Re: [PEIRCE-L] André De Tienne: Slow Read slide 23

[Edwina Taborsky]

 

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}Robert, List

Thank you for this clarification of the role of mathematics.

1] I find that De Tienne's slide 23 is troubling. Note how his five
paragraphs, which include an example of a mathematician, seem geared
to show the alienation of mathematics [and mathematicians] from the
real world.

De Tienne sets up mathematics as essentially irrelevant to us who
live in the real world. One has to ask: What's the point of doing
mathematics? He has given us the image of an isolate almost insane
mathematician, so engrossed in his own internal voices that he is
killed by the Real World [a Roman soldier]. Therefore one has to ask:
why did Peirce put mathematics in the foreround?

And we can see that answer in the quotations ignored by De Tienne. 
Robert gave us this one:

>1895 [c.] | On the Logic of Quantity, and especially of Infinity |
MS [R] 16:1

Mathematics may be defined as the study of the substance of exact
hypotheses. It comprehends
 1st, the framing of hypotheses, and
  2nd, the deduction of their consequences.
2] Note how mathematics is explained as an action. It is the action
of developing hypotheses! And then, examining the necessary results.
That's the function of mathematics: and what are some examples given
by Peirce? Not someone alienated from the real world - and after all
- can De Tienne really prove that Archimedes' death was due to his
'contemplation of a diagram'? 

But, what if we continue on with the selection offered by De Tienne
as his fourth paragraph - a selection of which he chose to leave out
the whole substance of what Peirce was writing: 1.646

"The host of men who achieve the bulk of each year's new discoveries
are mostly confined to narrow ranges. For that reason you would expect
the arbitrary hypotheses of the different mathematicians to shoot out
in every direction into the boundless void of arbitrariness. But you
do not find any such thing. On the contrary what you find is that men
working in fields as remote from one another as the African diamond
fields are from the Klondike reproduce the same forms of novel
hypothesis. Rieman had apparently never heard of his contemporary
Listing. The latter was a naturalistic geometer, occupied with the
shapes of leaves and birds' nests, while the former was working upon
analytical functions. And yet that which seems the most arbitrary in
the ideas created by the two men are one and the same form. This
phenomenon is not an isolated one; it characterizes the mathematics
of our times, as is, indeed, well known ...'The end that pure
mathematics is pursuing is to discover that real potential world".
[1.646]

And that is the substance of mathematics: developing hypotheses and
tracing their consequences.. And note - these examples are not of men
alienated from the real world but deeply involved in reasoning about
and attempting to explain it. As Peirce outlines in 1.641-645, this
'march of discovery [1.640] is not to be merged with 'practical
utilities'.  He writes that "the two masters, theory and practice,
you cannot serve" [1.642]. This, I suggest, is what he means by his
comments that 'the scientific man is not in the least wedded to his
conclusions" 1.635]. And his statements  that the mathematician does
not 'care a straw' to 'inquire into the truth of that postulate' and
was only focused on that deduction of their consequences. 

I suggest that this outline of mathematics as the development of
hypotheses - and tracing out their consequences does not mean, as De
Tienne seems to imply, an activity alienated from and irrelevant to
the Real World. Indeed, Peirce's outline seems instead to tell us
that mathematics offers us the basic means of 'discovering the real
potential world'.

Edwina
 On Sun 08/08/21  5:28 PM , robert marty robert.mart...@gmail.com
sent:
1-I have already pointed out in the Podium, Section 3:   Peirce, an
architectonic philosopher (p. 8), how much André De Tienne tried to
minimize the role of mathematics in scientific discovery and
particularly in phaneroscopy. Here are two significant extracts: 
1.1 "…after having acclaimed mathematics as "queen of all
sciences," he immediately sends mathematicians (and with them
mathematics) back to confinement in their own field: 'But the moment
inquiry turns the barest of attention to the conditions that give
experience its earthly flavor; the moment inquiry acquires a vested
interest in a realm of being purely detached mathematicians are not
concerned with, that of positive experience.'" (De Tienne. 2004:
1)[emphasize mine] 
1.2 "Both [Mathematics and phaneroscopy] are acritical since both
refrain from making assertions about the object of their
investigation; mathematics only draw consequences out of initial
hypotheses, while phaneroscopy only describes what self-presents."
(De Tienne, 

Re: [PEIRCE-L] André De Tienne: Slow Read slide 23

[Jon Alan Schmidt]

Robert, List:

I sincerely appreciate the correction of the excerpt from CP 1.53 (c.
1896). It is surprising and indeed troubling that André would insert his
own words where he is purportedly quoting Peirce. My first thought was that
perhaps the additional phrase was in the original manuscript and omitted
(inadvertently or otherwise) by the CP editors, which has happened in some
other places, but inspection of R 1288:7 confirms that it is not the case
here. As any examination of the List archives would amply demonstrate, I am
always eager to understand and convey Peirce's ideas accurately by
carefully citing and reproducing his actual texts.

