Jon Alan, List
*A MAGIC TRICK*
/How to make a pseudo-quote from a quote to create a desired meaning/
It is straightforward: you choose in the last sentence a piece that
suits you (1), then you go back to the beginning of the text by
selecting another piece (2), which you link with two others (3) and
(4) in the logic of the text. You obtain the following demonstration
(which you attribute to Peirce!) according to which:
"the mathematician "/without inquiring or caring whether it [the pure
hypothesis] agrees with the actual facts or not *(1)*, /while the
phaneroscopist (now an engineer)/ " finds it suits his purpose to
ascertain what the necessary consequences of possible facts would be"
*(2)*,/ then " calls upon a mathematician and states the question
*(3)*, and concludes whether the result "/simpler but quite
fictitious problem *(4)* /are consistent with observed facts.
**
*PROOF :*
**
JAS > This is a straw man, since no one is advocating what is
described here as an "impossibility." I have explicitly and repeatedly
acknowledged the role of mathematicians in /formulating /the pure
hypotheses ("skeleton-sets") from which they subsequently draw
necessary conclusions in accordance with the concluding sentence of CP
3.559 (1898). Nevertheless, as Peirce himself goes on to observe, they
do this */"without inquiring or caring whether it [the pure
hypothesis] agrees with the actual facts or not /**/(1)/*." It is the
phaneroscopist who */"finds it suits his purpose to ascertain what the
necessary consequences of possible facts would be/*"*/(2) /*and thus
/"calls upon a mathematician and states the question"/*/(3)/**,***and
it is the phaneroscopist who inductively evaluates whether the
mathematician's deductive conclusions from the resulting */"simpler
but quite fictitious problem /**/(4)/**"*are consistent with observed
facts.
PEIRCE > CP 3.559
A simple way of arriving at a true conception of the mathematician's
business is to consider what service it is which he is called in to
render in the course of any scientific or other inquiry. Mathematics
has always been more or less a trade. An engineer, or a business
company (say, an insurance company), or a buyer (say, of land), or a
physicist, */finds it suits his purpose to ascertain what the
necessary consequences of possible facts would be/*//*/(2)/*; but the
facts are so complicated that he cannot deal with them in his usual
way. */He calls upon a mathematician and states the question
/**/(3)./*Now the mathematician does not conceive it to be any part of
his duty to verify the facts stated. He accepts them absolutely
without question. He does not in the least care whether they are
correct or not. He finds, however, in almost every case that the
statement has one inconvenience, and in many cases that it has a
second. The first inconvenience is that, though the statement may not
at first sound very complicated, yet, when it is accurately analyzed,
it is found to imply so intricate a condition of things that it far
surpasses the power of the mathematician to say with exactitude what
its consequence would be. At the same time, it frequently happens that
the facts, as stated, are insufficient to answer the question that is
put. Accordingly, the first business of the mathematician, often a
most difficult task, is to frame another */simpler but quite
fictitious problem (4)/*(supplemented, perhaps, by some supposition),
which shall be within his powers, while at the same time it is
sufficiently like the problem set before him to answer, well or ill,
as a substitute for it. This substituted problem differs also from
that which was first set before the mathematician in another respect:
namely, that it is highly abstract. All features that have no bearing
upon the relations of the premisses to the conclusion are effaced and
obliterated. The skeletonization or diagrammatization of the problem
serves more purposes than one; but its principal purpose is to strip
the significant relations of all disguise. Only one kind of concrete
clothing is permitted -- namely, such as, whether from habit or from
the constitution of the mind, has become so familiar that it decidedly
aids in tracing the consequences of the hypothesis. 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
/**/(1/**/);/*and, secondly, he proceeds to draw necessary
consequences from that hypothesis."
