By "atomic particle", I mean everything from molecules to quarks---objects that are outside the realm of normal experience but used in physics and chemistry to explain macroscopic events.

By "empirical object", I mean a physical object of medium size that is part of normal experience like dogs, cats, rocks, trees, and other people. Empirical objects are inscrutable. By this I mean that they have an endless set of properties, many of which cannot be guessed at from general considerations, and the values of those properties tend to be imprecise and time-dependent. The more you examine them, the more you learn about them, and they change in chaotic ways.

There are lots of different accounts of abstract objects, but one of the main features of abstract objects is that they are scrutable. They have a finite, or at least finitely characterizable set of fundamental properties that determine their entire nature, and they never change.

Atomic particles seem more scrutable than inscrutable. They have a finite set of properties or a finite set of parts with a finite set of properties and they only change by undergoing quantum state transitions. They seem in some sense to be more like abstract objects than empirical objects. Furthermore, there is the property of identity. No two empirical objects are identical with each other, but among atomic particles, it is common for two of them to be identical.

Now, I'm not interested in an explanation of how an apparent inscrutability could arise from a collection of scrutable particles. I take it for granted that sort of thing is possible. My issue here is not physics but evolution and epistemology.

The evolutionary/epistemological problem is that our brains evolved to deal with empirical objects. We also have a talent for dealing with abstract objects and it is possible to tell a story for how that talent also evolved as a success strategy. There is no story to explain our astonishing good fortune that the building blocks of empirical objects are based on something completely different from the empirical objects that our brains evolved to deal with, yet to the great good fortune of the human race, the building blocks just happened to have a lot in common with abstract objects and the people who investigated the building blocks of matter happened to be extremely good at dealing with abstract objects.

How plausible is that scenario compared to the scenario that the building block of matter are pretty much just like empirical matter but the atomic physicists who came up with the Standard Model just happened to be extremely talented thinkers and extremely motivated puzzle solvers who just came up with a theory of the type that they find satisfying that fits observations but has nothing to do with underlying reality?

This strikes me as a serious problem for analytical philosophers of science, but I've seen no references to it other than some similar concerns from Earnst Mach and Pierre Duhem from over a century ago, and maybe the Vienna Circle, although they seem to have dropped the topic early in the 20th century.

Have any more recent philosophers discussed this issue? Have any tried to justify it?

  • "How plausible is that scenario compared to the scenario that the building block of matter are pretty much just like [macroscopic] matter" Macroscopic matter isn't like macroscopic matter. The whole point of the Standard Model is to accurately predict the behavior of macroscopic stuff like people, stars, Geiger counters, galaxies, photo-diodes, electron microscopes, and bubble chambers.
    – g s
    Commented Nov 20, 2023 at 21:12
  • I'm fairly certain that most physicists agree that the Standard Model is an effective theory that strongly reflects, but does not itself constitute, a deeply true description of reality. But the thing whose behavior it predictively describes is, ultimately, us and our measurement apparatus, in circumstances where classical assumptions lead to false predictions. The manifest falsehood of those predictions in 19th century physics provided the motivation for the quantum model in the first place.
    – g s
    Commented Nov 20, 2023 at 21:20
  • "All abstract objects yet discovered have “turned out” to come in handy as representational aids. How is this interesting coincidence to be explained? This should remind us (says the figuralist) of Wittgenstein’s fable in which we first invent clocks, and only later realize that they could be used to tell time. It is no big surprise if things with representing as their reason for “being” show a consistent aptitude for the task", Yablo, Go Figure
    – Conifold
    Commented Nov 21, 2023 at 0:09
  • See Ian Hacking's interesting argument in his book Representing and Intervening (1983), that we may summarize as follows : the strange "actors" of the subatomic world are difficult to imagine, but we may "interact" with them (with complex machines like the Large Hadron Collider of CERN, ...); so, if we can "push and pull" them, they must exists. Commented Nov 21, 2023 at 8:09
  • @MauroALLEGRANZA, it sounds like he has it backwards. You have to assume they exist in the first place in order to conclude that you are pushing and pulling them. Commented Nov 21, 2023 at 14:45

6 Answers 6


A very detailed analysis of what you are asking (in fact the whole book is about this) is written by one of the protagonists - Heisenberg - in his book "Physics and Philosophy". Just a quote from page 145, related to your concerns.

