Caledonian: What evidence do you offer us that mathematical descriptions cannot produce the properties of which you speak?
First of all, let’s be clear regarding what we have to work with. Things are complicated a little by the variety of specific theories and formalisms used in physics, but let’s take multi-particle quantum mechanics in the configuration basis as illustrative. The configurations are all of the form ‘A particle of species a1 at location x1, and a particle of species a2 at location at x2,...’, and so forth. The quantum states consist of associations of complex numbers with such configurations. There is the basic dynamical fact that a quantum state ψ evolves into another state ψ + dψ according to the Schrödinger equation, and (if you’re not taking the many-worlds path) Born’s postulate that the probability of there actually being particles a1, a2,… at locations x1, x2,… is |ψ|^2.
Then there are various entities and facts that can be obtained from these through abstraction, deduction, and comparison, e.g. ‘the number of particles in configuration c’ or ‘the average number of expected particles in quantum state ψ, as calculated via the Born probabilities’ or ‘the Hilbert-space inner product of states ψ1 and ψ2’. We could, if necessary, describe a formal combinatorial grammar describing all and only those entities and facts implied by the theory-defining postulates in my first paragraph. It would amount to saying: the entities and relationships directly postulated by the theory exist, and so do those which can be logically or mathematically inferred from those postulates. But speaking informally, all we have to work with are featureless spatial configurations of point particles, superpositions thereof, dynamics of superpositions, and empirical probabilities derived from superpositions.
And what sort of entity or property are we trying to extract from the theory, if we are trying to derive consciousness from physics? It’s tiresome to resort repeatedly to the same example, but nonetheless, let’s consider color: the variety of hues and shades which we lump together into the natural language categories of red, blue, and so forth. (I put it that way because I do not want to turn this into a discussion of whether those natural language categories are “natural kinds”. Focus instead on the numerous instances of color which populate visual experience and which unquestionably exist, regardless of how they get categorized.) On one side we have “quantity and causality”, as I put it above—and I’ll even throw in spatial geometry and dispositional behavior; on the other side, the colors. How might we go about making the latter out of the former?
There are some things we can do. We can quantify certain things about subjective color; and we can describe certain physical realities which are somehow correlated with color. Thus 450-nm wavelength light “is” a type of blue light. But I submit that it makes no sense to say that when you see a particular shade of blue, you are “seeing a length”; or that blue itself “is a length”. That might do as a poetic description of the physics behind the perception, but as an ontological statement, it simply substitutes the correlated geometric property for the sensory property we are trying to explain.
Another approach is the cognitive one: things are blue because your nervous system classified them that way. But although the correlated purely-physical property is a lot more complicated here, it’s the same story. Put informally, to use this as an explanation of blueness is to say that our perceptions turn blue because we call them blue or think they are blue.
I think Dennett would understand my point, but as usual he bites the bullet and denies that color is there. He calls it “figment”—figmentary pigment—because according to physics, there is nothing actually blue, inside or outside one’s head. But blueness is there, therefore that ontology is wrong.
“Emergence” is a popular dodge: colors and other subjective properties, though not being identical with any elementary physical property, somehow “emerge” when a brain enters the picture. Apart from being vague, that’s just dualism: if the emergent properties are not identical with one of the purely physical properties in that combinatorial grammar I mentioned, then it is different from all of them, no matter how correlated it is.
As I said, my answer is to turn it around, and to say that the existence of blueness (etc) is axiomatic, and so it must be one of the things that a true and complete theory of reality would be about. It is as if one were to look at electromagnetism and say, my God, those things we thought were lengths, they’re actually colors! - rather than vice versa. But it’s also my thesis that when you look at doing this in detail, some of the obvious candidates for this ontological inversion, such as “computational states of neurons”, present too many specific difficulties to work (in that case, because a computational state of a meso-scale system like a neuron is a vague property, microphysically speaking). Thus I find myself pursuing quantum ontological exotica.
