Keith’s Conundrums: Are We Classically Computational or Something Else?

Keith Douglas

Last time, I suggested reflecting on Kant’s “existence is not a predicate.” This was actually targeted to those who have studied formal logic, but only a little. Long story short, Kant is simply wrong, and Russell following him. There are perfectly respectable logics which have a “particularizer” and an existence predicate. Many of these are so-called “free logics.”

Does that entail that we should therefore believe the ontological argument and become theists? No, because the existence predicate tells you which things (and I suppose, properties, if done second order) exist by virtue of a systematic theory of what exists in a given domain. The problem then reduces to: Do gods play a role in the best system of the world (or of any subsystem thereof)? No, is the answer that I and many others would give. And so the system would either postulate that or derive it as a consequence from other principles.

Incidentally, this seems to be the current meaning of axiom; an organizing principle, not necessarily a basic one in some ontological or epistemic sense. Sometimes they are that too, but that itself is often not captured in their content. Another goal can be some sort of parsimony or to show how deletions or additions play a role. For example, the five or so axioms in Moshe Machover’s axiomatic presentation of propositional logic in Set Theory, Logic and Their Limitations each have a role; you get a collection of clearly defined well understood alternative logics by deleting each in turn.

Are We Classically Computational or Something Else?

This allows us to turn to this month’s puzzle. Daniel Dennett (in, for example, his Consciousness Explained) defends the idea that human cognition is essentially computational. Could it be that one reason that it is hard to teach and learn logic is that human cognition uses a different logic than the so-called classical logic? Yet brains are describable using classical mathematics — there’s not much of anything else in, for example, the computational neuroscience literature.

Does that entail that our brain is necessarily classical in that sense, and hence the hypothesis is wrong? Those who understand the notion of “implementation” can move on to another part of the puzzle, which is: If the notion of implementation is relevant, why is it we need to bother with all these non-classical theories anyway?

(Slight aside: This is a toe-in-the-water exploration of what I hope will be a longer work celebrating 30 years of that work of Dennett’s and approximately 25 years of its influence on me. Political philosophy fans can celebrate 50 years of Rawls’ A Theory of Justice too!)