
Re: Is logic part of mathematics  or is mathematics part of logic?
Posted:
Jul 3, 2013 3:00 PM



Perhaps logic is plural and new logics may be developed ?
On Wed, Jul 3, 2013 at 9:57 AM, Joe Niederberger <niederberger@comcast.net>wrote:
> 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 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 >