For that very reason, I am also surprised that anyone would suggest that
when I provided a link to the Commens Dictionary entry for "mathematics," I
somehow "didn't read it well" and thus would find it problematic that
Peirce included the formulation of mathematical hypotheses within the scope
of a mathematician's practice. On the contrary, I have never disputed this,
I have merely insisted with Peirce that mathematics is the science which
draws necessary conclusions about those hypothetical states of things.
Moreover, as I pointed out in an off-List exchange several months ago, CP
3.559 is the central passage of an entire series of articles that I wrote
for my fellow structural engineers on "The Logic of Ingenuity" (
https://www.structuremag.org/?p=10490). Its last sentence provides an
excellent summary of the whole lengthy paragraph.

CSP: Thus, the mathematician does two very different things: namely, he
first frames a pure hypothesis stripped of all features which do not
concern the drawing of consequences from it, and this he does without
inquiring or caring whether it agrees with the actual facts or not; and,
secondly, he proceeds to draw necessary consequences from that hypothesis.
(CP 3.559, 1898)


Returning to the subject at hand, the mathematician's hypothesis is
different from the phaneroscopist's hypothesis. Because the mathematician's
method is strictly deductive, it can only be applied to an idealization
that has been "stripped of all features which do not concern the drawing of
[necessary] consequences from it." That is precisely why the mathematician
must proceed "without inquiring or caring whether it [the idealization]
agrees with the actual facts or not." By contrast, the phaneroscopist is
inquiring about the phaneron and thus cares very much whether a given
hypothesis agrees with what is being observed there. Consequently, although
mathematics is an indispensable aid to phaneroscopy, phaneroscopy is by no
means reducible to mathematics--just as mathematics is an indispensable aid
to *every *other science, but *none *of them is reducible to mathematics.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sun, Aug 8, 2021 at 4:29 PM robert marty 
wrote:

> *1*-I have already pointed out in the Podium,
> 
>  Section
> 3:  Peirce, an architectonic philosopher (p. 8), how much André De Tienne
> tried to minimize the role of mathematics in scientific discovery and
> particularly in phaneroscopy. Here are two significant extracts:
>
>
>
> *1.1* "…after having acclaimed mathematics as "*queen of all sciences*,"
> he immediately sends mathematicians (and with them mathematics) back to
> confinement in their own field: '*But the moment inquiry turns the barest
> of attention to the conditions that give experience its earthly flavor*;
> the* moment inquiry acquires a vested interest in a realm of being purely
> detached mathematicians are not concerned with, that of positive
> experience.'" *(De Tienne. 2004: 1)[emphasize mine]
>
>
>
> *1.2* "*Both* [Mathematics and phaneroscopy] *are acritical since both
> refrain from making assertions about the object of their investigation;
> mathematics **only** draw consequences out of initial hypotheses, while
> phaneroscopy only describes what self-presents**."* (De Tienne, 2004: 17)
> [emphasize mine].
>
> *2*- After the publication of my preprint, I discover, on the occasion of
> the slow read, that 17 years later, De Tienne affirms even more strongly
> his position in a presentation on the Peirce Edition Project website
> presented in Milford (April 2019), Milan (April 2021) and also in Tokyo. I
> find the same strategy of a strong tribute followed by an even less gentle
> exit. I notice slide 23 and particularly the quotation CP 1.53, which
> provokes in my mind a feeling that I translate into "it is not possible
> that Peirce wrote that!" I do as Saint Thomas who only believes what he
> sees, and I go and check in the Collected Papers and here it is:
>
>
>
> *CP 1.53** in COLLECTED PAPERS :*
>
> "The most abstract of all the sciences is mathematics. That this is so,
> has been made 

Re: [PEIRCE-L] André De Tienne : Slow Read Slide 23

[Jon Awbrey]

Dear Robert, List ...

The catch, of course, occurs in the qua-le-fication
“(qua mathematician)”, by which the writer abstracts
an idealization from the concrete realities of being,
as does the reader who subscribes to the quale-fiction.

Regards,

Jon

CP 1.53 in COLLECTED PAPERS :

“The most abstract of all the sciences is mathematics.
 That this is so, has been made manifest in our day;
 because all mathematicians now see clearly that
 mathematics is only busied about purely hypothetical
 questions.  As for what the truth of existence may
 be the mathematician does not (qua mathematician)
 care a straw.”


On 8/8/2021 5:28 PM, robert marty wrote:

*1*-I have already pointed out in the Podium,

Section
3:  Peirce, an architectonic philosopher (p. 8), how much André De Tienne
tried to minimize the role of mathematics in scientific discovery and
particularly in phaneroscopy. Here are two significant extracts:

*1.1* "…after having acclaimed mathematics as "*queen of all sciences*," he
immediately sends mathematicians (and with them mathematics) back to
confinement in their own field: '*But the moment inquiry turns the barest
of attention to the conditions that give experience its earthly flavor*; the*
moment inquiry acquires a vested interest in a realm of being purely
detached mathematicians are not concerned with, that of positive
experience.'" *(De Tienne. 2004: 1)[emphasize mine]

*1.2* "*Both* [Mathematics and phaneroscopy] *are acritical since both
refrain from making assertions about the object of their investigation;
mathematics **only** draw consequences out of initial hypotheses, while
phaneroscopy only describes what self-presents**."* (De Tienne, 2004: 17)
[emphasize mine].

