Bernard, list, Yes, you can regard De Tienne’s statement about mathematicians in a non-existing world as a logical blunder; I regard it as a manifestation of his peculiar sense of humor.
As for the experience of mathematicians doing pure mathematics, you can indeed call it “experience,” but only in a peculiar sense which is contrary to Peirce’s regular usage. Usually in Peirce, the distinction between the internal and external worlds corresponds directly to the difference between a “world of imagination” and “the actual world.” The idea of externality is virtually identical with the idea of Secondness and is closely related to the metaphysical idea of reality. Peirce usually refers to “experience” as something forced upon us, indicating that Secondness is essential to it. In these Peircean terms, the “everyday work” of mathematicians, insofar is it is purely hypothetical, takes place in an internal world, a realm of “degenerate Secondness” (EP1:280, W6:211). As JAS has been reminding us, the context of De Tienne’s talk/slideshow involves a focus on pure mathematics and a corresponding neglect of mathematical applications. This is one reason why he (and Peirce) do not refer to pure mathematics as “experiential” in the sense that phaneroscopy is. Gary f. From: peirce-l-requ...@list.iupui.edu <peirce-l-requ...@list.iupui.edu> On Behalf Of Bernard Morand Sent: 11-Aug-21 09:18 To: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] André De Tienne: Slow Read slide 23 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 <mailto: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 <mailto:morand.bern...@neuf.fr> <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 _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu <mailto:peirce-L@list.iupui.edu> . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu <mailto:l...@list.iupui.edu> with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. 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