Are there infinitely many possible thoughts?
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First off, it is not quite clear how we define what a "thought" is and what it means for a thought to "be possible". I would like to take colloquial definitions, at least as far as possible one can come to answer the question:
My first thought and claim was that any thought must be determined by a finite sequence of brain states which in turn are determined by the particles the brain is made up of. Since each brain is made up of finitely many particles we would have the following statement:
However, it is not clear whether the premise is true. It would depend whether the space has infinitely many positions such as the four dimensional real space R^4 or the four dimensional space of rational numbers Q^4. However, if there would only be finitely many positions, for example considering the Planck length as the smallest unit of space measure, then the above premise would be true. In addition to that, I think it may not be clear if a thought is really determined by the brain states or the particles the brain is made up of.
