Mathematics, Logic, and Intuition

Date: 05/27/2003 at 03:47:28
From: Anne Xavier
Subject: Nature of math in view of logic and intuition

How is math related to logic and intuition?

Date: 05/27/2003 at 09:08:37
From: Doctor Edwin
Subject: Re: Nature of math in view of logic and intuition

Hi, Anne.

Strictly speaking, logic is just a kind of math. Instead of having 
values like 1, 99, or 2935112, in logic you have values of true and 
false.

Instead of operations like PLUS and DIVIDED BY, you have operations 
like AND and OR.

So instead of arithmetic equations like:

 4    PLUS   11  = 15

you get

 true AND  false = false

The mathematical treatment of logic was invented by George Boole in 
1854, so it's often called Boolean algebra. You can modify it to 
include more human concepts like "90% true" or "90% certain that it 
is true" (two different things, right?).

Some people say that intuition is a process that is beyond the 
explanation of logic and mathematics. That's an appealing idea. It'd 
be nice to think that there is a place in us that has some kind of 
magic, a place where we do a kind of thinking that can't be captured 
by rules.

But I think that there can be more magic in complex systems of rules 
than is obvious. What do you think?

- Doctor Edwin, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 05/28/2003 at 12:37:35
From: Doctor Peterson
Subject: Re: Nature of math in view of logic and intuition

Hi, Anne.

Did you try searching our site for the word "intuition"? Here is one 
discussion that you might find useful:

   Mathematics and Intuition
   http://mathforum.org/library/drmath/view/52284.html 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/