole crusade, which I consider a
distraction from more relevant issues. In fact I’m already regretting
giving so much time and thought to it in this post. Enough already.
Gary f.
*From:*Bernard Morand <morand.bern...@neuf.fr>
*Sent:* 9-Aug-21 12:02
Gary f., list
I think that the matter is much less simple than your way of stating
it. In my opinion the discussion would gain in clarity by
distinguishing 3 subjects.
First, the nature of mathematics qua science (as distinct from men who
make it ), the definition of which by Robert Marty seems to me correct
: " the exact study of idealized forms"
Second, the methods and reasonings in use in this discipline :
"drawing necessary conclusions about hypothetical states of things"
(being understood that "hypothetical" doesn't mean "not existing" nor
irreal. Can we say that the number theory is just an hypothetical
construct ?)
Third, the place and role of mathematics in some given classification
of sciences. In the actual dicussion, it is the question of the
relationship between mathematics and phaneroscopy, a relationship that
can be seen as a dependance from the one to the other, but it counts
only for the classification aspect. If phaneroscopy seems to depend
logically from mathematics for its principles, it does not entail that
mathematics cannot be feeded by the findings of phaneroscopy.
This last point makes me refuse since the beginning the starting point
in slide 23 ; "BECAUSE mathematics, in principle, is not concerned
with anything but itself. The world could stop existing, but to pure
mathematicians that would at most be an inconvenience."
By pointing at the opposition egocentrism / world existence, De Tienne
is repeating the well known duality between abstract and concrete,
imaginary and existence. BTW Marty is entitled to see it as excluding
mathematics out of a scientific realm that will end confined into the
experimental sciences. I don't think that such a project can be
qualified as peircian.
We have to hold together three elements : the Real, the Symbolic and
the Imaginary. It is a much more difficult task but it permits to ask
the question : how does a purely abstract science can partake its own
form discoveries with the experimental sciences ? It seems to me that
the concept of isomorphism that does not claim a community of contents
but a resemblance of forms is a good candidate by focusing on the
peircian property of iconicity.
Regards
Bernard Morand
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