Godel cant tells us what makes a maths statement true-thus his theorem is meaningless.

I've previously debated this topic with my opponent, but not very well. I'll attempt tackle this again, hopefully with more clarity. My opponent claims that "Godel cant tells us what makes a maths statement true-thus his theorem is meaningless." [sic] His argument, then, appears to be as follows: P1: A meaningful theorem must tell us what makes a maths statement true. P2: Gödel's theorem does not tell us what makes a maths statement true. C: Gödel's theorem is not meaningful.P1 is absurd and my opponent has not presented any argument to establish its truth. Since no mathematical theorem seeks to prove what makes a mathematical statement true, and instead seek to deduce logical consequences given certain true statements, P1 is the equivalent of assuming that all of mathematics is meaningless. Admittedly if all of mathematics is meaningless then so is Gödel's theorem, but this means my opponent's argument is begging the question. Either a statement or its negation is trueMathematics uses logic to deductively prove mathematical statements from more basic statements which are accepted to be true. In logic, the law of excluded middle states that any statement is either true or false. This is an important aspect of Gödel's proof; if neither a statement nor its negation can be deductively proven using the axioms of a mathematical system, then that system is incomplete. Similarly, the law of non-contradiction states that no statement can be both true and false; if both a statement and its negation can be proven in a mathematical system, then that system is inconsistent. [1] Gödel proves that for many mathematical systems there are statements which cannot be proven true or false; hence they are incompleteAs my opponent quotes, Gödel proves that in any mathematical system which includes some number theory (which is a vast variety of mathematical systems) there are statements which cannot be proven true or false. This means that neither the statement nor its negation can be proven to be true, or that there are true statements which cannot be proven. Therefore, any such mathematical system must be incomplete. He also proved that any mathematical system which can prove all true statements must be inconsistent.It's relevant to note that my opponent's source, Peter Smith, is correct; Gödel did not rely on the notion of truth - he relied on the notion of logical consistency and arithmetical capablilty. This means that Gödel's theorem is meaningful independent of what makes a mathematical statement true. [2] Significance of Gödel's theoremGödel's theorem is considered to be one of the most important mathematical proofs of the 20th century, with relevance to both mathematical logic and the philosophy of mathematics. Gödel demonstrated that a proof establishing the consistency and completeness of arithmetic (an answer to one of David Hilbert's famous questions, and an important aspect of mathematical formalism) is impossible. His theorem shows that mathematics isn't absolutely certain and that such absolute certainty is unattainable, despite the certainty and logic of mathematics often being considered an ideal for philosophers or scientists to strive for. Further, it provides interesting insights into philosophical questions such as whether absolute truth can be known, or the plausibility of artificial intelligence and the limits of computer science. Gödel's theorem extends far beyond mathematics; its conclusion itself is meaningful, as are its implications for mathematics, philosophy, and science: the resolution is negated. [3] References:[1] http://www.stanford.edu...[2] http://www.math.hawaii.edu...[3] http://www.miskatonic.org...