Caledonian: What evidence do you offer us that mathematical descriptions cannot produce the properties of which you speak?
First of all, let’s be clear regarding what we have to work with. Things are complicated a little by the variety of specific theories and formalisms used in physics, but let’s take multi-particle quantum mechanics in the configuration basis as illustrative. The configurations are all of the form ‘A particle of species a1 at location x1, and a particle of species a2 at location at x2,...’, and so forth. The quantum states consist of associations of complex numbers with such configurations. There is the basic dynamical fact that a quantum state ψ evolves into another state ψ + dψ according to the Schrödinger equation, and (if you’re not taking the many-worlds path) Born’s postulate that the probability of there actually being particles a1, a2,… at locations x1, x2,… is |ψ|^2.
Then there are various entities and facts that can be obtained from these through abstraction, deduction, and comparison, e.g. ‘the number of particles in configuration c’ or ‘the average number of expected particles in quantum state ψ, as calculated via the Born probabilities’ or ‘the Hilbert-space inner product of states ψ1 and ψ2’. We could, if necessary, describe a formal combinatorial grammar describing all and only those entities and facts implied by the theory-defining postulates in my first paragraph. It would amount to saying: the entities and relationships directly postulated by the theory exist, and so do those which can be logically or mathematically inferred from those postulates. But speaking informally, all we have to work with are featureless spatial configurations of point particles, superpositions thereof, dynamics of superpositions, and empirical probabilities derived from superpositions.
And what sort of entity or property are we trying to extract from the theory, if we are trying to derive consciousness from physics? It’s tiresome to resort repeatedly to the same example, but nonetheless, let’s consider color: the variety of hues and shades which we lump together into the natural language categories of red, blue, and so forth. (I put it that way because I do not want to turn this into a discussion of whether those natural language categories are “natural kinds”. Focus instead on the numerous instances of color which populate visual experience and which unquestionably exist, regardless of how they get categorized.) On one side we have “quantity and causality”, as I put it above—and I’ll even throw in spatial geometry and dispositional behavior; on the other side, the colors. How might we go about making the latter out of the former?
There are some things we can do. We can quantify certain things about subjective color; and we can describe certain physical realities which are somehow correlated with color. Thus 450-nm wavelength light “is” a type of blue light. But I submit that it makes no sense to say that when you see a particular shade of blue, you are “seeing a length”; or that blue itself “is a length”. That might do as a poetic description of the physics behind the perception, but as an ontological statement, it simply substitutes the correlated geometric property for the sensory property we are trying to explain.
Another approach is the cognitive one: things are blue because your nervous system classified them that way. But although the correlated purely-physical property is a lot more complicated here, it’s the same story. Put informally, to use this as an explanation of blueness is to say that our perceptions turn blue because we call them blue or think they are blue.
I think Dennett would understand my point, but as usual he bites the bullet and denies that color is there. He calls it “figment”—figmentary pigment—because according to physics, there is nothing actually blue, inside or outside one’s head. But blueness is there, therefore that ontology is wrong.
“Emergence” is a popular dodge: colors and other subjective properties, though not being identical with any elementary physical property, somehow “emerge” when a brain enters the picture. Apart from being vague, that’s just dualism: if the emergent properties are not identical with one of the purely physical properties in that combinatorial grammar I mentioned, then it is different from all of them, no matter how correlated it is.
As I said, my answer is to turn it around, and to say that the existence of blueness (etc) is axiomatic, and so it must be one of the things that a true and complete theory of reality would be about. It is as if one were to look at electromagnetism and say, my God, those things we thought were lengths, they’re actually colors! - rather than vice versa. But it’s also my thesis that when you look at doing this in detail, some of the obvious candidates for this ontological inversion, such as “computational states of neurons”, present too many specific difficulties to work (in that case, because a computational state of a meso-scale system like a neuron is a vague property, microphysically speaking). Thus I find myself pursuing quantum ontological exotica.