The ontology of materialism rested upon the illusion that the kind of existence, the direct "actuality" of the world around us, can be extrapolated into the atomic range. This extrapolation is impossible, however.


Are you asking about fundamental particles? Perhaps they are functions rather than objects? Why cannot they be concrete objects? Or a composite? I am afraid that the intent of your question is unclear and I do not follow your argument about plausibility. As a matter of fact, humans are good at dealing with both abstract and concrete objects. I do not agree that fundamental particles are scrutable, when they throw up properties like entanglement. In answer to your question, I think that it would be a mistake to consider matter to be qualitatively different at the fundamental and macroscopic levels.


One way to approach the scrutability issue is by appealing to the role of encoding-vs.-exemplifying in one modern characterization of abstract objects. If we say that an object is abstract when it has its properties mainly under the encoding relation, this is close to saying that it has its properties mainly by our ideal stipulation that it has them; there is little difference, if any real one, between encoded and stipulated properties as such.

Next, consider string theory. We have never clearly "perceived" these strings (I admit some vague wiggle room when it comes to our experience with gluon flux tubes, say), so the properties we have said that they (would) have, are not attributed to them on the basis of careful observation of their nature. Rather, it seems that for better or worse we indeed stipulate what kind of thing a pure string would be and what it would be able to do (by itself or in combination with other strings). And then the whole edifice of string theory did rise up like a Zaltaesque metaphysical dream come true...

And other such speculative theories proceed apace: causal-dynamical triangulation, causal-sets, world-crystals, etc. postulate objects (fundamental spacetime triangles, physically real sets, a crystallization of the entire universe) which can be introduced and then explored rather a priori, or at least in the light of something like talk about them encoding their primary natures (e.g. causal sets encode for cause-and-effect).

Now, as for the happenstance (or lack thereof) of us happening upon theories (of (sub)atomic field excitations) that happen to line up with both the intended ("closer-to-fundamental") factoids as well as the less abstruse factoids of closer-to-the-surface empirical objects, I would offer this passage from Kant's Transcendental Analytic:

It is quite possible that someone may propose a species of preformation-system of pure reason—a middle way between the two—to wit, that the categories are neither innate and first a priori principles of cognition, nor derived from experience, but are merely subjective aptitudes for thought implanted in us contemporaneously with our existence, which were so ordered and disposed by our Creator, that their exercise perfectly harmonizes with the laws of nature which regulate experience. Now, not to mention that with such an hypothesis it is impossible to say at what point we must stop in the employment of predetermined aptitudes, the fact that the categories would in this case entirely lose that character of necessity which is essentially involved in the very conception of them, is a conclusive objection to it. The conception of cause, for example, which expresses the necessity of an effect under a presupposed condition, would be false, if it rested only upon such an arbitrary subjective necessity of uniting certain empirical representations according to such a rule of relation. I could not then say—"The effect is connected with its cause in the object (that is, necessarily)," but only, "I am so constituted that I can think this representation as so connected, and not otherwise." Now this is just what the skeptic wants. For in this case, all our knowledge, depending on the supposed objective validity of our judgement, is nothing but mere illusion; nor would there be wanting people who would deny any such subjective necessity in respect to themselves, though they must feel it. At all events, we could not dispute with any one on that which merely depends on the manner in which his subject is organized.

The harmony, even integrity, of our capacities for both a priori and empirical representations, might be what allows us to bridge the idealizations of abstract objects with the increasingly complex/convoluted expression of those objects' arrangements/permutations in increasingly macroscopic space(time). At least, the "faculty" of stipulative definition might not be the most otherworldly ability of ours, and if it is sufficiently constitutive of our conception of abstract objects, maybe this is where talk of abstract objects originally gains its justification from? (I should note that historically, when Leo Szilárd envisioned the chain reaction that gives nuclear weapons their basic power, he was using imagination informed directly-or-indirectly by stellar dynamics theory, among several other things, to induce his scientific oracle.)


Atomic physicist here. This is more philosophy-speak than I'm used to. But your claim that atoms are "scrutable" and therefore "abstract"... for whatever all that means, seems to rest on

Atomic particles seem more scrutable than inscrutable. They have a finite set of properties or a finite set of parts with a finite set of properties...

First off, if you consider an atom to be an individual thing, then what you call "empirical objects" like cats or dogs, are also made up of finite (but large) of parts. In practice, it is challenging to know ALL of the properties of all of the atoms in a cat or dog, but it is, in principle, possible. So I think this is an internal inconsistency in your discussion.

