What is the foundations of mathematics?
when i look at the foundations of mathematics books 1st edition (by Thomas Q. Sibley). The first chapter is about laguange, logic and set. The second is about proof.
If the foundations is like that, what's the reason?
I though, foundation is something that make it strong and enough to grew up. The principals are quite similar with the building of a house and all the materials support it to stand up. Language, logic, set, proof is essential part. We can't share mathematics idea without language. Logic is about studying the correct reason, it's true or false. Mathematics investigations is just about true or false, so i think it's relevan, since it was developed a long time ago by Aristotles. Set is the most fundamental concept in mathematics, it's about how to collect a distinct objects. It's also relevan. At the end, i agree with Mr. Sibley.
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
From the philosophy it self. There are three school that very influent the mathematicians and philosophers at the first time.
when i look at the foundations of mathematics books 1st edition (by Thomas Q. Sibley). The first chapter is about laguange, logic and set. The second is about proof.
If the foundations is like that, what's the reason?
I though, foundation is something that make it strong and enough to grew up. The principals are quite similar with the building of a house and all the materials support it to stand up. Language, logic, set, proof is essential part. We can't share mathematics idea without language. Logic is about studying the correct reason, it's true or false. Mathematics investigations is just about true or false, so i think it's relevan, since it was developed a long time ago by Aristotles. Set is the most fundamental concept in mathematics, it's about how to collect a distinct objects. It's also relevan. At the end, i agree with Mr. Sibley.
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
From the philosophy it self. There are three school that very influent the mathematicians and philosophers at the first time.
- Platonism: "Platonist, such as Kurt Godel, hold that numbers are abstrack, necessarily existing objects, independent of the human mind."
- Formalism : "Formalists, such as David Hilbert, hold that mathematics is no more or less than mathematical language. It is simply a series of games..."
- Intuitionism : "Intuitionist, such us L. E. J. Brouwer, hold that mathematics is a creation of the human mind. Numbers, like fairy tale characters, are merely mental entities, which would not exist if there were never any human minds to think about them."
http://en.wikipedia.org/wiki/Foundations_of_mathematics
1 comment:
good luck
Post a Comment