To have a thought, you have to be able to represent the objects of that thought in your brain. One of the first answers you see in the thread is somebody making an argument related to mathematics: "N+1 is greater than N" counts as a thought, for any N (therefore there are infinitely many thoughts). But umm, for very very large N, I don't think anyone is actually representing N in their brain (practically or even theoretically). Some numbers are so large, so as to take days/months/years/decades to recite. Why should those thoughts count?

edit: looks like people are talking about that too.

I think when we alias numbers, we're not necessarily representing them cognitively.

I'd take recourse to https://en.wikipedia.org/wiki/Bremermann%27s_limit

All human thought processes appear to require some irreversible physical processes in order to occur. (not some fancy quantum process that might turn out to proceed in a way that avoids the energy limit of computation)

Together with Bremermann's Limit, this means that we can put a limit (albeit a very large one!) on the amount of thought that can ever happen. You'd get a smaller limit considering the earth or solar system vs the entire universe, but it'd still be finite.

So if you just start with the infinite thoughts "There is a natural number 0", "There is a natural number 1", and so on, there must be a unique smallest (finite!) natural number X for which the statement "There is a natural number X+1" will never be thought.

I think if you frame thoughts as the biochemical product of a set of neuron activations, then maybe the answer is no, there cannot be an infinite possible many thoughts because biochemical reactions can be deterministic, and stable biochemical reactions don’t have more than a few end states.

But maybe the answer could be yes, if the question is considered using a quantum chemistry framework, where thoughts and thinking are modeled using quantum mechanics. It’s an interesting question.

Yes.

Thoughts are formed through constructive and destructive interference, not linear logic (as in conventional computation.) In this way thoughts are more like chemical reactions.

The infinite nature of thoughts are similar to infinite infinites existing, though anyone will only ever have a finite number.

Most of your thoughts are in fact rubbish, and your brain filters them out unless they meet some learned threshold for normalization.