The central point about the temperature example is that facts about which properties really exist and which are just combinations of others are mostly, if not entirely, epiphenomenal. For instance, we can store the momenta of the particles, or their masses and velocities. There are many invertible functions we could apply to phase space, some of which would keep the calculations simple and some of which would not, but it’s very unclear, and for most purposes irrelevant, which is the real one.
So when you say that X is/isn’t ontologically fundamental, you aren’t doing so on the basis of evidence.
Temperature is an average. All individual information about the particles is lost, so you can’t invert the mapping from exact microphysical state to thermodynamic state.
Most of the invertible functions you mention would reduce to one of a handful of non-redundant functions, obfuscated by redundant complexity.
Causality, if we have the true model of physics, is defined by counterfactuals. If we hold everything else constant and change X to Y, what happens? So if we have a definition of “everything else constant” wrt mental states, we’re done. We certainly can construct one wrt temperature (linearly scale the velocities.)
Your model of physics has to have some microscopic or elementary non-counterfactual notion of causation for you to use it to calculate these complex macroscopic counterfactuals. Of course in the real world we have quantum mechanics, not the classical ideal gas we were discussing, and your notion of elementary causality in quantum mechanics will depend on your interpretation.
But I do insist there’s a difference between an elementary, fundamental, microscopic causal relation and a complicated, fuzzy, macroscopic one. A fundamental causal connection, like the dependence of the infinitesimal time evolution of one basic field on the states of other basic fields, is the real thing. As with “existence”, it can be hard to say what “causation” is. But whatever it is, and whether or not we can say something informative about its ontological character, if you’re using a physical ontology, such fundamental causal relations are the place in your ontology where causality enters the picture and where it is directly instantiated.
Then we have composite causalities—dependencies among macroscopic circumstances, which follow logically from the fundamental causal model, and whose physical realization consists of a long chain of elementary causal connections. Elementary and composite causality do have something in common: in both cases, an initial condition A leads to a final condition B. But there is a difference, and we need some way to talk about it—the difference between the elementary situation, where A leads directly to B, and the composite situation, where A “causes” B because A leads directly to A’ which leads directly to A″ … and eventually this chain terminates in B.
Also—and this is germane to the earlier discussion about fuzzy properties and macroscopic states—in composite causality, A and B may be highly approximate descriptions; classes of states rather than individual states. Here it’s even clearer that the relation between A and B is more a highly mediated logical implication than it is a matter of A causing B in the sense of “particle encounters force field causes change in particle’s motion”.
How does this pertain to consciousness? The standard neuro-materialist view of a mental state is that it’s an aggregate of computational states in neurons, these computational states being, from a physical perspective, less than a sketch of the physical reality. The microscopic detail doesn’t matter; all that matters is some gross property, like trans-membrane electrical potential, or something at an even higher level of physical organization.
I think I’ve argued two things so far. First, qualia and other features of consciousness aren’t there in the physical ontology, so that’s a problem. Second, a many-to-one mapping is not an identity relation, it’s more suited to property dualism, so that’s also a problem.
Now I’d add that the derived nature of macroscopic “causes” is also a problem, if you want to have the usual materialist ontology of mind and you also want to say that mental states are causes. And as with the first two problems, this third problem can potentially be cured in a theory of mind where consciousness resides in a structure made of ontologically fundamental properties and relations, rather than fuzzy, derived, approximate ones. This is because it’s the fundamental properties which enter into the fundamental causal relations of a reductionist ontology.
In philosophy of mind, there’s a “homunculus fallacy”, where you explain (for example) the experience of seeing as due to a “homunculus” (“little human”) in your brain, which is watching the sensory input from your eyes. This is held to be a fallacy that explains nothing and risks infinite regress. But something like this must actually be true; seeing is definitely real, and what you see directly is in your skull, even if it does resemble the world outside. So I posit the existence of what Dennett calls a “Cartesian theater”, a place where the seeing actually happens and where consciousness is located; it’s the end of the sensory causal chain and the beginning of the motor causal chain. And I further posit that, in current physical language, this place is a “quantum system”, not just a classically distributed neural network; because this would allow me to avoid the problems of many-to-one mappings and of derived macroscopic causality. That way, the individual conscious mind can have genuine causal relations with other objects in the world (the simpler quantum systems that are its causal neighbors in the brain).
