We can begin with the post quoted by quid. ]]>

" make everything written by said crank disappear..."

In this way it is possible to classify(blaze) of "not convenient", for someone, by some reasons, mainly subjective(we are people) ,questions/answers/comments as "crank", "spam" and so on.

In some cases this may leads to excessive usage of administrative resourse(reputation),

unfair competition with "punitive psychiatry" as main method.

I wish to MO do not slide towards banal censorship, possible in sheep's clothing.

The number of closed posts seems to be increasing and is a distraction. ]]>

And as a compromise solution: AFAIK, but I might be missing something, in such cases you could delete *the accounts* of OP of question, preserving whatever of the content might be perceived as valuable but keeping the danger from such accounts (in particular as soon as they have some points) under control.

1. keep a crank's question open when there are interesting answers.

2. make everything written by said crank disappear, even if it is a reasonable-looking question with good answers.

We've tried option 1 in the recent past. It seems to lead to a general increase in pointless arguments and some unhappy users. We've also tried Option 2, and it seems to lead to some collateral damage from deleted answers in the form of unhappy users.

Timothy Chow seems to advocate for option 1, but perhaps without full recognition of the context. ]]>

@Timothy Chow: Well said. The problem with many of these discussions is unstated or unclear assumptions. ]]>

In full it says:

The standard natural numbers do not form a set. Why is that?

IMO, this is not unrelated.

I really wished standards regarding "foundational question" were somewhat more in line with those of the rest of the site.

]]>Regarding trb456's question, I'm not closely in touch with pedagogical practice nowadays, but my impression is that there are very few if any people "officially" trying to indoctrinate the next generation with finitist philosophical presuppositions. What I see happening is similar to what trb456 mentioned: the influence of computer science has caused increasing numbers of people to develop a feeling that reality is finite and discrete and anything else is just so much metaphysical nonsense. People with this kind of attitude may not consciously try to promote it as an agenda, but it has a tendency to spill out whether they intend to or not.

In some ways, I prefer the zealots who are open about their agenda to the "silent majority" who don't state their assumptions explicitly, because the former tend to have thought through their position more carefully and are less likely to exude pure prejudice.

]]>trb456: I agree that teaching undergraduate students that ordinary classical mathematics is wrong will create difficulties, and not only for their potential interest in research mathematics. It will create difficulties for their understanding of the next semester's course if that's taught in the normal way. Even undergraduate mathematics, especially analysis, becomes considerably more difficult to develop if one restricts to subsystems rather than using the full power of classical mathematics. Bishop has shown how to carry out the development of a good deal of analysis in a constructive system, and I believe there were earlier efforts along such lines by Lorenzen, but the weaker logical and set-theoretic framework must be compensated by more work and more careful statements of theorems. (Some would say "weakenings" or "circumlocutions" instead of "more careful statements".) Reducing the framework further, to a form of finitism, we have even more difficult (to the best of my knowledge) work of Nelson. I don't think anything like this belongs in the undergraduate curriculum, except perhaps in a specialized and rather advanced course in foundations, for students who already know the standard approach. ]]>

One of his favorite rants on google sci.logic/math is that since we can't have uncountable names for things, we can't have uncountably many real numbers. He attempts to formulate "alternative theories", but nothing ever pans out.

He presents unfounded proofs of internal contradictions, and would accept his logic errors. He only writes statements in plain English and then uses ambiguities in the language to show that he is right.

I sure you know what I'm talking about.

Just a heads up.

Thanx, Drew ]]>

small team of people are posting the questions. I think you need to gather

more data before presupposing a shift in a larger system of education.

Regarding the subject matter, I think well behaved and cogent questions

within the intended demesne of MathOverflow are allowed even if they

are contrary to some conventional understanding of how things are.

The current question is close enough to it, and allows for specific answers,

and does not suggest that its point of view should be universal, just that it

should be considered. This is a slightly different presentation of Andreas

Blass's bottom line, with which in the main I agree.

Gerhard "Always Watch For The Bottom Line" Paseman, 2013.06.13 ]]>

Although the question about power set seems to be based on a form of "countabilism" or "definabilism" rather than "finitism", I regard finitism and even ultrafinitism as respectable topics for mathematical investigation. (In the case of ultrafinitism, the main technical problem seems to be to provide an axiomatization that captures the intended ideas. In the case of finitism, the system PRA of "primitive recursive arithmetic" seems to be widely accepted as an appropriate foundation, but I don't know how solid the philosophical support for this acceptance is.)

