Not one of the fundamental properties, but definable in terms of them.
In other words, present in the same way “diamond” is—there’s no property “green” in the fundamental equations of physics, but it “emerges” from them, or can (in principle) be defined in terms of them. (I’m embarrassed to use the word “emergent”, but, well...)
To use an analogy, there’s no mention of “even numbers” in the axioms of Peano Arithmetic or in first order logic, but S(S(0)) is still even; evenness is present indirectly within Peano Arithmetic. You can talk about even numbers within Peano Arithmetic by writing a formula fragment that is true of all even numbers and false for all other numbers, and using that as your “definition” of even. (It would be something like “Ǝy(S(S(0))y) = x)”.) If I understand correctly, “standard physical ontology” is also a formal system, so the exact same trick should work for talking about concepts such as “diamond” or “green”—we just don’t happen to know (yet) how to define “green” the same way we can define “diamond” or “even”, but I’m pretty sure that, in principle, there is a way to do it.
is exactly like saying that if you count through the natural numbers, all of the numbers after 5 x 10^37 are blue.
Let’s compare the plausibility of getting colors out of combinations of the elementary properties in standard physical ontology, and the plausibility of getting colors out of Peano Arithmetic. I think the two cases are quite similar. In both cases you have an infinite tower of increasingly complex conjunctive (etc) properties that can be defined in terms of an ontological base, but getting to color just from arithmetic or just from points arranged in space is asking for magic. (Whereas getting a diamond from points arranged in space is not problematic.)
There are quantifiable things you can say about subjective color, for example its three-dimensionality (hue, saturation, brightness). The color state of a visual region can be represented by a mapping from the region (as a two-dimensional set of points) into three-dimensional color space. So there ought to be a sense in which the actually colored parts of experience are instances of certain maps which are roughly of the form R^2 → R^3. (To be more precise, the range and domain will be certain subsets of R^2 and R^3.) But this doesn’t mean that a color experience can be identified with this mathematical object, or with a structurally isomorphic computational state.
You could say that my “methodology”, in attempting to construct a physical ontology that contains consciousness, is to discover as much as I can about the structure and constituent relations of a conscious experience, and then to insist that these are realized in the states of a physically elementary “state machine” rather than a virtual machine, because that allows me to be a realist about the “parts” of consciousness, and their properties.
Let’s compare the plausibility of getting colors out of combinations of the elementary properties in standard physical ontology, and the plausibility of getting colors out of Peano Arithmetic.
In one sense, there already is a demonstration that you can get colors from the combinations of the elementary properties in standard physical ontology: you can specify a brain in standard physical ontology. And, heck, maybe you can get colors out of Peano Arithmetic, too! ;)
At this point we have at least identified what we disagree on. I suspect that there is nothing more we can say about the topic that will affect each other’s opinion, so I’m going to withdraw from the discussion.
What does “present indirectly” mean?
Not one of the fundamental properties, but definable in terms of them.
In other words, present in the same way “diamond” is—there’s no property “green” in the fundamental equations of physics, but it “emerges” from them, or can (in principle) be defined in terms of them. (I’m embarrassed to use the word “emergent”, but, well...)
To use an analogy, there’s no mention of “even numbers” in the axioms of Peano Arithmetic or in first order logic, but S(S(0)) is still even; evenness is present indirectly within Peano Arithmetic. You can talk about even numbers within Peano Arithmetic by writing a formula fragment that is true of all even numbers and false for all other numbers, and using that as your “definition” of even. (It would be something like “Ǝy(S(S(0))y) = x)”.) If I understand correctly, “standard physical ontology” is also a formal system, so the exact same trick should work for talking about concepts such as “diamond” or “green”—we just don’t happen to know (yet) how to define “green” the same way we can define “diamond” or “even”, but I’m pretty sure that, in principle, there is a way to do it.
(I hope that made sense...)
Here I fall back on my earlier statement that this
Let’s compare the plausibility of getting colors out of combinations of the elementary properties in standard physical ontology, and the plausibility of getting colors out of Peano Arithmetic. I think the two cases are quite similar. In both cases you have an infinite tower of increasingly complex conjunctive (etc) properties that can be defined in terms of an ontological base, but getting to color just from arithmetic or just from points arranged in space is asking for magic. (Whereas getting a diamond from points arranged in space is not problematic.)
There are quantifiable things you can say about subjective color, for example its three-dimensionality (hue, saturation, brightness). The color state of a visual region can be represented by a mapping from the region (as a two-dimensional set of points) into three-dimensional color space. So there ought to be a sense in which the actually colored parts of experience are instances of certain maps which are roughly of the form R^2 → R^3. (To be more precise, the range and domain will be certain subsets of R^2 and R^3.) But this doesn’t mean that a color experience can be identified with this mathematical object, or with a structurally isomorphic computational state.
You could say that my “methodology”, in attempting to construct a physical ontology that contains consciousness, is to discover as much as I can about the structure and constituent relations of a conscious experience, and then to insist that these are realized in the states of a physically elementary “state machine” rather than a virtual machine, because that allows me to be a realist about the “parts” of consciousness, and their properties.
In one sense, there already is a demonstration that you can get colors from the combinations of the elementary properties in standard physical ontology: you can specify a brain in standard physical ontology. And, heck, maybe you can get colors out of Peano Arithmetic, too! ;)
At this point we have at least identified what we disagree on. I suspect that there is nothing more we can say about the topic that will affect each other’s opinion, so I’m going to withdraw from the discussion.