In his monumental Process and Reality, Alfread North Whitehead lists eight categories of existence and says that among them “actual entities and eternal objects stand out with a certain extreme finality.”^[1] Last time we focused on the former and only briefly mentioned the latter. The topic this time is a deep dive into the ontology of eternal objects.

An eternal object is one that is changeless; it’s not affected by time. (Being eternal is not the same as being immortal, meaning living forever. Something could live forever and still change over time.) Bertrand Russell, Whitehead’s colleague and former student, says such objects are “eternal and not in time.”^[2] They are called “eternal” because every time we encounter one, it is the same as it was before.

There are two kinds of eternal objects, those of mathematics and logic, now called “abstract objects,” and those of aesthetic and sensory experiences, known since medieval times as “universals.” The two kinds are related but not identical. An abstract object is something that is neither spatial nor temporal, such as a number.^[3] A universal is something that can be instantiated by different entities, such as a quality or characteristic that multiple things share.^[4] The difference will become clearer as we consider each in detail.

Abstract objects

Abstract objects can seem peculiar. An abstract object is something that, unlike the many physical objects in our world, is neither spatial nor temporal and hence has no causal power.^[5] Some examples are numbers, sets, geometrical figures, forms of logical inference, mathematical and logical proofs and the like. Whenever we think of the number two, for instance, it is always the same: an integer one more than one and one less than three. Whenever we think of a circle, it too is always the same: a two-dimensional round figure whose points are equidistant from its center. But we never encounter the number two alone; we always encounter sets of two things such as two potatoes or two sides of a coin. And, as Russell notes, we never encounter an ideal geometrical figure in the physical world either:

Geometry deals with exact circles, but no sensible object is exactly circular; however carefully we may use our compasses, there will be some imperfections and irregularities.^[6]

If we never encounter a pure abstract object, then where or in what circumstances does it exist? What is its ontological status?

Universals

Another kind of eternal object is what has historically been called a “universal”. A universal is something posited to explain how individual things can have qualities, features or attributes in common. It is something that can be instantiated by different entities.^[7] There are three major kinds of such attributes: types or kinds (e.g. mammal), properties (e.g. short, strong, red) and relations (e.g. father of, next to).^[8] Such attributes are called “universal” because each extends over, or is located in, many distinct things.^[9]

Take for example a specific shade of red, say that designated by the HTML code #FF0000. The Encyclopedia Britannica entry on universals says,

If a rose and a fire truck are the same colour, … they both exemplify redness, or the property of being red. … The property shared—redness—is [said to be] a third entity, distinct from both the rose and the truck. The two things resemble each other in virtue of standing in the same relation (“exemplification”) to this third entity, which is called a “universal” ….^[10]

Just as we never come across a pure abstract object, we also never come across a pure universal. We never encounter redness alone; we encounter only red things. Again, as with abstract objects, we can ask of universals where or in what circumstances they exist. What is the ontological status of a universal? Some researchers take universals to be a form of abstract object^[11], but as we shall see, their manner of being differs, so I think it best to treat them separately.

Ontological status

Historically there have been roughly two schools of thought about the ontological status of these things. I say “roughly” because there are numerous permutations and variations of the two schools and even different names for them. I refer to them as “Realism” and “Anti-Realism.” Traditional names are “Platonism” and “Nominalism.”

The Realist position regarding both abstract objects and universals is that they exist in some way independently of our thoughts or perceptions of them; they are said to be mind-independent, as are, obviously, physical objects. The Anti-Realist positions (there are several) say that abstract objects and universals do not exist independently of us. These positions hold that such objects are not real mind-independent entities but either merely concepts (a position sometimes called “conceptualism”) or names (whence the term “nominalism”).^[12]

In order to understand the two positions, we need to examine how we encounter the objects in question, abstract objects and universals. We need to look at how they function in our experience. Doing so will enable us to discern which school has a better take on the matter.

