Joe Niederberger posted: > G S chandy says: > >We do need p+sg for any effective and efficient > discussion > > OK, let me try again, again. I don't accept that at > all. Effectively the world of academic scholarship > and convivial discussion rejects your claim by virtue > of their practice. > *Effectively*, "the world of academic scholarhip and convivial discussion" has indeed ALWAYS attempted to reject my claim(s) "by virtue of their practice". (Their practice continues - as ineffectively as ever).
However, instances are there in plenty in the 'real world' to indicate that 'academic scholarship and convivial discussion' are (in **practically all** cases) not quite adequate to resolve real issues being faced in the real world by real people. The daily news on every front is replete with examples.
We have one such issue to hand right here at Math-teach, "improving public school education in the USA", I believe it is:
One side to the discussion has been claiming that the only way out now is to "PUT THE EDUCATION MAFIA IN JAIL!" and/or to "BLOW UP THE SCHOOLS OF EDUCATION!" (as advised by one Reid Lyon [reading research expert]) and someone else). The 'other side' apparently wishes to have further 'academic scholarship and convivial discussion' (in the same old way).
And so the issue continues: "'round and 'round the mulberry bush" - no real resolution in the real world seems to be possible.
**I have no empirical studies available, but I believe that 'the world of academic scholarship and convivial discussion' seems to have reached an inflexion point of sorts:
a) We can choose to continue with 'academic scholarship and convivial discussion' in the same old fashion (i.e., using 'pure prose'), which apparently leads only to further 'academic scholarship and convivial discussion' in the same old fashion - with issues rarely (if ever) getting resolved for real people in the real world.
b) We can consider the possibility of enhancing the 'academic scholarship and convivial discussion'. I claim this could be done if we would look to enhance the language used in 'academic scholarship and convivial discussion' so as to enable us actually to resolve and move ahead on issues confronted by real people in the real world. > > If you cannot say what "mathematics" and "logic" mean > (in your context, to support your propositions), > without recourse to your favorite formalism, indeed, > there is nothing to discuss. > OK, as you like. I disagree.
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 (in the context of that world, to support that world's propositions) in any of its own favorite formalisms"!
I believe we had in outline discussed 'logicism'; 'intuitionism'; 'formalism' and 'computationism'. The 'world of academic scholarship and convivial discussion' (using its own favorite formalisms) has failed thus far to say what 'mathematics' and 'logic' might be.
I do not necessarily disagree with the various propositions put up by these schools of thought; like you, I do have plenty of respect for what has been achieved through these approaches.
But (to me at least; and to a few others, I believe) it seems clear that we DO need a language that could perhaps help us resolve issues in the real world: as earlier noted, I do NOT have empirical studies in evidence - I 'intuit' that we need something more that could enable us to go somewhat deeper.
To put it in the simplest possible terms:
We all do want a process that enables anyone to put up an endeavour, say: "To improve my results in my math exams" and then, using his/her CURRENTLY AVAILABLE good ideas, to work effectively towards that, improving the available ideas as the individual or group goes along. (Of course, the process should fetch better results than the conventional means should - or there's no point in learning a new and unfamiliar way of working).
Or for goals like "To get myself a good and satisfying job". Like "To become a top-rate software designer".
ALL of the above (as well as many other goals) have been very successfully accomplished by a number of individuals, using precisely the 'formalism' I have proposed. A few 'organisational goals' have also been accomplished (with slightly lesser success than the individual goals).
It could possibly be done for a Mission like: "To clearly say what 'mathematics' and 'logic' are". This will, like the above, demand the active participation of those who wish to go further on the Mission than they have done thus far (through use of the conventional 'formalisms').
(I personally have not worked on this Mission at all as I am ENTIRELY satisfied simply to use 'math' and 'logic' as I have understood these subjects. There do seem to be some doubts in the current schools of thought on the subjects - my questions in the title of this thread reflect some of these doubts. I do believe some progress may be possible. As noted earlier, I do not have empirical studies available to confirm my belief).
It can be done likewise for very MUCH more ambitious goals, for instance: "To reduce, very significantly, malnutrition in India, within 5 years". I have not yet got the appropriate groups [involving voluntary organisations AND government bodies] to get together on this very ambitious Mission. However, there does seem to be some interest from a couple of voluntary organisations; however, we have not yet got the appropriate government bodies interested. So, let's see what happens.
Whatever, there DOES seem to be plenty more to discuss, though you seem to disagree on this.