Intuitionistic Logic
Author
Hey there oh wise ones, I have a bugging question to ask...
Bit 'o background,
I've recently deducted that my mind is better suited towards constructivism and intuitionistic logic, and always have been. From high school onwards I've always pretty much self-taught myself because the teaching methods in England weren't based upon constructivist views.
My mathematical question is this(not that I actually understand much maths apart from some of it's philosophical origins): Is it possible for me to remain within the intuitionistic branch of maths without using classical logic, and if it is possible, would it benefit me or not?
I'm actually wanting to learn maths because it ties in closely with how Lisp works and I'd like to understand it's mathematical origins. :)
Any help would be appreciated. :)
[Edited by - malune on February 22, 2005 8:16:44 AM]
Hi! I think you should instead stick to influentialisticism.
That word doesn't mean anything either, but it sounds way cooler than either of your two!
That word doesn't mean anything either, but it sounds way cooler than either of your two!
Author
Quote:Original post by Squirm
Hi! I think you should instead stick to influentialisticism.
That word doesn't mean anything either, but it sounds way cooler than either of your two!
That wasn't very nice. Have you heard of Socrates? Maybe you should read up about him and find out one of the reasons he was so famous - for thinking outside the box and not assuming he knew everything, in fact he prefered thinking he knew nothing.
Anyway, if you want to cure your ignorance: http://mathworld.wolfram.com/IntuitionisticLogic.html
I did check with dictionary.com first - both words definitely weren't in there :)
Have to admit, that page makes absolutely no sense to me whatsoever . . .
Have to admit, that page makes absolutely no sense to me whatsoever . . .
Constructivist
Intuitionist
Now where is that google smiley.... :D
I do not know what exactly you are asking though, Malune.
Intuitionist
Now where is that google smiley.... :D
I do not know what exactly you are asking though, Malune.
Author
Quote:Original post by Squirm
I did check with dictionary.com first - both words definitely weren't in there :)
Have to admit, that page makes absolutely no sense to me whatsoever . . .
Here's the dictionary reference to intuitionist.
http://dictionary.reference.com/search?q=intuitionist
I couldn't find anything for constructivism unfortunately in that dictionary - weird. I did spell it wrong in the OP though - sorry about that. I found a nice little page describing things adequately here(haven't had the chance to read it but it mentions socrates ;)): http://www.cdli.ca/~elmurphy/emurphy/cle.html
Author
Quote:Original post by TheWanderer
Constructivist
Intuitionist
Now where is that google smiley.... :D
I do not know what exactly you are asking though, Malune.
Basically, my understanding of maths is that it's foundations lie within logic. Now I may be very wrong, but if the foundations are logic, then if I take a completely different approach to studying logic, will this affect all further studies or will I be obliged to learn classical logic in order to be able to learn anything useful. In other words, can intuitionistic logic be used for the foundations of my mathematical knowledge - or will it dissalow me to learn methods which are based upon classical logic?
Well, intuition does play a large role in the mathematical process. If you've ever heard of a conjecture, then you know that I am talking about. Still, it is important that the logical basis behind a conjeture be thoroughly explored. Doing so usually leads to a better understanding of what is being studied (as well as possibly results that follow the conjecture).
No, it is not impossible to be an "intuitionist" (as I understand it) and learn math. You will be missing out on a very important part though.
No, it is not impossible to be an "intuitionist" (as I understand it) and learn math. You will be missing out on a very important part though.
Author
Quote:Original post by TheWanderer
Well, intuition does play a large role in the mathematical process. If you've ever heard of a conjecture, then you know that I am talking about. Still, it is important that the logical basis behind a conjeture be thoroughly explored. Doing so usually leads to a better understanding of what is being studied (as well as possibly results that follow the conjecture).
No, it is not impossible to be an "intuitionist" (as I understand it) and learn math. You will be missing out on a very important part though.
What do you mean by a very important part? As in what specifically will I miss out on?
Classical logic is entirely intuitive to me, so I don't have your problem.
The basis of lisp is in structural induction, recurrences and so on.
The basis of lisp is in structural induction, recurrences and so on.
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