&gt; Formal mathematics has no concept of absolute truth ...<p>Well, it does. If you drag the propositional calculus into the fray, &quot;true&quot; is arbitrarily but probably most elegantly defined as following:<p>true(x) = x or not x<p>False is defined like this:<p>false(x) = x and not x<p>These definitions are pretty much arbitrary. The lambda calculus does this:<p>true(a,b)=a<p>false(a,b)=b<p>It also works absolutely fine.<p>&gt; It&#x27;s just concerned with axioms and theorems (and their proofs)<p>In the general case, theorems are indeed &quot;provable&quot; or &quot;unprovable&quot; (not &quot;true&quot; or &quot;false&quot;).<p>However, if a theorem has exclusively been derived from propositional calculus, it can also be &quot;true&quot;.<p>Gödel&#x27;s incompleteness is exactly about statements that are &quot;true but unprovable&quot;. In terms of propositional calculus, the theorem is &quot;true&quot; but since you can show that the theorem can never be derived from the axioms, it is also &quot;unprovable&quot;.