Manners of being

My approach is loosely phenomenological in the Continental sense. I examine everyday experience of various kinds of entities without prejudging the status of their existence in order to find out how they appear to us. Metaphorically, at the risk of attributing agency where there is none, I investigate how they make themselves known to us. From the results of that inquiry, we can make judgments about their ontology. I follow Hans Jonas in thinking of ontology as the “manner of being” characteristic of various kinds of entities.^[13] The manners of being of abstract objects and universals are different from that of physical objects and from each other.

Physical objects’ manner of being

We take physical entities to exist independently of us because of how they appear to us and how they behave when we interact with them. (I speak here of physical things of middling size in the everyday world, not the very tiny things of the quantum scale, nor those that are astronomically large.) Things in our ordinary experience appear in perspective. We see one side of an object, a tree, say, but not the other side. We fully expect that if we walk around the tree, we will see its other side, and in fact when we walk around it, we do. If we try to occupy the same space as the tree by walking through it, we find that we can’t. A physical object occupies space and has a certain mass. If moving, it has a certain velocity (with respect to our frame of reference) and perhaps a certain acceleration. Physical objects appear in color, or at least in shades of dark and light. They persist. If we turn our back to the tree or close our eyes, when we turn around or open our eyes we see it again. Physical objects change over time, and we can predict the changes well enough to take advantage of them, knowing, for instance, the best time to pick fruit from the tree. Each particular physical object exists in only one place at any given time. Physical objects are knowable by more than one person. We can measure the tree’s height and the circumference of its trunk, and anyone else using the same instruments will come up with the same measurements. For all these reasons it makes abundant sense to believe that physical objects exist in their own right, independently of us. Such belief makes us Realists about physical objects.

Abstract objects’ manner of being

Abstract objects seem to exist independently of us as well, although they do so differently from physical objects. In contrast to physical objects, they have no perspective, no front and back. They have no mass, do not occupy space and have no velocity, acceleration or color. Unlike physical objects, which change over time, abstract objects do not. The number three is now, was always and always will be a prime number. But, like physical objects, abstract objects persist. Whenever we think of them, they appear to us just as they did before, somewhat as a tree does when we open our eyes after closing them. And there are established procedures for investigating them, just as there are for physical objects. If someone proves a mathematical theorem, anyone with the requisite knowledge can verify that the proof is correct.

There is quite a philosophical controversy over the exact ontological status of abstract objects. Do they exist independently of us, or do they depend on us for their existence? Do we discover them, or do we in some sense construct them? It is evident that some things certainly seem like mind-independent facts: that two plus two equals four, that true premises of a valid argument yield a true conclusion, that an equilateral triangle is also equiangular, and so forth. The reality of these things does not depend on whether we believe in them or not, nor on how we feel about them. If we somehow construct them, we do so within very rigid logical constraints; there is only one possible way for each of them to be. And where does that logical constraint come from? Do we construct it? I find it more reasonable to take a Realist position and assert that, like physical objects, abstract objects exist independently of us, although in a different manner.

Universals’ manner of being

Universals resemble abstract objects, but with some important differences. Like abstract objects, they have no perspective, no front and back. You can see the front and back of a red object, but not of the redness itself. They have no mass, and have no velocity or acceleration. Only the objects in which they inhere, not the universals themselves, have such things. But unlike abstract objects, which are not located in space, universals are, or at least the physical objects that instantiate them are. And unlike a physical object, a universal can be in more than one place, for instance in a red rose and a red truck, simultaneously.

Universals don’t have color, although some of them are colors. Many roses are red, but is the redness itself red? Arguably, it is not. Take a different universal, betweenness. A physical object can certainly lie between two others, but it makes no sense to say that betweenness itself is between anything.

Physical objects change over time. Universals, like abstract objects, do not. A particular shade of red is the same every time you see it. (I ignore the Wittgensteinian objection that you can’t know whether it is or not because you have only your memory to compare it to, and you can’t be sure your memory is correct. Whether you can know it or not, you can certainly believe it.) Like particular physical and abstract objects, universals persist, although only to the extent that the objects in which they inhere do so. The rose still appears red when you look back at it after glancing away, but that bit of redness fades when the rose withers and dies. There are established procedures for investigating some types of universals but not all. Art school teaches how to understand colors, and biology treats the classification of various species, but there are no procedures for investigating relations such as above/below, between, next-to and the like.

