
Re: Is logic part of mathematics  or is mathematics part of logic?
Posted:
Jul 3, 2013 1:57 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 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

