Robert, List: I am glad that we agree on the interpretation of CP 5.589. As for CP 3.559, there is no "magic trick" involved in simply recognizing that its last sentence is a *summary *of the entire paragraph. That is why it begins with "Thus, ..." Moreover, I was not laying out the *chronological *sequence of events, which is actually (2) (3) (1) (4). This is evident if we replace (1) with the following sentences, which say basically the same thing and come between (3) and (4) in the original text.
CSP: 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. Instead, I first quoted the summary (1) since it succinctly makes the point that I was primarily emphasizing, and then the other relevant phrases in order (2) (3) (4). I also did not claim or imply that the phaneroscopist is "now an engineer." Peirce *begins *the paragraph by stating, "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*" (emphasis added). He gives as examples not only an engineer, but also "a business company (say, an insurance company), or a buyer (say, of land), or a physicist." I see no reason why it would somehow be illegitimate to add a phaneroscopist to this list. For the record, I have no issue with the actual quote from de Waal, just how it was misrepresented as applied to the current List discussion. In fact, I have previously cited Daniel Campos likewise discussing Peirce's identification of imagination, concentration, and generalization as the intellectual abilities required for mathematical reasoning, and thus for the proper practice of phaneroscopy as well as pure mathematics ( https://list.iupui.edu/sympa/arc/peirce-l/2021-07/msg00052.html). Please stop repeatedly alleging hostility to mathematics and mathematicians where it does not exist. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Aug 27, 2021 at 11:50 AM robert marty <robert.mart...@gmail.com> wrote: > 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/>* >
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