*2*- After the publication of my preprint, I discover, on the occasion of
the slow read, that 17 years later, De Tienne affirms even more strongly
his position in a presentation on the Peirce Edition Project website
presented in Milford (April 2019), Milan (April 2021) and also in Tokyo. I
find the same strategy of a strong tribute followed by an even less gentle
exit. I notice slide 23 and particularly the quotation CP 1.53, which
provokes in my mind a feeling that I translate into "it is not possible
that Peirce wrote that!" I do as Saint Thomas who only believes what he
sees, and I go and check in the Collected Papers and here it is:

*CP 1.53** in COLLECTED PAPERS :*

"The most abstract of all the sciences is mathematics. That this is so, has
been made manifest in our day; because all mathematicians now see clearly
that *mathematics is only busied about purely hypothetical questions. As
for what the truth of existence may be the mathematician does not (qua
mathematician) care a straw."*

(I highlight the part of 1.53 concerned by slide 23)

*CP 1.53** in *SLIDE 23 :

"Mathematics is only busied about *purely hypothetical questions*, *tracing
out the consequences of hypotheses*. As for what the truth of existence may
be the mathematician does not (qua mathematician) care a straw" (CP 1.53)

I note the insertion of the subordinate proposition:

"* tracing out the consequences of hypotheses*.*"*

*3*- We can therefore see that André De Tienne has modified Peirce's
quotation. This statement illustrates a little more the determination of De
Tienne to hide the role and the function of Mathematics in its relations
with the phaneroscopy according to Peirce.

*4*- In addition, I recall that Jon Alan, in support of this viewpoint,
argued "that it was found nearly two dozen different quotations" in
http://www.commens.org/dictionary/term/mathematics.

He didn't read it well because it includes:

*   4.1* The most blunt:


1897 [c.] | On Multitude | MS [R] 26:1


Mathematics is a study of exact hypotheses, in so far as consequences can
be deduced from them. *To limit mathematics to the deduction of those
consequences would be to separate from it some of the greatest of the
achievements of modern mathematicians*, – achievements which nobody but
mathematicians could have performed, – such as the formation of the idea of
the *system of imaginarie*s, and of the idea of *Riemann surfaces**. It
must be allowed, therefore, that the formation of the hypotheses is a part
of the business of mathematics.*

*4.2* And a few others

*> *1895 [c.] | On Quantity, with special reference to Collectional and
Mathematical Infinity | MS [R] 14:4

Mathematics is the study of the substance of hypotheses *with a view to*
the tracing of necessary conclusions from them.

*>*1895 [c.] | On the Logic of Quantity, and especially of Infinity | MS
[R] 16:1

Mathematics may be defined as the study of the substance of exact
hypotheses. It comprehends
*1st, the framing of hypotheses*, and
2nd, the deduction of their consequences. [emphasize mine]

*>*1895 [c.] | Elements of Mathematics | NEM 2:10

… the mathematicians duty has three parts, namely,

1st, 

Re: [PEIRCE-L] André De Tienne: Slow Read Slide 23

[Jon Awbrey]

Helmut,

As it happens, I still remember a problem we had in Algebra I my freshman year
of high school.  A man fires a rifle at a balloon directly overhead (dumb thing
to do but that's just men).  The muzzle velocity of the bullet and the altitude
of the balloon are given and so we have a quadratic equation for the trajectory
of the bullet as a parabolic plot of the bullet's altitude over the time axis.
The quadratic equation gave two results, 3 seconds and 97 seconds, for the time
when the bullet hit the balloon.  Our textbook's advice in problems like these
was to choose the solution making the most sense and to ignore the other one.
The reason I remember all this probably due to the pat on the head I got for
figuring out what the other solution meant, and I'll bet you can, too.

Regards,

Jon

On 8/8/2021 4:18 PM, Helmut Raulien wrote:

Gary, List
I have a question for a mathematician: A quadratic equation delivers two
results. Is it clear in pure mathematics, whether these two results are
connected with an "and", so are both true, or are connected with an "xor", so
only one of them is true? Or can you only decide, whether it is "and" or "xor",
after aplying it to a real-world-problem? For example, you want to calculate a
volume. Volumes are only positive. So, if you have one negative and one positive
result, only the positive result can be true. So in this case it is "xor". But:
Isn´t it so, that this can only be seen after having applied mathematics to a
real-world-problem? Before having done that, the pure mathematician has not
known, whether it is "and" or "xor", but after the application to reality he
knows, that at least in some cases it is "xor". This is a result which concerns
pure mathematics too. So, isn´t it so, that pure mathematics does depend on
phaneroscopy and reference to reality outside itself, so it is not purely
hypothetical?
Best,
Helmut
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