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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    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
    Commented Jul 20, 2021 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
    Commented Jul 20, 2021 at 20:38
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    I am not making any arguments, especially my own, there is no name for what you are asking because materialists, or even physicalists, see themselves differently than what you describe. You may disagree, but under terminology as used, physicalism is compatible with abstract objects, see SEP.
    – Conifold
    Commented Jul 20, 2021 at 23:35
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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
    Commented Jul 21, 2021 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
    Commented Jul 21, 2021 at 6:01

3 Answers 3


The term is Ontological Pluralism. It is the acceptance of more than one type of thing in the universe.

Before elaborating, I offer a few corrections.

  1. Naturalism does not exclude gods, spirits, or minds from study. So long as they can be characterized (subject to reasoning) and evaluated (interacted with), they would not be "supernatural" -- IE beyond the reach of reasoning and evaluation.
  2. Reductionism does fit well with monistic materialism, but it has recently fallen out of favor among philosophers of science, due to the failure to reduce even all of physics, or more than half of chemistry or more than only a subset of biochemistry, and the identification of a set of intrinsic obstacles that appear insurmountable for much further reduction. See section 5 https://plato.stanford.edu/entries/scientific-reduction/
  3. The alternatives to reduction are emergence, plus pluralism. This is the current consensus view of the status of non-physics sciences -- they study emergent phenomenon and are a pluralist collection. Pluralism also extends to non-science knowledge -- as almost all philosophers accept that history and literary criticism are non-science fields of knowledge.

The simplest form of pluralism is dualism -- two types of things in the universe. The most common form of dualism would be mind/matter dualism, or mind/spirit. Physicalists tend to be unified in rejecting this. But one could also have a matter/abstraction dualism.

The next least complex form of pluralism would be triplism. There is a small heritage of triplism among naturalists. Frege outlined three "worlds" to our universe, world 1 of things with location and time properties (matter), world 2 of things with time property but not location (consciousness), and world 3 of things with nether time nor location properties (abstract objects). Then naturalist extraordinaire Popper articulated the concept in more detail: https://tannerlectures.utah.edu/_resources/documents/a-to-z/p/popper80.pdf

Popper's triplism postulated that world 2, consciousness, was emergent from matter, while world 3, abstract objects, was pre-existing. This is a VERY STRONG emergence, in that world 2 is two-way causal with world 1. Among mind/matter "dualist" philosophers today, consciousness as emergent from matter is the dominant view, as opposed to consciousness as fundamental (spiritual dualism). I use quotes for dualism, because mind/matter dualists have the same problem with abstract objects that materialists do.

Physicalism is very conflicted over abstract objects. Platonism (with a small "p", Plato's Idealism is designated with a large "P") is the term for the belief in the reality of abstract objects -- any one or all of math, ideas, or morality. And with both platonism and physicalism majority views among philosophers, there is some tension over this question among at least a few physicalists.

Three recent physicalist works all admit to the existence of abstract objects, but place them in an ill-defined "dependent" status relative to matter: https://www.amazon.com/Physicalist-Manifesto-Thoroughly-Materialism-Philosophy/dp/0521827116/ref=sr_1_1?keywords=physicalist+manifesto&qid=1639866528&sr=8-1 https://www.amazon.com/Physicalism-Problems-Philosophy-Daniel-Stoljar/dp/0415452635/ref=sr_1_5?keywords=physicalism&qid=1639866457&sr=8-5 https://core.ac.uk/download/pdf/74162.pdf

Many physicalists also treat "information" as something real, and it is very much of an abstract phenomena. Many elementary particle physicists also tend to treat math as more fundamental than, and causal of, matter.

It is not just the existence of abstract objects which is an issue for physicalists, it is also our awareness of them that is an issue. Physicalism postulates causal closure of the physical, which would prevent any interaction between abstract objects and matter. But if abstract objects could not interact with matter, then they would not be needed to explain anything in the universe. Reasoning, ideas, morality, math, information, aesthetics -- all appear to be causal in our world, and this causation is why they have been postulated as objects. We only infer abstractions, because we need them to explain our universe.

If these physicalists adopted Frege and Popper's terms, and accepted that they were world 1/3 dualists, and that physicalism is not a rejection of dualism, but a rejection of any independent status to consciousness, that would relieve some of the tension that physicalism suffers from over abstract objects. World 1/3 dualism would also allow for causal interaction between world 1 and world 3 objects, causal closure could still be asserted relative to this dualist pairing.

