# what true means

**What true means in Gödel’s setting**

True means true of the actual natural numbers, 0, 1, 2, 3 and so on. A statement like “there are infinitely many primes” is true if it holds for those numbers, whether or not anyone can prove it. Truth is the numbers themselves, and a proof is one way of getting at them.

This assumes the numbers are a definite thing that exists independently of our rulebooks. Some accept that (Gödel did). A formalist would say math is only the rules, so “true” means “provable”, and the Gödel sentence is neither true nor false, just undecidable.

Connects to:
- [outside is trust](https://mapideas.org/i/tr_trust)
- [seen from outside](https://mapideas.org/i/th_out)
- [the sentence](https://mapideas.org/i/th_sent)
- [the judge](https://mapideas.org/i/w_judge)
- [the triangle](https://mapideas.org/i/r_tri)
- [gluing obstruction](https://mapideas.org/i/c_glue)
- [Gödel](https://mapideas.org/i/godel)

Sources:
- [Wikipedia: True arithmetic](https://en.wikipedia.org/wiki/True_arithmetic)

Source: https://mapideas.org/i/tr_true · open on the map: https://mapideas.org/#tr_true