Importantly, universals differ from abstract entities in another way. Some abstract entities are complex and structurally related to others in a way that universals are not. Consider, for instance, the equation known as Euler’s identity,^[14] which contains five different abstract objects and the derivation of which contains more. Unrecognized before Euler proved it, that object is now recognized as always having been true even though nobody knew it. The same cannot be said of universals.

Because universals resemble abstract objects in many ways, we might reasonably say that they also exist independently of us. But because they differ from abstract objects in many ways, we might also reasonably say that they don’t.

The question of how best to characterize nonphysical objects is extensive and has been going on since the time of Plato and Aristotle. (The ancients did not clearly distinguish abstract objects from universals.) There are at least two different Realist views about them, which one author characterizes as Extreme and Strong Realism.^[15] The former is Plato’s theory of Forms (Greek Eidos), archetypes that exist entirely independently of physical space and time. The latter dates back to Aristotle and asserts that universals are indeed real, but exist only in particular objects, not outside of them. Depending on your definition of “real,” Aristotle’s view might be taken as Anti-Realist, but historically it is considered a form of Realism.

Anti-Realists about universals claim that there is no need to postulate such strange entities to account for our experience of properties, relations and kinds. There are numerous varieties of Anti-Realism about universals, many with clever names such as Trope Theory, Predicate Nominalism, Conceptualism, Ostrich Nominalism, Mereological Nominalism, Class Nominalism, Resemblance Nominalism and Causal Nominalism.^[16] (You may be forgiven for suspecting that philosophers make up puzzles in order to have fun trying to solve them.)

Of all these, the author’s favorite is Resemblance Nominalism, a form of Conceptualism. The basic notion is that we form concepts of universals based on how they resemble each other.^[17] Red things are obviously different from blue things, and we form a concept of redness based on their similarity to each other and their difference from things colored differently. In my opinion, there is no need to posit the existence of non-physical entities to account for universals. Whitehead, however, disagrees; he is a Realist about universals.

Summary

Abstract objects and universals are undeniably elements in our experience. Different as they are, they share one common characteristic: we never find them existing on their own. Regarding abstract objects, we never find a perfect circle; we only find particular images of circles. We never find an abstract logical form such as modus ponens; we only find particular instances of it with particular premises and conclusions. We never find just a number, say five; we only find collections of five things. Regarding universals, we never find just redness; we only find red things. We never find just mammalness; we only find particular mammals such as a dog or a beaver. We never find just fatherness; we only find particular fathers with their own particular offspring. This commonality leads Whitehead to lump abstract objects and universals together, calling them both “eternal objects”:

Any entity whose conceptual recognition does not involve a necessary reference to any definite actual entities of the temporal world is called an “eternal object.”^[18]

Whitehead actually has no need to posit universals that subsist in isolation from actuality. Arguably, Anti-Realism about universals makes more sense than Realism. We form concepts of qualities that resemble each other and differ from other qualities. We give names to them and then take the fact that the names exist to mean that the qualities exist wholly apart from the ways we use those names. But rather than referring to unchanging essences, the names serve as tokens in various language games, as Wittgenstein would call them.^[19] They enable us to talk about and deal with things that resemble each other. But that’s all. We don’t need to think that they refer to things that subsist on their own. But universals are only one kind of eternal object. The other kind is abstract objects, and they are better thought of as mind-independently real, as I argue above. Whitehead does need to account for them.

To summarize, we have two categories of things that can be said to exist independently of whether anyone is currently perceiving or thinking of them, physical objects and abstract objects, and another whose status is unclear, universals. (A fourth category, socially constructed entities, is beyond the scope of this paper.^[20]) The manners of being of the mind-independent ones are different. That difference leads Bertrand Russell to say that universals, in which category he includes abstract objects, “subsist” instead of exist.^[21] But that just puts a label on it; it does not explain this state of affairs. Whitehead aims to explain it. (To be continued.)

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References

Balaguer, Mark. “Platonism in Metaphysics”. The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta & Uri Nodelman (eds.). Online publication http://plato.stanford.edu/archives/spr2016/entries/platonism/ as of 5 January 2025.