*/The magic is that (2) (3) (4) (1) chosen in CP 3.559 became
(1)(2)(3) (4) ... /**/Well done, artist!/*
For the record, the quote from /Cornelis de Waal/ was as follows:
"/'The results of experience have to be simplified, generalized, and
severed from fact so as to be perfect ideas before they arc suited to
mathematical use. They have, in short, to be adapted to the powers of
mathematics and of the mathematician. It is only the mathematician who
knows what these powers are; and consequently the framing of the
mathematical hypotheses must be performed by the mathematician/.' (R
17:06f)"
https://www.jstor.org/stable/40321072 p.288
<https://www.jstor.org/stable/40321072%20p.288>
*QED …***
Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
<https://fr.wikipedia.org/wiki/Robert_Marty>
_https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>_
Le ven. 27 août 2021 à 03:28, Jon Alan Schmidt
<jonalanschm...@gmail.com <mailto:jonalanschm...@gmail.com>> a écrit :
Robert, List:
RM: To state the logical order (of the discovery), we must
follow Peirce "/I am partially inverting the historical order,
in order to state the process in its logical order/"(CP 5.589,
EP 2:54-55, 1898), as quoted by Jon Alan Schmidt.
I agree, but in that passage he is not /specifically /addressing
phaneroscopy, since at the time (1898) he had not yet even
recognized it as a distinct science that needed to come between
mathematics and logic in his classification. Instead, he is
talking about the scientific method /in general/ and giving "the
process in its logical order," which is induction followed by
retroduction.
CSP: The only end of science, as such, is to learn the lesson
that the universe has to teach it. In induction it simply
surrenders itself to the force of facts. But it finds, at
once,--[italicized quote above]--it finds I say that this is
not enough. It is driven in desperation to call upon its
inward sympathy with nature, its instinct for aid, just as we
find Galileo at the dawn of modern science making his appeal
to /il lume naturale/. (CP 5.589, EP 2:54-55)
This is "partially inverting the historical order," which is
retroduction followed by deduction and then induction.
CSP: But in so far as it does this, the solid ground of fact
fails it. It feels from that moment that its position is only
provisional. It must then find confirmations or else shift its
footing. Even if it does find confirmations, they are only
partial. It still is not standing upon the bedrock of fact. It
is walking upon a bog, and can only say, this ground seems to
hold for the present. Here I will stay till it begins to give
way. Moreover, in all its progress, science vaguely feels that
it is only learning a lesson. ... Science, feeling that there
is an arbitrary element in its theories, still continues its
studies, confident that so it will gradually become more and
more purified from the dross of subjectivity ... . After a
while, as Science progresses, it comes upon more solid ground.
It is now entitled to reflect: this ground has held a long
time without showing signs of yielding. I may hope that it
will continue to hold for a great while longer. This
reflection, however, is quite aside from the purpose of
Science. It does not modify its procedure in the least degree.
(ibid)
Scientific theories about the outer world of existence are never
/certain /because they always rely on idealized hypotheses about
the logical world of mathematics, which inescapably include "an
arbitrary element." Consequently, the third phase of induction is
never finished, which is why the truth about reality is whatever
/would /be affirmed in the /ultimate /opinion after /infinite
/inquiry by an /infinite /community.
RM: "Phaneroscopists" cannot constitute a category in
themselves and that, since they do not study mathematics, they
would be better advised to collaborate with mathematicians who
have "forms in mind".
On the contrary, phaneroscopy /is /a distinct science in Peirce's
mature classification, so in his view there /are/ phaneroscopists,
distinct from mathematicians and other kinds of inquirers; and as
quoted below, he states explicitly that "phaneroscopic research
/requires /a previous study of mathematics" (R 602; emphasis
added). This is not to say that they cannot or should not
"collaborate with mathematicians," just that their purpose is
different--they are studying whatever is or could be present to
the mind in any way, rather than strictly hypothetical states of
things.
