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> That doesn't mean "there are truths that humans can never prove", all it means is that we have to extend our axiomatic systems in order to prove some truths.
by KMag 8y ago
> That doesn't mean "there are truths that humans can never prove", all it means is that we have to extend our axiomatic systems in order to prove some truths.
But the very interesting part is that you might keep extending and extending two axiomatic systems until every true statement is provable in one or the other system. However, you're guaranteed that in that case, the two systems will be inconsistent with each other such that they cannot be combined into a consistent whole.
- paganel 8y agoGenuine question: how will we know that we have reached the point where “every true statement” is provable? What about unknown unknowns? Is there a “concept” (for a lack of a better word) for these “unknown unknowns” in modern logic? I know neo-Platonism (Plotinus and his friends) was circling around this idea/concept, but truth be told I haven’t read all that much coming from them, plus they may be reguarded by modern logicians/mathematicians as maybe too “mystical”.