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Some of the more pressing arguments against materialism involve their inability to account for abstract objects such as meaning or reference. A few definitions before I continue:

Abstract object: an object that exists outside of time or space and that is causally inert (that is, it doesn't effect matter in any way except possibly through the action of a mind). Common examples are sets, numbers, propositions, facts, and meanings.

Materialism: the position that all facts, or all truths are at base truths about matter. All properties are reducible to physical properties. All things are material things. This position specifically rules out not only God and immortal souls, but also abstract objects, moral goodness, and even minds and thoughts, strictly speaking.

Naturalism: the position that all truths are natural truths. Naturalism is weaker than materialisms; it rules out supernatural entities such as God and immortal souls, but it doesn't necessarily rule out natural things like minds, moral goodness, or abstract objects.

There don't seem to be hardly any naturalists today that are not materialists (this is no doubt due in large part to the astonishing successes of scientific reductionism); however, some of the strongest arguments against materialism involve their inability to account for abstract objects. For example, what physical property could account for the fact that when I think about my car, I am thinking about my car? What physical property of my brain, or the car, or the space between my brain and the car, or anything else could constitute the fact that what I am thinking about is the car?

It can't be just a structureless token in my brain; if the token is structureless then an identical token could constitute a reference to something else, so there is nothing physical about the token that makes it about the car. It can't be a similarity or homomorphism between structures in my brain and the car, because those structures can be decomposed into structureless tokens, which, as I previously argued, can't represent anything, so they can't uniquely represent their corresponding parts of the structure of the car. It can't be a causal chain from the car to my brain, because the causal chain is gone by the time I'm thinking about the car, and the physical property that make my brain refer to the car has to be a property that exists when I'm doing the referring.

This is a serious problem for materialism, one I've never seen a good answer to, and there are other serious problems that come up if you don't acknowledge the existence of abstract objects. However, there is a response if the materialist is willing to retreat to naturalism, and that response is to acknowledge that abstract objects exist. One possible formulation would be the position that all contingent facts are facts about matter, but that there are non-contingent facts that are about abstract objects.

So, the question: I don't know of any philosophers who take this position or what the position would be called. Can anyone provide that information?

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  • Does structural realism fit? "According to Worrall, we should not accept standard scientific realism, which asserts that the nature of the unobservable objects that cause the phenomena we observe is correctly described by our best theories. However, neither should we be antirealists about science. Rather, we should adopt structural realism and epistemically commit ourselves only to the mathematical or structural content of our theories. " plato.stanford.edu/entries/structural-realism There's also Ontic Strucutral Realism "the claim that there are no things...structure is all there is"
    – J Kusin
    Jul 20 at 19:09
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    Your description of materialism is incorrect, reducible to physical properties does not rule out abstract objects, or minds and thoughts. Some of them are so reduced even by non-materialists, nominalism about universals dates back to middle ages, at least. One only needs to believe that certain material processes have stable behaviors that share enough properties with material objects to be assimilated to them. Those will be the abstract objects. A machine that exhibits two distinct types of behaviors when presented with a metal vs non-metal reduces the metal concept, for example.
    – Conifold
    Jul 20 at 20:28
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    @DavidGudeman Actually I don't think that's quite accurate. It does not make as the strong claim physical entities exist, unobservable or otherwise. Look at this quote "Ladyman and Ross (2007) argue that no account can be given of what makes the world-structure physical and not mathematical. " But I agree it does not separate the world into abstract entities vs material/physical entities that you require.
    – J Kusin
    Jul 20 at 20:38
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    That's not my claim, it's theirs, and plausibility is moot as far as use of terminology is concerned. Materialists and physicalists hold that what they mean by their doctrines reduces abstract objects. It may be that your idea of what those doctrines should mean makes it implausible, or even that they, in fact, are, to others. But the reason there is no terminological niche you are looking for is that it would have to be empty. You are trying to split off "materialism" that nobody professes.
    – Conifold
    Jul 21 at 3:39
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    There is a distinction within physicalism that is perhaps in the vicinity of what you are looking for in some ways, it is between reductive and non-reductive physicalism. Non-reductive physicalists hold that some mental properties do not reduce to physical ones, only supervene on them, track them in a sense. My previous link above explains why supervenience physicalists have easier time accommodating abstract objects as well.
    – Conifold
    Jul 21 at 6:01
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https://www.britannica.com/topic/naturalism-philosophy

“While naturalism has often been equated with materialism, it is much broader in scope. Materialism is indeed naturalistic, but the converse is not necessarily true. Strictly speaking, naturalism has no ontological preference; i.e., no bias toward any particular set of categories of reality: dualism and monism, atheism and theism, idealism and materialism are all per se compatible with it.”

I think we are in the wrong general area. Naturalism only claims that all knowledge that can ever be had is discoverable scientifically by studying the natural world (even, technically, the supernatural iff it affects the natural world).

Furthermore, this article outlines that naturalism in philosophy is ill-defined: https://plato.stanford.edu/entries/naturalism/

If you disagree and see a well-defined naturalism, and/or one very different than the above definition, please comment.

If I’m understanding OP’s general thrust though, it is that there must be a philosophy that posits a primary monism (such as material, or the physical) but says abstract objects also exist? So maybe the question could stand just changing naturalism to physicalism? But Im not sure. (If not that, then...?).

If that is the larger question, then whatever it’s called, it would be a dualism whether the adherents admitted that or not. But maybe not a dualism by its name and technical definition, because they cheat in many ways: Dennet uses phrases like “gives rise to” and “bottoms out in”. Others also use “supervenes”, “corresponds to”, “is reducible to”, etc. But if one’s philosophy truly is a monism, then all you get to use is “is”, “equals”.

Im becoming more and more convinced that no abstract objects can exist in either physicalism or materialism, and if someone admits them in addition, then they are dualists. There are no ontological one-and-half-ists, only dualists calling themselves monists.

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    Personally, I have no objection to your calling me a dualist in this sense, but it does nothing to alter or invalidate my position on various specific claims about minds, that are also called dualist. Nothing of consequence will be decided by tinkering with dictionary definitions.
    – sdenham
    Aug 20 at 11:54
  • Well the claims Im objecting to more generally go beyond definitions. Such as, “Only material exists. And from that we can be agents and makes claims and be correct and incorrect. We can get outside of it all to know it, and I get to apply a cartesian theater apart from it all day long without ever saying how Im supposed to be able to do that if inly material exists, and in fact without ever noticing Im doing it.”
    – Al Brown
    Aug 20 at 12:20
  • @sdenham Also, You might like roger penrose on this
    – Al Brown
    Aug 20 at 12:22
  • Is that a direct quote from Dennett? I am curious because I have learned that almost every statement about what Dennett's position is, from someone who disagrees, misrepresents him, and, as far as I can tell, Dennett regards materialism as a working hypothesis about minds, not a metaphysical axiom from which all else follows. Also, I am quite familiar with Penrose's materialist but anti-AI views - what about them is relevant here?
    – sdenham
    Aug 20 at 12:48
  • @sdenham His triunism. Or trinitism. Whatever the word is after monism and dualism. If i see the video later i’ll put it here.
    – Al Brown
    Aug 20 at 13:07

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