Falguera, Jose L., Martinez-Vidal, Concha, & Rosen, Gideon. “Abstract Objects.” The Stanford Encyclopedia of Philosophy (Summer 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.) Online publication https://plato.stanford.edu/archives/sum2022/entries/abstract-objects/ as of 5 January 2025.

Jonas, Hans. Mortality and Morality: A Search for the Good after Auschwitz. Ed. Lawrence Vogel. Evanston, Illinois: Northwestern University Press, 1996.

MacLeod, Mary C. and Eric M. Rubenstein. “Universals.” Internet Encyclopedia of Philosophy. Online publication https://iep.utm.edu/universa/ as of 3 November 2024.

Meacham, Bill. “Reassessing Morality”. Online publication https://bmeacham.com/whatswhat/ReassessingMorality_v3.html, Also available at https://www.academia.edu/42263176/Reassessing_Morality as of 17 May 2025.

Rodriguez-Pereyra, Gonzalo. “Nominalism in Metaphysics”. The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Edward N. Zalta & Uri Nodelman (eds.) Online publication https://plato.stanford.edu/archives/sum2019/entries/nominalism-metaphysics/ as of 5 January 2025.

Russell, Bertrand. A History of Western Philosophy. New York: Simon and Schuster, 1945.

Russell, Bertrand. The Problems of Philosophy, Project Gutenberg PDF edition. Online publication http://www.gutenberg.org/files/5827/5827-h/5827-h.htm as of 8 July 2018.

Whitehead, Alfred North. Process And Reality: An Essay in Cosmology, Corrected Edition ed. David Ray Griffin and Donald W. Sherburne. New York: The Free Press, 1978. (Original edition New York: Macmillan, 1929.)

Wikipedia. “Euler’s identity.” Online publication https://en.wikipedia.org/wiki/Euler%27s_identity as of 9 January 2025.

Wikipedia. “Universal (metaphysics).” Online publication https://en.wikipedia.org/wiki/Universal_(metaphysics) as of 2 November 2024.

Wittgenstein, Ludwig. Philosophical Investigations. Tr. G. E. M. Anscombe, P. M. S. Hacker and Joachim Schulte, fourth edition tr. Hacker and Schulte. Oxford: Blackwell Publishing Ltd., 2009.

Zimmerman, Dean W. “Universal.” Britannica Encyclopedia Online publication https://www.britannica.com/topic/universal as of 3 November 2024.

Notes

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[1] Whitehead, Process and Reality, p. 22.

[2] Russell, History of Western Philosophy, p. 37.

[3] Rodriguez-Pereyra, “Nominalism in Metaphysics”, single column PDF p. 2. See also Falguera et al., “Abstract Objects.”

[4] Rodriguez-Pereyra, “Nominalism in Metaphysics”, single column PDF p. 2. See also Zimmerman, “Universal.”

[5] Rodriguez-Pereyra, “Nominalism in Metaphysics”, single column PDF p. 4.

[6] Russell, The Problems of Philosophy, Chapter IX.

[7] Rodriguez-Pereyra, “Nominalism in Metaphysics”, single column PDF p. 2.

[8] Rodriguez-Pereyra, “Nominalism in Metaphysics”, single column PDF p. 7.

[9] Zimmerman, “Universal.”

[10] Zimmerman, “Universal.”

[11] Balaguer, “Platonism in Metaphysics”, single column PDF p. 3.

[12] Wikipedia, “Universal (metaphysics).”

[13] Jonas, Mortality and Morality, p. 88.

[14] Wikipedia, “Euler’s identity.”

[15] MacLeod, et. al., “Universals.”

[16] Rodriguez-Pereyra, “Nominalism in Metaphysics”, single column PDF pp. 11-18.

[17] Rodriguez-Pereyra, “Nominalism in Metaphysics”, single column PDF pp. 16-18.

[18] Whitehead, PR, p. 44.

[19] Wittgenstein, Philosophical Investigations, Remark 7.

[20] See Meacham, “Reassessing Morality.”

[21] Russell, The Problems of Philosophy, pp. 37-38.