RM: I conclude this part B1 by quoting an article ... by
Cornelis de Wall, who says much better than I do the
impossibility of relegating mathematics and mathematicians to
a corner where they would devote day and night in endless
deductions, while self-proclaimed "phaneroscopists" would
propose specific informal bricolage without "skeleton-sets" to
support them:
This is a straw man, since no one is advocating what is described
here as an "impossibility." I have explicitly and repeatedly
acknowledged the role of mathematicians in /formulating /the pure
hypotheses ("skeleton-sets") from which they subsequently draw
necessary conclusions in accordance with the concluding sentence
of CP 3.559 (1898). Nevertheless, as Peirce himself goes on to
observe, they do this "without inquiring or caring whether it [the
pure hypothesis] agrees with the actual facts or not." It is the
phaneroscopist who "finds it suits his purpose to ascertain what
the necessary consequences of possible facts would be," and thus
"calls upon a mathematician and states the question"; and it is
the phaneroscopist who inductively evaluates whether the
mathematician's deductive conclusions from the resulting "simpler
but quite fictitious problem" are consistent with observed facts.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt
<http://www.LinkedIn.com/in/JonAlanSchmidt> -
twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt>
On Wed, Aug 25, 2021 at 3:24 PM robert marty
<robert.mart...@gmail.com <mailto:robert.mart...@gmail.com>> wrote:
List,
Following ...
*B1 *– To state the /logical order/ (of the discovery), we
must follow Peirce "/I am partially inverting the historical
order, in order to state the process in its logical order/"(CP
5.589, EP 2:54-55, 1898), as quoted by Jon Alan Schmidt.
I recall the /chronological order/ observed in part A
(https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00177.html
<https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00177.html>)
:
1- observation of phanerons by "phaneroscopists" who identify
"candidate" forms. Peirce himself has found forms that come
from his knowledge of theoretical chemistry: the "valences" of
the elements.
2- for each "candidate" form found, search in the mathematical
repository or creation of isomorphic mathematical forms.
3-choosing, by the scientific community involved in the
discovery, of the "best form."
4-generate, by pure mathematical activity, new mathematical
forms to be submitted to a new validation process.
What is then the order advocated by Peirce? It is the
dependencies stated in his classifications of sciences with
respect to mathematics, which generates the process of the
Sciences of Discovery described below:
1- Mathematics (the "good" forms found in 3 above)
2- Cenoscopy - Philosophia prima- positive science (which
rests upon familiar, general experience): continuation of the
"phaneroscopic" activity which may give rise to the emergence
of new competing candidates.
3- Phenomenology - Phaneroscopy (1904-) - study of Universal
Categories (all present in any phenomenon): Firstness,
Secondness, Thirdness. Work of the phaneroscopists driven by
the mathematics of the 1.
/"//Phaneroscopy... is the science of the different elementary
constituents of all ideas. Its material is, of course,
universal experience, -- experience I mean of the fanciful and
the abstract, as well as of the concrete and real. Yet to
suppose that in such experience the elements were to be found
already separate would be to suppose the unimaginable and
self-contradictory. They must be separated by a process of
thought that cannot be summoned up Hegel-wise on demand. They
must be picked out of the fragments that necessary reasonings
scatter/, and* therefore it is that phaneroscopic research
requires a previous study of mathematics.*(R602, after 1903
but before 1908")
4 - unchanged
*/The chronological order 1,2,3,4 is changed to logical order:
3, 2, 1, 4./*
*//*
*"Phaneroscopists" cannot constitute a category in themselves
and that, since they do not study mathematics, they would be
better advised to collaborate with mathematicians who have
"forms in mind".*
In his writings, Peirce presents his research relative to the
categories either in chronological order by reporting his
observations (CP 1.284, 1.286), or in a logical order by
reporting the result of his observations in formal terms, in
particular by reasoning by analogy with the notion of valence
in chemistry (CP 1.292 ) and more formally with the monad,
dyad, and triad.
