[PEIRCE-L] Conflict between deduction and discovery in mathematics

List, I am new to Peirce's work, but I am curious to know if this is a valid interpretation of his work. I would also like to thank you for your answers to my previous post. In various places, Peirce states that all deduction is diagrammatic. For example, in a letter to William James (1909,

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Matias, Jon, list, Jon is quite right.  Don't get hung up on Peirce's remark on the ampliative-explicative distinction as applied to deduction. SIDE NOTE: I'm getting a bit rusty.  In a previous post I said Peirce never discussed nontriviality or depth in their later sense, but that was my

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Matias, List: In the quoted passage, Peirce suggests "that there are two kinds of deductive reasoning, which *might, perhaps*, be called explicatory and ampliative" (emphases mine). However, he immediately adds that "no mathematical reasoning is what would be commonly understood by ampliative,"

[PEIRCE-L] Conflict between deduction and discovery in mathematics

The Bourbaki were a group of brilliant mathematicians, who developed a totally unusable system of mathematics. That example below shows how hopelessly misguided they were. Sesame Street's method of teaching math is far and away superior to anything that the Bourbaki attempted to do. Sesame

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Jon, list, I thank you very much for your answer. As you suggest, I believe that Peirce's answer to the problem lies in his notion of theorematic deduction. However, I'm having trouble understanding what he means by that. For example, I am confounded by the meaning of this citation. "It was

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Recently I have seen a paper below that could be of interest to this discussion as it shows that to work deductively even with the number 1 is not that easy. Best wishes, Evgenii Mathias, Adrian RD. "A Term of Length 4 523 659 424 929." Synthese 133, no. 1 (2002): 75-86 "Bourbaki suggest

Aw: [PEIRCE-L] Conflict between deduction and discovery in mathematics

t" Betreff: Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics Matias, Phyllis, all, Peirce didn't talk a whole lot about novelty in deduction, and I doubt that he ever discussed non-triviality or depth in later mathematicians' sense of those ideas (which are allied,

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

*Matias, Phyllis, all,** * *Peirce didn't talk a whole lot about novelty in deduction, and I doubt that he ever discussed non-triviality or depth in later mathematicians' sense of those ideas (which are allied, though not the same as, the idea of difficulty) though he did focus quite a bit,

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Ben, Phyllis, Thank you both for your answers. I appreciate your insights. Ben, I will check out the Gilman article you mentioned. I didn't know about it, but it sounds like it could be helpful. I believe that Peirce's answer to the paradox lies in his notion of theorematic deduction. However,

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Matias, Jon: First, I am very curious, Matias, on where your critical question emerges from? What are the sources of your curiosity? The fuller the ascriptions of your cognitive status, the better I will be able to respond to this simple but daring question. Jon, in your numerous posts that

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Matias, List: Although I cannot offer "any information that traces the history of this problem" as requested, I can suggest Peirce's own explanation of it. CSP: Deductions are of two kinds, which I call *corollarial *and *theorematic*. The corollarial are those reasonings by which all

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

* I just found B.I. Gilman's article at Google Books.  The whole article was accessible to me here in the USA. https://books.google.com/books?id=dPhl9SLIU54C=PA38=PA38 I'll try to see (not immediately!) what to think of it. Best,

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Matias, Phyllis, One does often start with guessing, retroduction, etc., in trying to solve a mathematical problem, be the problem trivial or deep. However this guesswork or the like is usually not formalized in publications.  Occasionally a mathematician publishes a mathematical conjecture,

Re: [PEIRCE-L] Conflict between deduction and discovery in mathematics

Wouldn't this be true for all of nature versus the all of discovery? Discovery is human and therefore retroductive (as are "newspapers and great fortunes"). Nature is. On Fri, Aug 18, 2023, 4:14 PM Matias wrote: > Dear list members, > > I am trying to contextualize Peirce's reference to the

[PEIRCE-L] Conflict between deduction and discovery in mathematics

Dear list members, I am trying to contextualize Peirce's reference to the long-standing conflict between the notion of mathematical reasoning and the novelty of mathematical discoveries. I would appreciate any information that traces the history of this problem. Here are two citations in which