Responding to Joe Niederberger's post of Jul 3, 2013 11:27 PM (pasted below my signature for reference):
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'm not claiming that Warfield's developments [by way of what I call 'p+sg'] WILL provide the complete and firm foundation for math. Merely that it could help make what's now current a little bit firmer - at least for us ordinary mortals. That would be quite useful to help us find out just what 'the world of academic scholarship and convivial discussion' may be accomplishing in the real world by all that convivial discussion.
I quote from my earlier post dt. Jul 3, 2013 7:29 AM (http://mathforum.org/kb/message.jspa?messageID=9152752), to which points you had (cannily?) not troubled to respond: > >My argument broadly claims: > > > >1. Ordinary language often fails to communicate > adequately about the inter-relationships between > factors in the complex systems within which we live > and work (and play). We do try to do that but > generally fail to do so effectively, BECAUSE, in > ordinary language, we lack a means to communicate > clearly about such inter-relationships. > > > >A great many of (if not most of) our disputes - > sometimes even amounting to war! - arise because of > this lack. > > > >2. A very similar proposition holds for 'formalised > languages' (notwithstanding your above-noted claims > about the many successes of the developments over the > last 150 years or so posted by 'the world of academic > scholarship and convivial discussion'). > > > >In fact, 'the world of academic scholarship and > convivial discussion' often appears - to people > OUTSIDE that world - to be interested in talking only > to people INSIDE that world. (Note CAPS). That world > generally does not appear to have much interest in > helping ordinary people resolve the problems and > issues that ordinary people face at every level in > their real lives. Some of these issues are of > earth-shaking importance; some are relatively simple > everyday concerns. To provide just a couple of > instances that come immediately to mind: > > > >i) 'Anthropogenic climate change'; > > > >ii) "Enabling ordinary people to UNDERSTAND just what > it is that 'the world of academic scholarship and > convivial discussion' may be convivially discussing. > > > > > >By 'ordinary people' I mean John and Jane Doe - which > here includes the political and bureaucratic leaders > who make HUGE decisions that impact all of us in our > daily lives. By and large (in fact, in MOST cases), > these decisions are made wrongly, causing enormous > difficulties to people at large - even raining death > and destruction upon them. The 'world of academic > scholarship and convivial discussion' could surely > help, very significantly, to improve the 'quality of > decision making in public affairs' that we see all > around us every day of our lives - but it shows > little interest in anything except more 'academic > scholarship and convivial discussion'. > > > >A specific instance: The recent flash floods in > Uttarakhand state in India - which have cost at least > 10,000 lives and billions of rupees of loss and > damage, which will take generations to repair - were > almost entirely attributable to wrong decisions being > made over at least the last two to four or five > decades made by our political and bureaucratic > leaders. Most of those decisions could have easily > been made correctly so as today to have prevented > much of that death and destruction - if only 'the > world of academic scholarship and convivial > discussion' had taken the least seriously its > connection to the real world. > > > >iii) "Improving our educational systems". We have, > >by and large, broadly come to agree that this is a > crucial 'systems improvement' needed in all nations > around the world (including the USA). In the US, you > seem to have reached a state in which one faction > wishes to: > > > >- -- "PUT THE EDUCATION MAFIA IN JAIL!" and > >- -- "BLOW UP THE SCHOOLS OF EDUCATION!" > > > >while another faction wishes to conduct further > 'academic scholarship and convivial discussion'. > > > >We have reached somewhat a similar state in India > (given cultural and other societal differences > between the US and India). > > > >I don't see 'the world of academic scholarship and > convivial discussion' contributing much to the > resolution of this state of apparent societal > paralysis. Actually, the resolution to this specific > issue is rather simple: stakeholders just need to > understand, with greater clarity, just what is the > 'action meaning' of the relationship "CONTRIBUTES > TO". (Note all CAPS). > > > >In 'p+sg' we have a minor extension to 'pure prose' > that could contribute quite significantly to 'fill in > the gaps'. > > In fact, looking over that response of mine, I observe that you've not responded to ANYTHING argued there!! This IS what does tend to happen when discussions are conducted in 'pure prose' when a vehicle like 'prose + structural graphics' is required.
For instance you claim (something to the following effect): "I haven't got the vaguest of notions from this discussion ....".
In the main, I'd guess that is BECAUSE we're using an inappropriate 'language vehicle' for the discussion.
In part, it is probably because you are unwilling (or unable) to step beyond the bounds of what is already familiar to you. This is quite a common condition, and I believe it must have been precisely to address such a condition that Warfield developed his approach to systems science, involving the creation of an appropriate 'language vehicle' to help us discuss complex issues. (I do see there is an apparently irreconciliable conflict here. So be it: we humans have encountered many such in our journey through history. History does resolve all issues, in some way or the other).
I notice that Anna Roys (dt. Jul 4, 2013 12:30 AM - http://mathforum.org/kb/message.jspa?messageID=9153112) has made the useful point: > > Perhaps logic is plural and new logics may be developed > ? > There is much to explore in that idea. Unfortunately, the 'language of pure prose' is, by and large, an inadequate vehicle to enable any such exploration.
Joe Niederberger posted Jul 3, 2013 11:27 PM: > G S Chandy says: > - > ------------------------------------------------------ > - > When I print the phrase "IS INCLUDED IN" in all > capital letters I do "INCLUDE" 'set theoretical > inclusion' - but something more, which has not > (quite) been captured yet by 'the world of academic > scholarship and convivial discussion', I'm afraid: at > least not with the precision you attribute to it. > This failure arises mainly, I claim, from their > r failure to use a form of language adequate to > resolve the issues being discussed. > > In brief, I mean that it is a 'transitive > relationship' AND that the idea of the functions of > various transitive relationships in any system - > including 'systems of thought' - have not been > adequately or *effectively* explored by that world of > academic scholarship and convivial discussion. > - ------------------------------------------------ > > Set theory seems to me to do an admirable job of > defining precisely what the word (or symbol) > "includes" means (when used in that theory.) And if > we can borrow that precise meaning outside the theory > proper, by that meaning, its easy to see most of the > world would not consider it true, or even useful, > that math includes logic. In a Venn diagram we > wouldn't draw logic as a little circle inside an > encompassing circle labelled math. We might draw two > intersecting circles, or, if one is a holdout for > logicism, draw math as a little circle inside a > larger circle labelled logic. Or forget the diagrams. > It seems uncontroversial that there is more to logic > than math. Likewise, it seems that there is more to > math than just logic, but that really only comes into > play when dealing with infinity is some way or other. > Most of the world, seems to me, doesn't really need > the > actual infinities some mathematicians prize so > highly, but I'm duly impressed by Hilbert calling it > Cantor's paradise. Some people absolutely *adore* the > idea. > > So, I think that's precise enough, whereas what you > write above (and I've quoted,) I find completely > vague. > > G S Chandy says > >There are, as you may have noticed, a huge number of > people in this world (other than you). A great many > of them do feel (in their 'real' lives) that 'the > world of academic scholarship and convivial > discussion' has not adequately captured their real > needs and concerns by way of 'academic scholarship > and convivial discussion'. Instances of such > 'feelings' on their part abound everywhere in every > aspect of our real lives. Instances that indicate > that these feelings are not unjustified also abound. > > So, you think answers to these questions you have > posed about math, logic, and your vague "IS INCLUDED > IN" relation, have some vital interest for the mass > of humanity? I don't believe it. Math, and the > technologies it helps make possible, are doing fine, > I think, without those particular answers. I could be > wrong, but I haven't gotten even the vaguest of > notions from this discussion what those interests > might be. > > Cheers, > Joe N