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Our reading group is working through Hegel’s The Philosophy of Mind, Part III of the Encyclopedia. In view of previous connections with nLab interests, I’m keeping an eye open.
How about Section 391 Zusatz:
The soul, when contrasted with the macrocosm of nature as a whole, can be described as the microcosm into which the macrocosm compresses itself and thereby sublates its asunderness. Accordingly the same determinations which in outer nature appear as freely disengaged spheres, as a series of independent shapes, are in the soul demoted to mere qualities.
as hinting at Type as object classifier?
Then again the continuation is less plausibly about HoTT:
The soul stands midway between the nature which lies behind it, on the one hand, and the world of ethical freedom which extricates itself for natural mind, on the other hand. The simple determinations of soul-life have their dispersed counterpart in the universal life of nature; similarly, that which in the individual man has the form of subjectivity, of a particular urge, and is within him unconsciously, as simply something he is, unfolds in the political state into a system of distinct spheres of freedom, into a world created by self-conscious human reason.
I think from the nature of the subject matter we had a justification to hope that some of the first book of the “Science of Logic” had a decent reflection in modern foundations of mathematics and physics. But when it comes to life and the mind it seems unreasonable to expect direct (instead of complex emergent) reflections in foundational formalism.
If I were asked to say where a “Philosophy of Mind” might connect to a mathematical-scientific picture of reality I would go for something that when I was a kid I found well-expressed in Erich Jantsch’s book “The Self-Organizing Universe”.
I am hoping that once I finally understand the foundations of physics, I’ll still have time left to come back to this kind of exploration… :-)
With Hegel, though, there are always reflections of the Logic with first Nature and then Mind. Later chapters of the Logic talk about mechanism, chemism, teleology, life, cognition, and all this before the Idea becomes absolute and it comes to see that it needs to externalise itself. Logic is supposed to be God’s thinking before the Creation. The Creation is a necessary manifestation of God, echoed by the Gospel story of God made flesh.
You can decide not to buy into the later parts of the Encyclopedia, but since there is a continual re-running of the same structures as in the Logic, it shouldn’t be a surprise to find resonant passages in the later parts.
All right, but I feel something is being pushed too far if we have “soul” and “object classifier” in the same sentence. Not sure how to handle this at this point…
’Soul’ is more like Aristotle’s psuche, if that helps. Plants and animals have lesser forms of them. Hegel has emphasised how the passage from matter to plant to animal to mind is one of overcoming separation, e.g., all pieces of matter can do is exclude one another from occupying the same space.
Yes, actually I am sympathetic to this. I have a feeling that resonates well with what you say and quote above, a deep feeling actually.
But I am worried about communication. Hegel is the towering example of what happens when one expresses deep feelings as theory: people who don’t get the vibes will become upset and eventually bend over backwards to avoid further interacting with such kind of thoughts. I suppose that’s why it says: That which can be said should be said clearly, that which cannot be said (yet…) we should remain silent about.
Here when we speculate that we might find psuche (or Atman, I suppose) in the concept of “object classifier”, actually myself, I can connect to that,vaguely. But I am worried that we repel everybody else… unless we provide more substance.
That’s why I mentioned that book. I expect that actually one can (or could) give more substance to this. Do you know that book by Jantsch which I mentioned above? That book tries to sketch a route from the foundations of physics to concepts such as “soul” which is, I think, plausible as a template for what could once become hard science. At the same time it is such that when one steps back (and squints ones eyes) one can recognize the old ideas of Brahman/Atman etc. realized, which it seems Hegel has picked up.
No I haven’t read Jantsch.
We have a student working on historical conceptions of the boundary between poetry and philosophy. In the twentieth century it becomes much more sharply defined. So Carnap sees metaphysicians as failed poets or musicians, resorting to the wrong medium to express an attitude towards the world. And then there’s Wittgenstain in the Tractatus warning us to be silent about things which cannot be said. Not that this is to belittle the latter. He was a thoroughgoing mystic himself. Curious how things changed from earlier times, where evocations of the transcendental were more the norm.
But this internal reflection of the external has a long history, including Leibniz’s monads, reflecting better or worse the happenings of all other monads. While this has admittedly a strongly speculative flavour, it’s surely quite traditional to think about thought as capturing the world, as in p. 84 of Conceptual Mathematics.
I’m reminded of something I came up against when I started my MSc in London, having previously read categorical logic. It was evident to me that logic was just a fragment of mathematics, but this completely went against Anglo-American philosophy at the time, for which there was a great divide between a structureless logic, capable of expressing propositions and their deductive relations, and mathematics, whose content was expressed in axioms. With propositions-as-some-types, the passage from what seems on the side of judgement, say, an existentially quantified statement, to what seems to be just things in the world, as with a dependent sum, can now be used to promote the logic-as-fragment view.
Still, logic as calculus of judgements has a grip. Perhaps one sees this in trying to interpret modal types. It seems much easier to think in terms of propositions being qualified by the modalities of possibility and necessity.
Thanks, that’s very well said. Maybe we could have an Lab entry with some thoughts along these lines?
Regarding modal types: I came to think that modality is actually better expressed in types than in propositions. For propositions, a modality is a “way of being true”. (For instance “being necessarily true”.) But for a type, a modality is just “a way of being”. For instance “being pointed” for maybe-modal types.
I am really unsure if the standard choice of terminology in modal logic “necessity”, “possibility” is more than wishful thinking in that I don’t see that what the S4 modalities express is well captured by these words.
On the other hand for modal types, the situation is much better. “being pointed”, “being homotopy invariant”, “being codiscrete” are all modalities of types that make clear sense.
But what distinguishes such “ways of being” from the possession of properties? “The blue ball” and “the ball which is blue-ly”.
Is it that in the case of general properties there’s no unit/counit mapping? For any space I can consider what it would be for it exist codiscretely or discretely, and even have a comparison morphism in each case, but for a red ball I can’t consider what it would be for it to be blue, or at least wouldn’t have any way of relating them?
So for instance “being pointed” is not property, but structure.
It is precisely idempotent (co-)monads which, when thought of as modalities of types, encode just property, no structure, in that the EM category of algebras over an idempotent monad is just the full subcategory of the original category of types on those that have the given property. In general the “algebra structure over the modality” is genuine extra structure.
As for the red/blue example, one might formalize this by looking at the slice topos over a set of colors. Then there is on that one idempotent monad for each color whose modal types are the uni-colored objects.
Incidentally, did you see this here from a few days ago:
Penrose and Hameroff on quantum vibrations in microtubules and conciousness
Haven’t watched the video yet, but from the summary I gather that 20 years after one of Penrose’s more concrete suggestions for how the Hegelian triangle works
he ran into somebody who had been studying structures of the kind Penrose may have been envisioning as necessary for part of this story.
Since we came back to this in another thread, I’ll mention here, too:
I have added some of the above discussion about modal operators expressing a “way of being” of types at the beginning of modal type.
Regarding #11 above: maybe we don’t want an entry on this “orch OR” thing itself on the Lab, but given that this is Penrose speaking here, maybe we might at least have a pointer to it in the outskirts of the Lab, I have created an entry quantum biology in order to accomodate such a pointer.
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