Every step of this discussion serves to challenge arguments used to defend the plausibility of physicalism. The failure of reductionism, and acceptance of emergence and pluralism within science and knowledge -- strongly supports the application of emergence and/or pluralism to philosophy and ontology. The acceptance of abstract objects would make physicalism non-monistic, and hence "complex". The complexity is increased with emergence and knowledge pluralism. One of the major arguments physicalists use to reject consciousness dualism is that unlike things cannot interact, which interaction between worlds 1 and 3 would refute. These are cumulatively enough that some "near physicalist" philosophers who still reject world 2, are reluctant to call themselves physicalists today. A better term would be that they are pluralists, who hold by world 1/3 dualism.

  • This is a very good answer, thanks. I'll agree that naturalism can include the mind (I was trying to be careful about distinguishing it from materialism, but was not entirely successful), however, naturalism cannot include spirits or gods, which are by definition supernatural. It can at most include natural objects which are called spirits or gods, but that are not outside of nature as true spirits and gods are. Edit: I just went to look at my question, and I did say that minds can be included in naturalism. Commented Dec 20, 2021 at 17:09
  • @DavidGudeman -- Definitions do not constrain reality, they instead are a statement of your assumptions, which may or may not match that reality. As a shortcut, one may appeal to "definitions" when they are shared universally. But Spiritual dualism is based on the premise that the spirit world is interactive with the physical, so your definition is far from universal.
    – Dcleve
    Commented Dec 20, 2021 at 23:21


“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
    Commented Aug 20, 2021 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
    Commented Aug 20, 2021 at 12:20
  • @sdenham Also, You might like roger penrose on this
    – Al Brown
    Commented Aug 20, 2021 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
    Commented Aug 20, 2021 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
    Commented Aug 20, 2021 at 13:07

Nature by definition is whatever we can observe around us using our perception senses. So, do we observe any actual abstract object?

The notion of abstract object seems to be based on the idea that our abstract ideas may, or possibly must, correspond to objects outside our mind. If this is true, numbers may or must correspond to some observable aspect of the world. However, it doesn't seem that we observe any number at all. We observe for example five rabbits or five dots on a die. That is, we observe rabbits, which we would all agree are natural objects, or we observe dots on a die, also natural objects.

So how do you define abstract objects such that we can say that we observe them like we observe rabbits?

Here is the definition you provide:

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.

Why should we think of sets as abstract objects as opposed to concepts in our mind, i.e., ideas? When is it that we perceive abstract objects? I don't seem to be able to observe any set around me. I can observe for example a group of rabbits and may think of them as a set of rabbits but I never get to see the set itself. The group of rabbits exists but only if the rabbits themselves exist. There does not seem to be anything on top of the rabbits that would be the set of rabbits. All there seems to be are the rabbits I can see and my idea that they together form a set.

  • You are simply begging the question by assuming that anything that exists outside of the mind must be observable with the senses. Commented Dec 20, 2021 at 17:05
  • The only things we actually observe are internal experiences. Qualia. We do not have direct realism access to rabbits, ecosystems, or covalent bonds. Explicitly, what we "see" is a manufactured construct. We DO have direct experience of some abstract concepts, some ideas are experienced as qualia, so your claim that rabbits are real, but numbers are not -- is inverted from the actuality of our experience. Quine pointed out in Two Dogmas of Empiricism that indirect realism leads to as valid an inference to the reality of abstractions as it does to the reality of physical objects.
    – Dcleve
    Commented Dec 20, 2021 at 23:14
  • @DavidGudeman I don't think so. Please provide the relevant quote. Commented Dec 21, 2021 at 11:39
  • @Speakpigeon: "The notion of abstract object seems to be based on the idea that our abstract ideas may, or possibly must, correspond to objects outside our mind. It this is true, numbers may or must correspond to some observable aspect of the world." This is begging the question. I maintain that abstract ideas are outside of the mind and yet are not observable aspects of the world. Commented Dec 23, 2021 at 11:07
  • @DavidGudeman To answer the question, I assume that naturalism allows for abstract objects and, as such, as observable, and my point is that there are no such observable abstract objects, no observable sets of rabbits beyond the rabbits themselves. Whether there are any non-observable abstract objects is irrelevant to the question. Still, the same reasoning applies: How are you going to prove any such abstract object since all we have are the ideas we have of numbers, sets and such, not direct experience? Commented Dec 23, 2021 at 11:50

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