Friday, October 18, 2019

Hegel's Absolute Idealism from an AI perspective

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A second pass these last few days at Hegel's The Phenomenology of Mind (Spirit), a notoriously obscure but central work of the great German philosopher.

I ought to have read Hegels' book in the original German, but of course even native German speakers struggle with Hegel's technical and obscure terminology. It's never going to happen for me.

I rejected reading it in translation - it's still too hard and in any case, I'd be studying the translator's view of what Hegel really meant.

Perhaps a guide to The Phenomenology of Spirit? I have this:


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.. but it still presupposes that the reader has grasped the problem Hegel is trying to address.

So in the end I reverted to Peter Singer (top of page) who assumes no special prior knowledge. And I learned that in the Middle-Ages under feudalism, there was no real questioning of what kind of thing the world might be (ontology) because the Bible told us that God had made it. Likewise there was no discussion about how we could come to know things (epistemology) because divine revelation was always to hand.

The rising bourgeoisie, with its campaign against superstition and arbitrary authority and its championing of transactional-rationality demanded a rethink. So we had Descartes' famous 'Cogito' and Kant's famous 'thing-in-itself' which we could never know .. and Hegel's attempt to finally resolve these issues and put Kant right.

Marxists believe that Marx in the end resolved most of these problems and I think that's right.

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There is a tradition that says that philosophers create artificial problems by over-abstracting - and then spend their careers failing to solve them. Over-abstraction means ignoring essential features of the problem - things like agency (in epistemology) and evolutionary biology (in ethics, morality and aesthetics) and social praxis (in ontology).

AI has often allowed philosophical problems of excruciating obscurity to be recast as engineering problems badly misunderstood.

What does AI (and mathematical logic) have to say about Hegel's Phenomenology of Mind?

I have some notes.

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Hegel's forms of consciousness

1. Sense-certainty

The raw elements of percepts. Like bitmaps.

The problem: uninterpreted, private and incommunicable as knowledge.

2. Perception

Codification of sensory data in a language of object and predicate names (like first-order logic). Requires a prior language. Formalised as a set of grounded atomic formulae ('facts').

The problem: where did the language come from? Not sense-experience - so must be a-priori.

3. Understanding

The interpretation of categorised sensory data in a web of knowledge and inference. Formalised as grounded atomic terms plus a relevant prior theory ('facts' + 'rules').

The problem: where did it come from? Similarly problematic to Perception above.

4. Self-consciousness

We now consider a consciousness which knows itself to be a consciousness and worries about how it comes to have facts and rules about the world. This requires a transition to named agents and epistemic logic.

Let a, b, .. be agents and K the epistemic operator.

If a knows the fact: 'the cat is in the mat' we write:

K(a, on(cat, mat)).

Trying to understand the concept of self-consciousness leads Hegel to his celebrated master-slave discussion and the notion of the 'unhappy consciousness'.

Mind becomes aware of itself as mind. It becomes aware of its theories, which give meaning to reality, as subsets of some universal theory which accurately captures all the objects and relationships which constitute universal history in its great narrative of development and progress.

Agents (individual people) are able to internalise part of this overarching theory - reflecting their partial and historically-limited experiences. But they can also be aware that absolute knowledge nevertheless exists - the upper bound of what can ever be collectively known about the universe.

Singer observes that it's difficult to understand what Hegel's ontological commitments are in his Absolute Idealism.

Consider this.

If there is some universal theory, U, then we can consider the model of that theory which comprises formal agents and their separate cognitive states in their environments over all time. The movie of the universe, if you like, expressed in a mathematical, computational sequence of states.

Yet this description is also a notated object in some 'programming language' and therefore also a theoretical construct.* Perhaps this program-plus-output is what is meant by 'universal knowledge'?

Could this be what Hegel was groping for, a century before programming languages were developed?

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* For more technically-inclined readers, what we are talking about here is a term algebra, or Herbrand universe. See the Wikipedia article.

3 comments:

  1. I wonder whether the "Master-Slave" model is better represented in a different way in Agent Theoretic/Computational form. My point is to consider two Agents A and B - each modelled computationally. We need to examine whether the pair {A,B} is itself an Agent/Computational agent of the same "type" as A and B separately.

    Very naïve formally that is:

    (Hegel's Question) -- Given A:T and B:T is {A,B} :T ?

    Hegel's answer (and mine) is "no". Agent's A and B can see that a larger entity exists which comprises them both - but can they access it??

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    Replies
    1. I agree: Hegel doesn't seem to want the concept of a composite mind. The 'Universal Ideal' seems his underlying ontology - one to which the philosopher is led by reason alone. I'm still thinking about this.

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    2. Well if you agree with this, then hopefully you will be interested in the other work I have been doing in this area.

      Right now I am studying "Game Semantics" (which I mentioned in a recent comment). One form of it called "Computability Logic" has been very active over the last 15 years. The idea here is that the two agents are "Agent" and "Environment". It is an attempt to invent a logic semantically, and does map onto FoL and has solved problems not solvable in Denotational Semantics.
      I am expecting to uncover some issues involving "idealist structures" in this logic, as I have found elsewhere.

      One of the origins of "Idealist" structures in Mathematics comes from D.Hilbert's classification of mathematical proofs and objects into "Constructive/Real" objects and "ideal" objects. His source of this was "Ideal Points" which appear in Algebraic (or Projective) Geometry. These are needed to prove some theorems, but they aren't "real".

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