Joe Niederberger posted Jul 4, 2013 6:42 PM: > > G S Chandy says: > >I refer to some ideas in the excellent article > "Three Crises in Math..." to which you had pointed > me: (In my own words), > << 'Logicism', 'Intuitionism' and 'Formalism' all > tried - AND FAILED - to provide a firm foundation for > math >> To the best of my understanding the needed > firm foundation has not developed since 1979 when the > article was published. > > I think if you look at logicism (and teh others), and > the *failure* of it, it helps shed light on the > relationship between math and logic, which is what > you originally asked about. > > If, on the other hand, you are looking for "firm > foundation", why not study ZFC? But that's not how > you started this thread. > True enough, 'logicism' has shed light, as you claim, on the relationship between math and logic. Some light, true, but not quite sufficient to clarify matters for even the practitioners of 'academic scholarship and convivial discussion' (insofar as I can make out from the little study that I've been able to do by way of a fair amount of academic scholarship along with some convivial discussion) - and definitely there has NOT been sufficient light shed for the people at large, most of whom are unable to fathom the 'academic scholarship and the convivial discussions' in which you rest your faith.
Likewise, so have 'intuitionism' and 'formalism' shed some light on a variety of important issues (including on the 'foundations of math'; on how the practitioners of 'academic scholarship and convivial discussion' understand the relationship between logic and math; and so on and so forth).
BUT not enough, clearly, for those practitioners themselves (as the paper you have pointed to observes).
AND VERY DEFINITELY not sufficient light has been shed for the people at large who have innumerable problems and issues to which they would keenly like to apply the fruits of all that 'academic scholarship and convivial discussion'. My claim is that, in fact, very little light has been shed (for people at large; relative to the light and knowledge that is actually available - much of which has come, I agree, through 'academic scholarship and convivial discussion'. I am not denying the power and utility of 'academic scholarship and convivial discussion' - merely that a lot more needs to be done in the way of practical application to real-life issues - and this can be done right today).
One major underlying difficulty, to my mind, is that the practitioners of 'academic scholarship and convivial discussion' generally seem to be talking mainly to themselves and, no doubt, to each other (to an extent). [As seems to be confirmed by the story of a famous and important paper by Gottlob Frege on differential equations that for years no one could understand until it was translated into ordinary German!!! I don't know where this story appears - perhaps it is in "Three Crises..."??]
I claim that 'the practitioners' are not talking sufficiently (or effectively enough) to the people at large who need real help in tackling the issues and problems they confront in their real lives. I agree that there are a sizable number of books and pop articles and suchlike that do address the needs of people at large to be informed about scientific, technical, philosophical issues. Some of them work well enough; some of them are, indeed, excellent - but clearly the need for clarity is far greater than currently brought by the light that's been shed.
Doubtless the professional and other practitioners of 'academic scholarship and convivial discussion' are entirely capable of identifying in just what 'technical areas' they feel they need to progress; doubtless they are entirely capable of conducting enough 'academic scholarship and convivial discussion' to make whatever progress they feel they may need; doubtless they're also largely capable of discussing issues with each other (notwithstanding the Gottlob Frege story recounted above).
However, I'd suggest that, thus far, 'the practitioners' have not been able to find out just how they might effectively communicate their work and their findings to the people at large who're crying out for help in most of their daily concerns. (Very little such help is actually reaching them from all the vast amounts of knowledge that has been gathered by 'academic scholarship and convivial discussion').
For people at large, the light that's been spread has not been quite sufficient to help them in their daily lives.
Much of the debate and discussions right here at Math-teach confirms this claim.
I further claim that it's entirely possible - RIGHT NOW! - to shed plenty of light on a variety of complex issues for people at large, to make immediate improvements to a host of systems within which we live and work and play (and think).
AN EXAMPLE: One such issue (of interest to the people at large) is the fairly important question of how to bring about 'effective public school education'. As I've understood from the debate I've seen here, the major recommendations that have come about (from one faction) are to:
"PUT THE EDUCATION MAFIA IN JAIL!" and/or "BLOW UP THE SCHOOLS OF EDUCATION!"
Now these clearly are recommendations - clear to me, at least - that simply cannot work, which are, in two words, utterly ridiculous. They don't work as 'real recommendations'; they don't work as satire or irony or jest.
However, the opposing faction(s) have not yet, to the best of my understanding, come out with any kind of action plan to ensure (at least some) progress on effective public school education. This is simple enough to do, given an appropriate language and simple tools to enable the variety of *stakeholders* in the issue to:
a) articulate their ideas; and then to b) 'integrate' those available ideas into an effective action plan to accomplish appropriate Missions on the issue.
+++ *Stakeholders: students; teachers; parents; school administrators; educational experts; subject experts; politicians; others interested in the issue. +++
Instead of identifying these simple 'things to do', the practitioners of 'academic scholarship and convivial discussion' are, unfortunately, conducting YET MORE 'academic scholarship and convivial discussion' - which is not needed AT ALL to start work towards developing systems to ensure effective public school education.
Indeed, I claim that with available knowledge - of human psychology; of how people learn; of how teachers and students interact; of systems; etc, etc - we are indeed capable RIGHT NOW of creating pretty effective public school education within just a couple of years. (But those foolish recommendations continue unabated - and 'the practitioners' continue their unending 'academic scholarship and convivial discussion'!)
By the way, it does sometimes strike me that there MUST be some profound flaw in the understanding - by 'the practitioners' themselves - of the 'foundations of 'logic' [and possibly of math as well] that they go this route of conducting YET MORE 'academic scholarship and convivial discussion' - when all that's needed is to:
a) get the stakeholders together; b) gather their available ideas; c) 'integrate' the good ideas into an action plan. I observe that items 'a' and 'b' above are already being done regularly in the many forums of debate we currently have today. There is little or no understanding of HOW to accomplish 'c' amongst members of both the faction that has come out with those fatuous recommendations or amongst 'the practitioners of academic scholarship and convivial discussion'.
The above is the way to tackle the issue of 'improving the public school education system'. END OF EXAMPLE
On looking through the above, I find that, in fact, what I've described in outline is also the 'general system' approach to tackling almost any societal problem or issue confronted. All that's needed is simply to identify the appropriate 'stakeholders' for each specific problem or issue that comes to mind and then to get to work in the simple way suggested above. In practically EVERY case, you'll find that we do have right to hand, right now, ALL the needed knowledge to tackle most of the underlying problems and to make some real and quite significant progress - without any further 'academic scholarship and convivial discussion' (of the kind that has been conducted thus far). [I'm NOT suggesting that 'academic scholarship and convivial discussion' be discontinued - just that we should start practically applying to real issues what is readily available]. PLENTY of knowledge is available; little ever gets practiced).
It may also happen that the above simple approach suggested to problem solving and decision making on the systems issues that we confront may also lead to progress on foundational issues, and of issues about 'logic' and 'mathematics'. But that's for the stakeholders in there (i.e., 'the practitioners' themselves) to do, in any way they please.
By the way, I do happen to know ZFC 'fairly well', though I will not claim now (many years after grad school in math) that I'm an 'expert practitioner'.
It's very good stuff indeed (often even profound), but - as you surely know - by no means does ZFC take care of 'the foundations' adequately (as you seem to be claiming it does). It was, in fact; to some extent at least, this perception of mine that led me to study 'systems' - and since then I've been occupied in trying to develop practical means of using 'systems' to enable people apply the results of 'academic scholarship and convivial discussion' to issues of concern to people at large. (I have, from time to time, been outlining thoughts on some of these issues).