There are three different to test for truth on knowledge claims.
1) Coherence test, which checks if everything works together without any contradictions. You use your own personal knowledge to check if it works. "You have to think"
2) Correspondence test, you examine what happens in the world and relate it back to the truth that you are trying to check. You have to look carefully at the language and then go look for the answer yourself or look at what others might have come up with. "You have to go and check"
3) Pragmatic test. You have to look at the knowledge in which it could be used in practice and estimate if it applies or not. "You have to ask yourself if it works"
Sometimes we use our own experiences to know if something is true or not. We find out if we can accept a certain truth or not. Sometimes people speak of "truth-for-me" this is a concept in which you think something to be true but another person doesn't accept it and consider it to be true. Therefore it is only true for ourselves and it is the same as a belief.
A mathematical truth offers knowledge if you can actually prove that true to be true. But sometimes mathematical truths might not give you the knowledge that you were hoping for but just a formula to which you will never have an answer. For example in math when you say something is equal to something else by using this symbol = this automatically shows to another person reading the problem that something is = to something else and so this must be true. Then using a known formula you try to find the answer to the certain problem.
Another example of a mathematical truth is Andrew Wiles, he believed a theorem to be true but in order to demonstrate that the to the world and have people believe him he had to come up with a proof for this truth. As he worked for it for a very long time and really believed in the certainty that this theorem was true he finally came up with a proof that was correct and was able to call this theorem: true.
One of the ways that you can know if mathematical knowledge is by looking at the mathematical language. Mathematical language is said to be something that is always true. With the theorems and proofs that are made for each problem, people rely greatly on mathematics.
A mathematical truth is said to be: "Most often used to mean in accord with fact or reality, or fidelity to an original or to a standard or ideal. The commonly understood opposite of truth is falsehood, which, correspondingly, can also take on a logical, factual or ethical meaning." And a mathematical language is: "The system used by mathematicians to communicate mathematical ideas among themselves." So does that mean that others who aren't mathematicians can't use this language or don't understand it? To speak the mathematical language you have to be able to understand the different registers of the language, it is something, like every other language, that you have to learn. So when we talk about the truth given by the mathematical language i don't think that this is something that everyone can comprehend. The mathematicians between them when they talk they understand each other because they have specific words and terms that they use to explain what they want to say. If you don't know these terms and don't understand them how can you know if what they are saying is true?
Then again, when mathematicians make proofs to make a certain mathematical statement correct there are always other mathematicians that come after that try to make their proof true so how can you truly know when something is true or not.
So in conclusion, I think I would say that mathematical knowledge gives you truth to some extent. If you have proofs to prove that a certain mathematical equation is true or if you do all the truth checks than you can say that it is true. But even after all those truth checks how can you know if something is completely true? Won't there always be little things keeping us from getting to a pure truth? Sometimes in math you just have to trust the formulas and the givens and you have to believe that in the world that we live in today this is what is true.
Good girl: you went right to the 3 truth checks and you incorporated language as a WoK. That was good thinking. In terms of the truth checks, though, after you mentioned them, you dropped them; a better idea would have been to apply those truth checks to mathematics with real examples. I think that would have revealed interesting insights. Anyway, you're on the right track.
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