GPT4 is certainly not fulfilling the definition of reasoning. It's borrowing the intelligence of every human who wrote something that went into its model.

To demonstrate this, ask it to prove something that most or all people believe. Say some "intuitive" math thing. Perhaps the fact that factorial grows faster than exponential functions.

And no, don't just have it explain it, have it prove it, as in a full mathematical proof. Give it a minimal set of axioms to start with.

Merriam-Webster's definition of "reasoning" [1] says that reasoning is:

> the drawing of inferences or conclusions through the use of reason

So starting GPT4 off with some axioms would give it a starting point to base its inferences on.

Then, if it does prove it, take away one axiom. Since you started with a minimal set, it should now be impossible for GPT4 to prove that fact, and it should tell you this.

Having GPT4 prove something with as few axioms as possible and also admit that it cannot prove something with too few axioms is a great test for if it is truly reasoning.

[1]: https://www.merriam-webster.com/dictionary/reasoning