John: Huh?
I think we are on totally different wavelengths. To me, following Tarski, any argument that explains everything, explains nothing. Let’s just drop this thread. Cheers Jerry > On Oct 20, 2017, at 3:16 PM, Jon Alan Schmidt <jonalanschm...@gmail.com> > wrote: > > Jerry, List: > > That is not what you claimed, nor what I requested as evidence. Again, for > Peirce, all necessary reasoning is mathematical reasoning by definition; he > did not limit it to manipulation of "the mathematical symbol system." > Obviously not everyone adheres to this terminology. > > In any case, your specific examples strike me as cases of induction, rather > than deduction. Again, for Peirce, "in regard to the real world, we have no > right to presume that any given intelligible proposition is true in absolute > strictness." > > Regards, > > Jon S. > > On Fri, Oct 20, 2017 at 3:03 PM, Jerry LR Chandler > <jerry_lr_chand...@icloud.com <mailto:jerry_lr_chand...@icloud.com>> wrote: > >> On Oct 20, 2017, at 2:53 PM, Jon Alan Schmidt <jonalanschm...@gmail.com >> <mailto:jonalanschm...@gmail.com>> wrote: >> >> Jerry C., List: >> >> JLRC: Of course, the qualified phrase, ‘… of the nature of…’ leaves the >> meaning vague. >> >> There is no such qualification in the sentence that I quoted from CP >> 5.148--"all necessary reasoning ... is mathematical reasoning.” > > CSP: Now all necessary reasoning, whether it be good or bad, is of the > nature of mathematical reasoning ... all necessary reasoning, be it the > merest verbiage of the theologians, so far as there is any semblance of > necessity in it, is mathematical reasoning. (CP 5.147-148, EP 2:206, 1903) >> Peirce then adds, "Now mathematical reasoning is diagrammatic." So the >> unstated conclusion of this little syllogism is that all necessary reasoning >> is diagrammatic. >> >> JLRC: My feeling is that CSP’s remarks are now out of date in the sense >> that many forms of mathematical reasoning are used in different structural >> forms - sets, groups, rings, vector spaces etc. with different modes of >> reasoning, even about addition and multiplication. >> >> Can you offer some specific examples of mathematical reasoning that are not >> also correctly characterized as necessary reasoning? > I can give you examples of reasoning that is necessary but not mathematical. > > Example: origins of rainbows. (extensive scientific hypothesizes are > necessary to invoke the spectra.) > Example: chemical analysis and chemical transformations. It is what it is. > Example: seeds sprout to give rise to plants. > Example: eggs hatch to give baby chickens. > And so forth. > > Mathematical reasoning is constrained to the mathematical symbol system, is > it not? > > Cheers > > Jerry >> The initial framing of pure hypotheses is indeed more retroductive than >> deductive--Daniel Campos has written about this quite a bit--but it is still >> always done with a view to working out the necessary consequences. For >> example, engineering modeling is all about representing a contingent (and >> uncertain) situation in such a way that a deterministic analysis will >> adequately capture the actual behavior. >> >> Regards, >> >> Jon S. >> >> On Fri, Oct 20, 2017 at 2:26 PM, Jerry LR Chandler >> <jerry_lr_chand...@icloud.com <mailto:jerry_lr_chand...@icloud.com>> wrote: >> Thanks, Jon! >> >> OK, the passages speak for themselves. >> >> Of course, the qualified phrase, ‘… of the nature of…’ leaves the meaning >> vague. >> >> My feeling is that CSP’s remarks are now out of date in the sense that many >> forms of mathematical reasoning are used in different structural forms - >> sets, groups, rings, vector spaces etc. with different modes of reasoning, >> even about addition and multiplication. >> >> Just the consequences of further inquiry… >> >> Cheers >> Jerry >>> On Oct 20, 2017, at 2:15 PM, Jon Alan Schmidt <jonalanschm...@gmail.com >>> <mailto:jonalanschm...@gmail.com>> wrote: >>> >>> Jerry C., List: >>> >>> Here is the first passage that comes to my mind, probably because it was >>> the key text for my articles on "The Logic of Ingenuity." >>> >>> CSP: Of late decades philosophical mathematicians have come to a pretty >>> just understanding of the nature of their own pursuit. I do not know that >>> anybody struck the true note before Benjamin Peirce, who, in 1870, declared >>> mathematics to be "the science which draws necessary conclusions," adding >>> that it must be defined "subjectively" and not "objectively." A view >>> substantially in accord with his, though needlessly complicated, is given >>> in the article "Mathematics," in the ninth edition of the Encyclopaedia >>> Britannica. The author, Professor George Chrystal, holds that the essence >>> of mathematics lies in its making pure hypotheses, and in the character of >>> the hypotheses which it makes. What the mathematicians mean by a >>> "hypothesis" is a proposition imagined to be strictly true of an ideal >>> state of things. In this sense, it is only about hypotheses that necessary >>> reasoning has any application; for, in regard to the real world, we have no >>> right to presume that any given intelligible proposition is true in >>> absolute strictness. On the other hand, probable reasoning deals with the >>> ordinary course of experience; now, nothing like a course of experience >>> exists for ideal hypotheses. Hence to say that mathematics busies itself in >>> drawing necessary conclusions, and to say that it busies itself with >>> hypotheses, are two statements which the logician perceives come to the >>> same thing ... 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 ... >>> 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; and, secondly, he >>> proceeds to draw necessary consequences from that hypothesis. (CP >>> 3.558-559, 1898; italics in original, bold added) >>> >>> I suspect that if Peirce had written this paragraph a few years later, when >>> he was being more careful about distinguishing existence and reality, he >>> would have substituted something like "existing world" or "actual world" >>> for "real world." Here is another relevant passage. >>> >>> CSP: Now all necessary reasoning, whether it be good or bad, is of the >>> nature of mathematical reasoning ... all necessary reasoning, be it the >>> merest verbiage of the theologians, so far as there is any semblance of >>> necessity in it, is mathematical reasoning. (CP 5.147-148, EP 2:206, 1903) >>> >>> Peirce essentially defined the mathematical realm as encompassing all >>> circumstances in which necessary reasoning can be done. >>> >>> Regards, >>> >>> Jon Alan Schmidt - Olathe, Kansas, USA >>> Professional Engineer, Amateur Philosopher, Lutheran Layman >>> www.LinkedIn.com/in/JonAlanSchmidt >>> <http://www.linkedin.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt >>> <http://twitter.com/JonAlanSchmidt> >>> On Fri, Oct 20, 2017 at 1:36 PM, Jerry LR Chandler >>> <jerry_lr_chand...@icloud.com <mailto:jerry_lr_chand...@icloud.com>> wrote: >>> Gary: >>>> On Oct 20, 2017, at 12:48 PM, Jeffrey Brian Downard >>>> <jeffrey.down...@nau.edu <mailto:jeffrey.down...@nau.edu>> wrote: >>>> >>>> Gary F., Mike, List, >>>> >>>> Should we expand the claim about mathematical objects? Gary F says: "That >>>> includes mathematical and other imaginary objects, which may be >>>> intelligible without being perceptible by the senses. Indeed it is only in >>>> the mathematical realm that necessary reasoning can be done, because the >>>> objects of pure mathematics have no being except what they are defined to >>>> have." >>> >>> I concur with Jeffrey’s definition, which,I think, is widely accepted. >>> >>> In addition, I am curious about your Peircian grounding of the assertion: >>>> it is only in the mathematical realm that necessary reasoning can be done, >>> >>> Do you have specific passages in mind? >>> >>> Cheers >>> >>> Jerry > > ----------------------------- > 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 > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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