Is this statement true about mathematical propositions?

[TruthIsBeauty]

Homework Statement

"The propositions of mathematics work like this: we believe them first, and only later do we try to prove them."

Homework Equations

N/A

The Attempt at a Solution

I read it in some philosophy book but I'm not sure if it's true because I thought the propositions were not believed nor disbelieved until they were proven.

I apologize if I posted in the wrong section. I've just started using forums and I couldn't find any other section that seemed relevant to my question.

 

[HallsofIvy]

I don't believe for a moment that is true. Of course, we have to decide which propositions we are going to try to prove and perhaps the author is asserting that those are the ones we "believe" are true. I would say, rather, that they are the ones we suspect are true.

 

[micromass]

No, this is not true at all. This is not how mathematics works.

 

[TruthIsBeauty]

No, this is not true at all. This is not how mathematics works.

Would you mind explaining why it's not true? I would really appreciate it.

 

[Mark44]

In mathematics, we don't start off with a large number of propositions that we assume are all true ("believe" to be true), and then later work our way through them, proving that they are true.

How it really works is that we start with a small number of axioms or postulates (e.g., Axiom of Choice, Parallel Postulate - parallel lines never intersect), and using them, derive and prove many more statements (often called theorems). What the proofs do is show that the theorems must be true as long as the initial axiomatic hypotheses are true.

Sometimes mathematicians challenge the axioms, and end up developing new areas of mathematics. For example, non-Euclidean geometry arises from assuming that parallel lines can intersect (see http://en.wikipedia.org/wiki/Non-Euclidean_geometry).

The writer whom you quote lumps all these into one amorphous word: proposition. It's no surprise to me that the writer is not a mathematician.

 

[TruthIsBeauty]

In mathematics, we don't start off with a large number of propositions that we assume are all true ("believe" to be true), and then later work our way through them, proving that they are true.

How it really works is that we start with a small number of axioms or postulates (e.g., Axiom of Choice, Parallel Postulate - parallel lines never intersect), and using them, derive and prove many more statements (often called theorems). What the proofs do is show that the theorems must be true as long as the initial axiomatic hypotheses are true.

Sometimes mathematicians challenge the axioms, and end up developing new areas of mathematics. For example, non-Euclidean geometry arises from assuming that parallel lines can intersect (see http://en.wikipedia.org/wiki/Non-Euclidean_geometry).

The writer whom you quote lumps all these into one amorphous word: proposition. It's no surprise to me that the writer is not a mathematician.

Thank you very much. I knew something was wrong when the author tried to substantiate his weak argument by using that quote.

 

[genericusrnme]

You are correct, the author is wrong
If you want a good book on propositional logic try How to Prove it - A Structured Approach

A proposition is simply a statement that you want to try and prove
The closest thing to what your author described would be an axiom, axioms are assumed but you can't prove axioms since you'd be using the axioms to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using to prove the axioms that you're using