Monday, September 28, 2020

Causal finitism and functionalism

Say that a possible thought content has finite complexity provided that the thought content can be represented by a sentence of finite length in a language whose basic terms are the fundamental concepts in the thought content.

  1. Necessarily, if functionalism is true, then the occurrence of a thought content with infinite complexity requires infinitely many states to cooperate to produce a single effect.

  2. Infinitely many states cannot cooperate to produce a single effect.

  3. It is possible for a thought content with infinite complexity to occur.

  4. So, functionalism is false.

I have two separate ideas to defend (1). First, it seems like a system capable of producing a thought content must go through a number of states proportional to the complexity of that thought content in producing it if functionalism is true. Second, the occurrence of a thought content of infinite complexity requires infinitely many constituent states. Moreover, thoughts have to be unified: to think the conjunction of p and q is not just to think p and to think q but to think them in a unified way. On functionalism, the unification has to be causal in nature. To unify the infinitely many constituent states would require them to have the capability of producing some effect together.

If I were a functionalist, I would deny (3). The cost of that is that then most truths end up unthinkable, which seems implausible.


IanS said...

I would deny (3) regardless of functionalism. We can’t think arbitrarily complex thoughts in a unified way. Maybe God and angels can, but humans cannot.

Suppose I’m given long list of numbers on a sheet of paper. I might work through it thinking “804 is even, 352 is even, …”. At the end, I might conclude that “all the numbers are even”. But I’m not thinking the complex conjunction “804 is even and 352 is even and …”. Rather I’m thinking, “I’ve checked all the numbers, and found them all even.”

On this view, many merely finite conjunctions are in practice unthinkable, and all infinite conjunctions are in principle unthinkable. I don’t see this as a problem: most complex conjunctions, true or not, are just not interesting, not worth thinking about.

Alexander R Pruss said...

But functionalism is not just a thesis about human beings.

IanS said...

True, but isn’t the motivation for functionalism to give an account of our minds? Maybe functionalists would be prepared to concede that minds capable of thinking infinitely complex thoughts (assuming this to be possible) would not be amenable to functionalism.

You evidently think that (3) is true, and that there is a (necessarily non-functionalist) way of thinking infinitely complex thoughts without this being the causal result of infinitely many constituent states. Could you explain how you see this as working?