tea.mathoverflow.net - Discussion Feed (Logic of motivation)

Henry Cohn comments on "Logic of motivation" (14372)

2011-05-02T05:51:10-07:00

I imagine Michael is thinking of the following quote, from the preface (written by Rota) to "Discrete Throughts: Essays on Mathematics, Science, and Philosophy" by Kac, Rota, and Schwartz:

"Sometime, in a future that is knocking at our door, we shall have to retrain ourselves or our children to properly tell the truth. The exercise will be particularly painful in mathematics. The enrapturing discoveries of our field systematically conceal, like footprints erased in the sand, the analogical train of thought that is the authentic life of mathematics. Shocking as it may be to a conservative logician, the day will come when currently vague concepts such as motivation and purpose will be made formal and accepted as constituents of a revamped logic, where they will at last be allotted the equal status they deserve, side-by-side with axioms and theorems. Until that day, however, the truths of mathematics will make only fleeting appearances, like shameful confessions whispered to a priest, to a psychiatrist, or to a wife."

I'm skeptical about the idea of formalizing motivation and purpose as part of mathematical logic, and I'm not aware that Rota ever seriously proposed working on it, but he at least mentioned it in this preface, and perhaps elsewhere too.

Pete L. Clark comments on "Logic of motivation" (14371)

2011-05-01T21:24:34-07:00

@Michael Hardy:

"I'd have thought it was obvious that persons' motivations, as that term is usually understood, is not what this is about."

I would have thought it was obvious that people here have had a lot of trouble understanding what your question was actually about. In case not: we are not being intentionally obtuse. We really don't understand what mathematical question you wish to ask.

Several people asked you a week ago to supply the Rota quote on which your question is based. Have you found it yet? If not, I hope that at a certain point you will retract this attribution: that would seem to be good scholarship, and also a courtesy to a venerated mathematician that is no longer around to speak for himself.

Todd Trimble comments on "Logic of motivation" (14367)

2011-05-01T13:37:46-07:00

+1 to DL. Best would be to track down that passage, Michael.

DL comments on "Logic of motivation" (14366)

2011-05-01T13:24:25-07:00

Michael, it would be obvious what you were talking about if you provided a reference to it.

Are you sure the Rota proposal you have in mind is not the one he makes in Chapter XII of "Indiscrete Thoughts"? While quite far from what you seem to have in mind, it's the closest I could find in Rota's writing. I think a question about *that* proposal (which has the virtue of actually having been made by Rota) would not be closed, though it seems unlikely to generate any good answers.

Michael Hardy comments on "Logic of motivation" (14365)

2011-05-01T12:52:25-07:00

Pete L. Clark wrote: "a person, let alone their motivations, is not within the purview of mathematical logic".

I'd have thought it was obvious that persons' motivations, as that term is usually understood, is not what this is about.

I believe I read both that passage from _Indiscrete Thoughts_ and something else Rota wrote, and at least one of them was urging people to pursue that line of research.

Michael Hardy comments on "Logic of motivation" (14192)

2011-04-25T05:43:34-07:00

@Pete: I had not realized before posting this question that this particular idea of Rota's was not widely known.

DL comments on "Logic of motivation" (14175)

2011-04-23T22:00:12-07:00

@Sergei, Emerton:

Pete L. Clark's comment addresses exactly why I thought Rota's name was relevant; if the question is a reference request about some program of Rota's, it should at least be clear that this is indeed something Rota proposed. On the other hand, if this is an idea of the OP's, it would be silly for him to ask for references about it.

Pete L. Clark comments on "Logic of motivation" (14173)

2011-04-23T21:14:47-07:00

[I deleted the second part of my response. I now think it is not necessary for me to explain in such gruesome detail why I didn't like the question.]

Pete L. Clark comments on "Logic of motivation" (14172)

2011-04-23T21:14:37-07:00

In the second formulation of the question, the OP has mostly retreated into asking for a reference request. The second question is however informed by the first question which the OP admits he has not backed off of in any way except by being told that he should not include it lest his question be closed. So let me begin with the second question and work my way to the first.