Anyway, the existence of a one-to-one mapping is a necessary but not a sufficient condition for a proposed identity statement to be plausible
What are the other conditions?
That’s way too hard, so I’ll just illustrate the original point: You can map a set of three donkeys onto a set of three dogs, one-to-one, but that doesn’t let you deduce that a dog is a donkey.
(part 1)
Temperature is an average. All individual information about the particles is lost, so you can’t invert the mapping from exact microphysical state to thermodynamic state.
Most of the invertible functions you mention would reduce to one of a handful of non-redundant functions, obfuscated by redundant complexity.
Your model of physics has to have some microscopic or elementary non-counterfactual notion of causation for you to use it to calculate these complex macroscopic counterfactuals. Of course in the real world we have quantum mechanics, not the classical ideal gas we were discussing, and your notion of elementary causality in quantum mechanics will depend on your interpretation.
But I do insist there’s a difference between an elementary, fundamental, microscopic causal relation and a complicated, fuzzy, macroscopic one. A fundamental causal connection, like the dependence of the infinitesimal time evolution of one basic field on the states of other basic fields, is the real thing. As with “existence”, it can be hard to say what “causation” is. But whatever it is, and whether or not we can say something informative about its ontological character, if you’re using a physical ontology, such fundamental causal relations are the place in your ontology where causality enters the picture and where it is directly instantiated.
Then we have composite causalities—dependencies among macroscopic circumstances, which follow logically from the fundamental causal model, and whose physical realization consists of a long chain of elementary causal connections. Elementary and composite causality do have something in common: in both cases, an initial condition A leads to a final condition B. But there is a difference, and we need some way to talk about it—the difference between the elementary situation, where A leads directly to B, and the composite situation, where A “causes” B because A leads directly to A’ which leads directly to A″ … and eventually this chain terminates in B.
Also—and this is germane to the earlier discussion about fuzzy properties and macroscopic states—in composite causality, A and B may be highly approximate descriptions; classes of states rather than individual states. Here it’s even clearer that the relation between A and B is more a highly mediated logical implication than it is a matter of A causing B in the sense of “particle encounters force field causes change in particle’s motion”.
How does this pertain to consciousness? The standard neuro-materialist view of a mental state is that it’s an aggregate of computational states in neurons, these computational states being, from a physical perspective, less than a sketch of the physical reality. The microscopic detail doesn’t matter; all that matters is some gross property, like trans-membrane electrical potential, or something at an even higher level of physical organization.
I think I’ve argued two things so far. First, qualia and other features of consciousness aren’t there in the physical ontology, so that’s a problem. Second, a many-to-one mapping is not an identity relation, it’s more suited to property dualism, so that’s also a problem.
Now I’d add that the derived nature of macroscopic “causes” is also a problem, if you want to have the usual materialist ontology of mind and you also want to say that mental states are causes. And as with the first two problems, this third problem can potentially be cured in a theory of mind where consciousness resides in a structure made of ontologically fundamental properties and relations, rather than fuzzy, derived, approximate ones. This is because it’s the fundamental properties which enter into the fundamental causal relations of a reductionist ontology.
In philosophy of mind, there’s a “homunculus fallacy”, where you explain (for example) the experience of seeing as due to a “homunculus” (“little human”) in your brain, which is watching the sensory input from your eyes. This is held to be a fallacy that explains nothing and risks infinite regress. But something like this must actually be true; seeing is definitely real, and what you see directly is in your skull, even if it does resemble the world outside. So I posit the existence of what Dennett calls a “Cartesian theater”, a place where the seeing actually happens and where consciousness is located; it’s the end of the sensory causal chain and the beginning of the motor causal chain. And I further posit that, in current physical language, this place is a “quantum system”, not just a classically distributed neural network; because this would allow me to avoid the problems of many-to-one mappings and of derived macroscopic causality. That way, the individual conscious mind can have genuine causal relations with other objects in the world (the simpler quantum systems that are its causal neighbors in the brain).
That’s way too hard, so I’ll just illustrate the original point: You can map a set of three donkeys onto a set of three dogs, one-to-one, but that doesn’t let you deduce that a dog is a donkey.