Math exists in the minds of humans, [not animals].

This is incorrect. Every animal we’ve ever researched, including insects like bees, can do arithmetic.

Anyway, not a single one of the examples you’ve given involves second-order reasoning. These are all prosaic interactions with the environment, which is how most animas (yes, including dumb humans) experience the world.

First-order reasoning: “What is moral?” Second-order reasoning: “Do moral beliefs constitute knowledge claims?”

First-order reasoning: “One plus one is two.” Second-order reasoning: “number theory is either inconsistent or incomplete.”

First-order reasoning: “What does this word mean?” Second-order reasoning: “How do words connect with their meanings?”

The examples I gave you are extreme, but to be fair so is your confusion.