/"I invite you to consider, not everything in the phaneron,
but only its indecomposable elements, that is, those that are
logically indecomposable, or indecomposable to direct
inspection.[ … ] Fortunately, however, all taxonomists of
every department have found classifications according to
structure to be the most important/." (CP 1.288)
Depending on the context, the "phaneroscopists" will find by
"pressicive" observation and/or by "abstractive
hypostatization", either pure forms (expressible in
mathematical diagrams) or informal "bricolage" to which
mathematicians may or may not give form. One finds in
particular in Categories (Peirce) - Wikipedia
<https://en.wikipedia.org/wiki/Categories_(Peirce)>the
following compiled table:
*Name:*
*Typical characterization*
*As universe of experience:*
*As quantity*
*Technical definition:*
*Valence, "adicity":*
Firstness
Quality of feeling
Ideas, chance, possibility.
Vagueness, "some."
Reference to a ground (a ground is a pure abstraction of a quality
Essentially monadic (the quale, in the sense of the
/such/,^[11]
<http://en.wikipedia.org/wiki/Categories_(Peirce)#cite_note-11>
which has the quality).
Secondness
Reaction, resistance, (dyadic) relation.
Brute facts, actuality.
Singularity, discreteness, “this
<http://en.wikipedia.org/wiki/Haecceity>
Reference to a correlate (by its relate).
Essentially dyadic (the relate and the correlate).
Thirdness
Representation, mediation.
Habits, laws, necessity.
Generality, continuity, "all".
Reference to an interpretant*.
Essentially triadic (sign, object, interpretant*).
We see that the only terms that can be linked to mathematics
are "monadic," "dyadic," and "triadic." No other mathematical
object is mentioned.
I conclude this part B1 by quoting an article
(https://www.jstor.org/stable/40321072
<https://www.jstor.org/stable/40321072>, 2005) widely/by
Cornelis de Wall/, who says much better than I do the
impossibility of relegating mathematics and mathematicians to
a corner where they would devote day and night in endless
deductions, while self-proclaimed "phaneroscopists" would
propose specific informal bricolage without "skeleton-sets" to
support them:
"By defining science in terms of the activities of its
promoters, Peirce's division of the sciences largely comes
down to a division of labor. This attitude toward science
enables Peirce to argue that it is the mathematician who is
best equipped to translate the more loosely constructed
theories about groups of positive facts generated by empirical
research into tight mathematical models:
/'The results of experience have to be simplified,
generalized, and severed from fact so as to be perfect ideas
before they arc suited to mathematical use. They have, in
short, to be adapted to the powers of mathematics and of the
mathematician. It is only the mathematician who knows what
these powers are; and consequently the framing of the
mathematical hypotheses must be performed by the
mathematician/.' (R 17:06!)
Now what constitutes a well-equipped mathematician? The three
mental qualities that in Peirce's view, come into play are
imagination, concentration, and generalization. The first is,
as Peirce put it, /"the power of distinctly picturing to
ourselves intricate configurations/"; the second is
*"*/the**ability to cake up a problem, bring it to a
convenient shape for study, make out the gist of it, and
ascertain without mistake just what it does and does not
involve/"; the third is what allows us "/to see that what
seems at first a snarl of intricate circumstances is but a
fragment of a harmonious and comprehensible whole/" (R
252:20).^6 In particular the power of generalization, which
Peirce believes "/chiefly constitutes a mathematician/" (R
278a:9 l ), is a difficult skill to attain. Peirce's emphasis
on imagination, concentration, and generalization draws the
attention away from the notion that it is the premier business
of mathematics to provide proofs."
In section B2, I will study how some of the most prominent
Peircean have confronted this dependence of phaneroscopy on
mathematics and the responses they have provided.
Best regards,
Robert Marty
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
<https://fr.wikipedia.org/wiki/Robert_Marty>
_https://martyrobert.academia.edu/
<https://martyrobert.academia.edu/>_
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