Theories of Mind (Part 5): Armstrong’s Identity Theory

This post marks the fifth installment in my series on the nature of the mind. In this post, we will critically evaluate Armstrong’s identity theory. For requisite context, it would be best to check out Parts 1, 2, 3, and 4. Let’s dig in!


  1. Armstrong’s Identity Theory

In this section, I outline Armstrong’s central argument for his identity theory of the mind. I then critically evaluate the plausibility of this theory.

3.1 Armstrong’s Central Argument

Armstrong’s theory (presented in his article “The Nature of Mind”) is a version of reductive materialism according to which (i) only physical, material things (objects, properties, relations, etc) exist, and (ii) mental properties, states, and events (in particular) are identical to physical processes, states, and events of the physical brain (in particular).

The primary motivation Armstrong adduces in support of this view is that the progress and tremendous success of science gives us reason to think that a complete account of humans can and will be given in purely physico-chemical terms. The tremendous successes of molecular biology and neurophysiology, in particular, along with their progress and trajectory, make it very likely that the complete account of the human person will be wholly physical and chemical.

3.2 Critical Appraisal of Armstrong’s Central Arguments

Criticism One: Neuroscience does not tell in favor of Armstrong’s hypothesis

Rather than validating Armstrong’s hypothesis that neuroscience will give a complete account of the human person in purely physico-chemical terms, arguably neuroscience has reinforced the inadequacy of such an account in principle. For, despite the success and progress of neuroscience, we are not closer to solving the hard problem of consciousness: why are any of those neural firings, ion movements, chemical transmissions, and so on associated with any qualitative, subjective, first-personal states?

Indeed, the more we study neuroscience, the more intractable the problem seems. We can specify as many of the facts as we want about the velocities, positions, momentums, sizes, shapes, colors, masses, charges, textures, movements, and so on about the neurons, molecules, and atoms in the brain, but it seems there will always be the further question: why is any of that accompanied by inner, subjective, qualitative experience?

Criticism Two: Question-begging

Suppose the mind is, after all, immaterial. If that is true, then science is methodologically inept to determine its intrinsic nature and existence. This is because science is inherently restricted to the investigation of publically accessible, third-person, physical things. But that means that anything immaterial, private, and first-person is beyond the scope of scientific methodology. But if that is true, then science could not possibly arbitrate on the nature and existence of the mind. It follows, then, that the very claim that science can and will arbitrate on the nature and existence of the mind presupposes that the mind is not immaterial (i.e. is material). But that is the very thing Armstrong aims to establish by means of his argument. Hence, he seems to beg the very question at issue.


Criticism Three: Rasmussen’s counting argument contra identity theory

Philosopher Joshua Rasmussen5 provides a forceful counting argument against materialism. Premises one and two are based on Rasmussen’s original argument, while the other premises are my additions.

P1: For any class of physical properties, the ps, there could be a mental property of thinking that the ps are physical.

P2: There are more classes of physical properties than there are physical properties.

C1 (P1, P2): Therefore, there could be more mental properties than physical properties.

P3: If the nature of mental properties were identical to the nature of physical properties, then there could not be more mental properties than physical properties.

C2 (C1, P3): Therefore, the nature of mental properties is not identical to the nature of physical properties.

P4: If C2 is true, then Armstrong’s identity theory is false.

C3 (C2, P4): Therefore, Armstrong’s identity theory is false.

To motivate premise one, it is useful to consider an example. Consider shapes. “Given any class of shapes,” writes Rasmussen, “we can coherently describe a unique mental property in terms of those shapes. There is a procedure for doing so: for any class of shapes, the qs, there is a distinct mental property of thinking that the qs are shapes.” Similar procedures can be run for other physical properties and, importantly, physical properties as such. In this way, we actually have a coherent procedure for identifying a unique mental property for any class of physical properties so this is not a matter of merely begging the question against the physicalist by a premise without independent procedural support.

Premise two is simply Cantor’s theorem: for any particular items, the classes of those items have a higher cardinality than (i.e. outnumber) the items themselves. From this, it follows that the classes of physical properties outnumber the physical properties themselves.

Premises three and four seem reasonably self-evident. We therefore seem to have reason to reject Armstrong’s identity theory on the basis of the counting argument. What’s more, it seems that the counting argument lends support to some form of dualism, since it shows that the nature of mental properties cannot be identical to the nature of anything physical.

Author: Joe



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  5. The counting argument is interesting. Reminds me a little of Patrick Grim’s Cantorian argument against omniscience. I haven’t read Rasmussen’s presentation of the argument, but I wonder how it would fare against a more up-to-date version of physicalism. It seems like a functionalist could just admit that there are more mental properties—understood as abstract functional properties—than physical properties, but deny that all those mental properties are actually realized and thereby avoid committing herself to the claim that there must be at least as many physical properties as mental properties. But I may be missing something.

  6. I found a paper in which Rasmussen presents his counting argument. Very interesting. Rasmussen seems to agree that his argument—which clearly targets the type-identity theory—isn’t necessarily a problem for every kind of materialist theory. But it seems to me that there’s even a version of the type-identity theory that survives the counting argument—David Lewis’s version, which holds that mental properties are (analytically) functional properties that (as a matter of contingent fact) are realized only physically, and that mental properties are identical to the physical properties that realize them. A Lewisian identity theorist would just have to admit that there are unrealized mental properties that are not identical to physical properties. And I don’t see why that would be contrary to the spirit of Lewis’s theory, since it already allows that there are possible worlds in which realized mental properties are not identical to physical properties.

    Although I haven’t read Armstrong, Lewis seems to think he and Armstrong share pretty much the same theory. Which makes me wonder how much Rasmussen’s argument really threatens Armstrong’s view.

    Also, even if there are more mental properties than physical properties, it doesn’t seem like the counting argument can show that there are more phenomenal properties than physical properties, since Rasmussen’s procedure doesn’t seem to allow us to define a corresponding phenomenal property for each set of physical properties. So the argument also seems to leave open the possibility that phenomenal properties are identical to physical properties.

    If you need something to help you sleep, I go on about all this at greater length at

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