Register to reply

Math and logic

by alvin51015
Tags: logic, math
Share this thread:
alvin51015
#1
Jul31-14, 03:48 AM
P: 10
In the late 1980's I asked my logic professor if there was some kind of logical and/or mathematical process which unified numerically based mathematics with true-false based symbolic logic.He told me that someone had written a lengthy book which apparently proved that it was totally impossible to do such a thing.But I keep thinking that there must be a way.So my question is whether any progress had been made in this area in the last twenty plus years.
Phys.Org News Partner Mathematics news on Phys.org
Researcher figures out how sharks manage to act like math geniuses
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space
jedishrfu
#2
Jul31-14, 07:51 AM
P: 3,097
You're not thinking of fuzzy logic right? It places a percent to truth values.

http://en.m.wikipedia.org/wiki/Fuzzy_logic

The other thought that comes to mind is Goedels theorem where systems of logic can't prove all their propositions that there will always be something that is unprovable.

http://en.m.wikipedia.org/wiki/Gödel...eness_theorems
HallsofIvy
#3
Jul31-14, 07:54 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682
I really have no clear idea what you mean by "unified numerically based mathematics with true-false based symbolic logic". There were, in the late 19th century, attempts to reduce all forms of mathematics to an "axiom based" form of logic but Curt Goedel, in the early twentieth century showed that such a thing was impossible: given any set of axioms, there exist a statement that can neither be proved nor disproved from those axioms.

Indeed, rather than "true-false based symbolic logic", much of the recent work in logic has been the other way- "multi-valued logics" and "fuzzy logic" where statement are NOT just "true or false" but may have varying degrees of "trueness".

homeomorphic
#4
Aug1-14, 01:26 PM
P: 1,303
Math and logic

given any set of axioms, there exist a statement that can neither be proved nor disproved from those axioms.
Any set of axioms powerful enough to do arithmetic. Proposition logic is an exception, for example.

The numerically-based math reduced to symbolic logic sounds kind of like the construction of the real numbers and all that from set theory. It's not really reduced to symbolic logic, but it's reduced to sets.

As far as recent developments go, this came to mind:

http://blogs.scientificamerican.com/...al-revolution/
HallsofIvy
#5
Aug1-14, 01:47 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682
Quote Quote by homeomorphic View Post
Any set of axioms powerful enough to do arithmetic. Proposition logic is an exception, for example.
Yes, I should have said that.


Register to reply

Related Discussions
Question in math logic Calculus & Beyond Homework 2
Math logic Set Theory, Logic, Probability, Statistics 1
Math Logic problem Calculus & Beyond Homework 4
Prove this math logic Calculus & Beyond Homework 2
Suppose Math and Logic were all there is General Discussion 37