The bottom line, for me, is that I have no problem with people saying "we should study such-and-such notion of set" and asking "what can we prove with this notion", provided they give a clear indication of what their notion is, and provided they don't preach "this is the right notion of set and everybody who uses a different notion is crazy." ]]>

An annoying side effect of this particular shift is, of course, that cranks have quickly caught up to it because it is quite visible (even MO had its share of legit constructivism discussions already) and everybody, except probably mathematicians, seems to believe he is perfectly capable of understanding any issue on mathematical logic. The latter reason seems to be the prevalent one -- I've seen a lot of logic cranks without any finitist/constructivist agenda. (Cantor is still the most popular subject: http://scientopia.org/blogs/goodmath/tag/cantor-crank/ . And this one works just as well in constructive logic, even if "uncountable" isn't the same as "bigger than countable" there.)

]]>Questions that have an ideological axe to grind, so to say, would also generally be viewed askance.

Speaking only for myself, calls to restrict exploration into acquiring knowledge is profoundly anti-scientific and anti-mathematical.

Maybe I'm not understanding what trb456 has in mind here, but I can safely say that many, probably most professionals who pursue predicative mathematics, constructive mathematics, etc. do not do so because of some ingrained philosophical prejudice, but for pragmatic reasons, and such pursuits are inevitably all about expansion of knowledge, not suppression. In the case of intuitionist or constructive mathematics, a major point is that by weakening the logic, one can dramatically expand the worlds or semantics in which the mathematics will still be valid -- quite a powerful tool. For example, categorical logicians are frequently interested in intuitionist mathematics because the results therein are valid in toposes much more general than the category of sets. Another case study is intensional dependent type theory, which is exceedingly active these days.

]]>I want to make my query specific. This question, http://mathoverflow.net/questions/133597/what-would-remain-of-current-mathematics-without-axiom-of-power-set, is only the latest in a series of many questions (it seems to me) questioning the validity of transfinitism and nonconstructivism. Any trained mathematician knows that these controversies have been around for a long time. So my question is: why now? Has something happened in the world of mathematics or math education that is causing what seems to me a rethinking on this?

I saw one comment that jokingly suggested it was Wiles' fault for solving FLT, with the cranks moving on to Cantor and the like. More seriously, though:

1) Is the rise of computer science and coding in importance driving any of this? Specifically, does anyone actually involved in CS see examples of educators opening suggesting/calling for finitist teaching universally? I know of some examples, but how widespread? I realize that theoretical CS deals with essentially finite objects, but why now the urge to shut down the rest of the mathematical world?

2) It strikes me that finitism and the like is a claim that we should restrict knowledge, since finitism and constructivism are perfectly fine subsets of classical mathematics. If you a writing a computer program, what you are doing is necessarily computable. But why restrict the exploration into the non-computable? Again, I'm looking for examples from the practicing mathematicians here of examples they see where this idea of pedagogy is taking hold. I can understand how much of this is non-intuitive at first, but a key part of math education is learning to follow the logic wherever it leads. Why now the urge to suppress this?

I ask this because I am not a practicing mathematician or an educator (I have an MS degree, and use math in an applied field; but I am thoroughly classical in outlook). Perhaps I'm just seeing things that aren't there. Perhaps increasing interconnectedness just amplifies some voices beyond their actual influence. But I sense that it may be more than this, and since I don't actively deal with the research and educational community, I'm interested in their views. I'm wondering if some more grassroots in education is happening.

Speaking only for myself, calls to restrict exploration into acquiring knowledge is profoundly anti-scientific and anti-mathematical. As I saw one wise contributor suggest, if some area doesn't interest you, study something else. But why the desire to shut off other discussion? I'm talking about non-crank motives--we'll never reach them. In particular, why teach impressionable students to not be curious and chase knowledge wherever it leads? Again, not here to discuss philosophy, but is anyone here seeing this urge in some area of teaching, and if so, what are their stated motives?

Thanks in advance! ]]>