But, stepping back, as an atomic physicist, I would say it is incorrect that an atom has a finite set of properties. There are infinite but countable number of quantum states accessible to an atom, and it can occupy each of those states with a probability amplitude given by a complex number. The upshot of this is that there an infinite and uncountable number of states a single atom can occupy. Technically/mathematically speaking the state of the atom is described by a vector in a Hilbert space, and the cardinality of that Hilbert space is uncountable.

How plausible is that scenario compared to the scenario that the building block of matter are pretty much just like empirical matter but the atomic physicists who came up with the Standard Model just happened to be extremely talented thinkers and extremely motivated puzzle solvers who just came up with a theory of the type that they find satisfying that fits observations but has nothing to do with underlying reality?

This makes it sound like people just thought hard and then atomic theory popped into being. But this is not the case. At each stage there was someone in a lab running some real experiment that they built with their hands and we needed a better theory to explain the results. It's true the objects of study are getting smaller and smaller, but that is thanks to a continuous chain of tools that can be traced from macroscopic to microscopic that allow us to extend our gross senses into the microscopic realm.

But then a question: what's the point of abstract/concrete? Seems kind of silly to me. Is it just a synonym for material/immaterial? Is there an accepted example of a material but abstract object? It seems like that's what you're looking for in this question. I doubt that there is such an example, so this colors my answer.

  1. According to your quote from SEP there are several different attempts to distinguish abstract objects from concrete objects.

    • You define “abstract := scrutable” (= open to being understood),
    • and you qualify atomic objects as being scrutable.

    From where do you take this definition, from the SEP-article? In any case, the definition does not seem helpful. Because quantum mechanics (QM) being the scientific theory of atomic and subatomic particles is the prototype of a successful, but inscrutable theory. There is no agreement about the interpretation of QM, since about one hundred years.

    At least, QM is counter-intuitive. You yourself give the example that “among atomic particles, it is common for two of them to be identical.”

    On the basis of your definition of “abstract = scrutable” your question reads “Are atomic particles scrutable objects?“ The answer can only be NO.

    Aside: Do you really mean what you say literally?

  2. Added due to the comments concerning the term "inscrutinable": Your question asks about the relation between the whole and its parts:

    If the parts are simple, how can the whole be complex?

    The answer is the antique principle: The whole can be more as the sum of its parts. Because the whole depends not only on the parts in separation, but depends also on the interaction of the parts. That’s the explanation of Democritus’ atom model: The atoms are simple but their configuration is manifold.

    Or a simple metaphor: Each Lego brick is simple, but what one builds from Lego bricks is manifold.

  • I defined "inscrutable" and assumed the reader would understand by "scrutable" I meant an object that did not meet the definition I gave for "inscrutable". My definition is not "incapable of being understood". Commented Nov 20, 2023 at 22:35
  • @DavidGudeman I took the explanation for inscrutable from collinsdictionary.com/de/worterbuch/englisch/inscrutable and the translation from dict.leo.org/englisch-deutsch/inscrutable. - I agree that inscrutable is the opposite of scrutable. - Which definition do you mean is not "incapable of being understood"?
    – Jo Wehler
    Commented Nov 20, 2023 at 22:44
  • The definition I gave is not the definition "incapable of being understood". When a writer gives a definition of a word, you have to use that definition, not look it up in the dictionary. I defined it in the second paragraph. Commented Nov 20, 2023 at 23:32

I may be struggling to appreciate nuances of your suggestion, but it seems to me that even in the treatment of macroscopic phenomena physicists tend to abstract general relationships and identify them separately from the real objects and systems that conform to them. Take Hooke's law, for example. To use your definition of scrutable, Hooke's law reduces all real springs to an abstract scrutable spring whose only two properties are its length and stiffness. That abstract spring can be used to model any number of real springs in real circumstances, and doesn't explicitly depend on any understanding at all of the more fundamental building blocks of matter. Indeed, you could argue that even if atoms, quarks etc were not scrutable in your sense of the word, scientists would model them as if they were, with abstract representations of them. So my sense is that humans have a tendency to look for abstract patterns in reality, and as you break down reality into smaller and smaller building blocks, those building blocks will naturally become more and more like their abstract counterparts simply because they have no 'hair' to differential themselves.

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .