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P obviously can't be infinite, even in theory, if you want the computation to terminate.

Right, but then as others said, then you are also arguing that humans cannot reason, since the universe is a system with a finite number of particles. Or if we exclude external factors, because humans have a finite number of brain cells.

In the end it all depends on what your definition of reasoning is, which you did not provide.

The bit precision of computation is always finite for halting computations and any finite computation can be turned into a lookup table which does no thinking or reasoning other than comparing two numbers and then extracting the value corresponding to the input key.

My argument carries through for any piece of software so if you think software can think and reason then you can remain unconvinced by my argument.

In any case, I have to drop out of this thread.

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