A reference request seems rather benign, if only we can figure out exactly what is being requested. I'm having trouble figuring out what sort of thing a "logical theory of motivation" would be. The question is given the arxiv tag LO, which refers to mathematical logic. But a person, let alone their motivations, is not within the purview of mathematical logic -- not by a long shot. So I guess we are looking for some kind of "applied logic" or, better, some kind of mathematical model of...something having to do with motivation. Well, I suppose such things either exist or they don't exist, and it is fair to ask which of these possibilities is actually the case. I have to say though that basing your question on an idea from Rota's writings and not supplying the quote or reference seems to be faltering to meet a minimum standard of due diligence for asking a question: if we can actually see the relevant passage by Rota there would be something more or less concrete to hang on to (although people who are familiar with Rota's writings -- as many people here seem to be -- know that they are, albeit intriguing, often speculative in a manner which is far away from what MO questions and answers are supposed to be). If the OP can supply a quote and merely ask, "Has this been followed up on in any way?" then I think he will have met the minimal standards of a valid question.

(continued...)

Emerton comments on "Logic of motivation" (14171)

2011-04-23T21:13:36-07:00

I agree with Sergei that Rota's name is not particularly relevant.

sergei tropanets comments on "Logic of motivation" (14170)

2011-04-23T21:07:07-07:00

I do not think that either the presence of name of Rota or its absence would make any significant changes in content of the question.

DL comments on "Logic of motivation" (14169)

2011-04-23T20:57:29-07:00

I took the time to leaf through some Rota looking for any proposal of his concerning a so-called "logic of motivation." The closest I found was the following passage, which appears in Chapter XIII of Rota's "Indiscrete Thoughts" (p. 160 in my copy):

"Motivation and desire are essential components of mathematical reasoning. We have no right to dismiss these aspects of mathematics as 'purely psychological,' any more than we would dismiss Cauchy's results on integration as 'purely heuristic,' because he failed to provide a full axiomatization..."

This is the closest I could find to the proposal the OP claims Rota made; having read this, and a good deal of other writing by Rota, I find it doubtful that Rota ever made such a proposal (I would be pleased to find otherwise, if the OP can find the reference he has in mind). Indeed, in the essay I quote itself, Rota expressly discusses his belief that mathematics is about more than the axiomatic method--espousing a "logic of motivation" would be an attempt to reduce the non-axiomatic parts of mathematics Rota considers so important to dry logic.

In any case, it seems likely to me that the OP has dressed up an idea of his own as an idea of Rota's; again, I would be pleased if this is not the case, so I hope he provides a reference. It would drastically improve the question in any case; without the name Rota in the question, I think there would have been little discussion as to whether it should be closed in the first place.

sergei tropanets comments on "Logic of motivation" (14167)

2011-04-23T20:44:35-07:00

I agree with Emerton to a large extent. I do not think that motivation in mathematics may be formalized in its entirety, but I do think that it may be formalized to some extent. It is quite possible that someboddy is working on that. (I know about similar attempts to formalize the concepts of being natural for notion or proof or being the most deep explanation(or proof) for a fact in mathematics.) My advise to Michael is to be more precise about formalization he talks about. Therefore, to my view, at least the first part of the question (reference request) is appropriate.

Ryan Budney comments on "Logic of motivation" (14166)

2011-04-23T20:28:03-07:00

If the OP put in some comments to clarify what he means by "motivation" that takes it away from the purely emotional realm I'd consider voting to reopen but I don't see the point of these threads, at least, not for a forum like MO.

Emerton comments on "Logic of motivation" (14165)

2011-04-23T20:17:30-07:00

Dear Anton,

My impression is that the question is a reference request plus a little more. "What has been done" is a reference request. "In what directions should further work go" is evidently not a reference request, and could certainly be interpreted as discussiony (although in other contexts, I think that the question "what are the important directions to pursue in this subject" would be a reasonable question).

I have voted to reopen both versions of the question (although one should ultimately be closed as a duplicate of the other). I don't think that the question will have much of an answer (i.e. I doubt many or even any relevant references exist), but I don't think the question is a priori unreasonable. For example, the investigation of relative dependencies of various axioms and theorems is a well-established part of mathematical logic. The logic of motivation that is being asked about may well have something of this flavour, but other elements as well.

Regarding tags (discussed in the comments of the second question) I would think that both logic and math education are appropriate.

Best wishes,

Matt

Anton Geraschenko comments on "Logic of motivation" (14164)

2011-04-23T20:08:52-07:00

This question seems to have generated a long comment thread that should have taken place on meta, so I'm opening a thread here.

first instance of the question
second instance of the question

I agree with the closing of this question. I don't understand the goal of the question or the motivation of the OP (ironically). The most generous reading of it I can muster is that it's a reference request—this seems to be the position the OP takes—but as far as I can tell there is little reason to believe any reference exists, and little reason to believe the OP is interested in anything but a philosophical discussion.