Joe Niederberger posted Jul 2, 2013 7:00 PM (GSC's remarks interspersed): > > G S Chandy > >Our previous exchanges at this thread clearly > indicate that the 'world of academic scholarship and > convivial discussion' itself has thus far failed to > "say what 'mathematics' and 'logic' may mean > > This is quite absurd. This is large body of > literature from the last 150 years which shows that > people have not only agreed to fix the terms math and > logic precisely enough to discuss, study, and draw > conclusions, they've delved into incredibly precise > details about exactly how, why and where logic fails > to capture "classical" mathematics, and this has led > to a profusion of new understandings about logical > systems, formal systems, axiomatics, new sorts of > restricted mathematics, etc. etc. etc. > What IS absurd is something quite different from what you have supposed.
Did I ever disagree with your above claims? I do dispute that the job undertaken by "people" (i.e. logicians, mathematicians and philosophers over the past 150-odd years) has been done with the "precision" that you wrongly attribute to their agreement. In fact, the job has not been done with 'adequate *effectiveness*' to make much of a difference to the lives of ordinary people, and this can be readily demonstrated (though I do not here undertake to provide that demo in full). There are, however, a couple of interesting instances discussed.
As clearly in evidence (see below, for a specific instance) in the daily lives of people everywhere, the 'agreements' that have no doubt been reached in the world of academic scholarship and convivial discussion have not adequately impacted the real world around us. (This statement applies to scholarship much more broadly than just to math and logic [and philosophy]).
In any case, I don't believe that the world of academic scholarhip and convivial discussion would dispute that there is considerable room for improvement and progress in practically all the 'discussions, studies and conclusions' that have occurred over the past 150 years. (In fact, this very 'argument' between the both of us is - to my mind - clear evidence that our entire discussion needs to move into another mode for any progress to be made).
I believe I've already explicitly stated my broad agreement with your claims above - except for the description "precise" (and the implicit satisfaction that you are expressing with the studies made, conclusions drawn: the studies made, conclusions drawn are not adequate at all).
I quote from the first paragraph of the paper to which you had kindly provided a link (at yours dt. Jun 30, 2013 1:29 AM at http://mathforum.org/kb/message.jspa?messageID=9150440): QUOTE "THE THREE CRISES IN MATHEMATICS: LOGICISM, INTUITIONISM AND FORMALISM", by Ernst Snapper:
The three schools, mentioned in the title, all tried to give a firm foundation to mathematics. The three crises are the failures of these schools to complete these tasks" UNQUOTE > > That was the entire point of my first response to > this thread. > OK.
And that, by the way, was not AT ALL my point of disagreement with you!!! (OR, for that matter, with 'the world of academic scholarship and convivial discussion'. I do have great admiration for what has been accomplished, though - as earlier stated - I do disagree with your description "precise").
(Note CAPS). > > On the other hand, when you print in all capital > letters "IS INCLUDED IN", I have no idea what you > mean. Do you mean set theoretical inclusion? Why not > say so? Or if its not, how does it differ? As I > pointed out, if you do mean something like that then > the notion that logic "IS INCLUDED IN" math is quite > out there on the spectrum of craziness. Why bother? > 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 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.
(It probably also "INCLUDES" something a bit more than what I've stated above - which I'm unfortunately unable adequately to specify in 'pure prose'. I am not sure I can specify it in p+sg either. However, Shakespeare does seem to have gotten it just about right in some words he gave to Hamlet: "There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy"). > > As far as I can tell ps+g doesn't even turn over, > much less take off. > That's "as far as you can tell". I.e., that's your opinion. OK by me.
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.
There is much in the Ernst Snapper article that I'd like to quote in support of the above contentions - but unfortunately I'm unable right now to 'cut-paste' from there. (I hope to be able to do something about this in due course). I try to recall just one of the arguments in it:
<<...even Peano had seriously mistaken ideas about the real purpose of formalization. He published one of his most important discoveries in differential equations in a formalised language that no one could understand until someone translated it into ordinary German...>>
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'.