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://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*
Le ven. 27 août 2021 à 03:28, Jon Alan Schmidt <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 - twitter.com/JonAlanSchmidt
>
> On Wed, Aug 25, 2021 at 3:24 PM robert marty <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) :
>>
>>
>>
>> 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, 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://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*
>>
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