Universals and Particulars (2): Universals and Infinite Regresses



In this post, I argue that infinite regresses are not successful philosophical explanations. An infinite regress of concepts cannot ground understanding; nor can an infinite regress of beings ground the existence of another being. Thus, postulating an infinite regress of universals such as “having a universal” cannot ultimately answer the question “what is the thing that has a universal?”

In the first post in this series, I explained the distinction between universals and particulars. The existence of universals is supported by the argument from exact resemblance. But the same reasoning that leads us to postulate universals in the first place seems to suggest that “having a universal” is a universal. And that leads to an infinite regress of universals. But then why bother saying particulars are an underlying reality that possess universals? Why not just say that particulars are infinite chains of universals, each with one (or more) different properties to individuate them? This post intends to answer that question.


Usually when a philosopher realizes that a philosophical theory generates an infinite regress, that is grounds for dropping the theory. Some philosophers take “infinite regresses are not explanations” as a basic assumption in philosophy that does not need to be argued for; I’m inclined to agree. But for those who do not find it inherently problematic to offer explanations by way of infinite regress, I will argue for the conclusion that infinite regresses do not succeed as explanations.

Philosophy is supposed to answer questions about what things are. Philosophy answers such questions (at least in part) by offering explanations or definitions. For example, let’s say you ask “what is knowledge?” If a philosopher replied “knowledge is wullumps” you might be kind of confused. It is reasonable to reply by asking the philosopher “what do you mean by ‘wullumps’?” For if the philosopher leaves it at that, it is hard to see how an explanation has been given. You have no starting point from which to understand the meaning of the word “wullumps”. If a person is left with “wullumps”, bafflement and frustration set in.

Let’s suppose that after a few minutes, the philosopher starts to answer your question “what do you mean by ‘wullumps’?” As he opens his mouth, your eyes light up in anticipation. At last! A helpful reply that will illuminate what you don’t understand. Much to your satisfaction, he begins to offer a definition: “the word ‘wullumps’ means…” He pauses to consider the most fitting answer. After several seconds of puzzlement, he exclaims “It means ‘fishfakers’!” With increasing anger and disappointment, you might ask, “what on earth do you mean by ‘fishfakers’?” “Well,” he starts, “by fishfakers I mean… ‘gorpulshrunkle.’”

Now assuming this philosopher is not speaking some foreign (extraterrestrial?) or made-up language, it should be obvious that he is not actually giving a good answer to a philosophical question. He has just pushed the question back a step, by using another non-answer. That lands us with no successful explanation. What is needed to give a good explanation of knowledge is a definition that can be grasped by a listener. To grasp the definition requires that I more-or-less understand the content of that definition. I have to start from a point of understanding in order to clarify what I do not understand (and the clarification process is by means of comparison of the understood to the myserious). We must start from a “foundation” and then build.[1]

It just doesn’t make sense to claim “I understand!” when someone keeps giving me answers that I do not grasp. It would be silly to claim “oh, I see!” after the philosopher told you knowledge was “wullumps.” But what if the philosopher told you “knowledge is justified true belief”? Perhaps this is an incorrect answer (I actually think it is correct). But at least it is a possible answer to the philosophical question posed, so long as the listener can grasp the meaning of “justified”, “true” and “belief”. Whether it is a correct definition or not, “knowledge is justified true belief” is an explanation of what knowledge is for people who indeed understand the words involved; “wullumps” is not an explanation (unless we can define “wullumps”).

It might be objected that when a definition is offered, it does not require understanding. For if you ask me to define “red ball” and I show you several red things and say “these all share red” and I explain that a ball is a spherical object, you can grasp this definition. But giving this reply does not require you to comprehend whether red is adjacent to or opposite of orange on the color wheel. Just because I answer one question (“what is a red ball?”) it does not follow that I know how to answer other questions (“is red adjacent to orange?”). More questions can be asked; that means every attempted explanation will lead to an infinite regress, so long as we have breath to ask new questions.

But we must distinguish answers to different questions. If I hear a bump outside and ask you “what made that noise?” and you check outside and see a polar bear and then tell me “a bear made that noise”, I can ask “what made that bear?” But if you can’t answer where the bear comes from, should I scoff and say “hah! You haven’t explained anything! Because you cannot tell me where the bear came from, I don’t even know what made that noise now”? No. You have given me one adequately-grounded explanation (noise-bear) and the issue of where the bear comes from (bear-source?) does not have to be resolved for me to have understanding of the noise’s cause.


So it seems that with definitions, an infinite regress of things not understood does not succeed in giving understanding. An infinite regress is not an explanation of what a concept is or what a word means. But is this also true of beings? Even if our understanding of the concept or meaning of the term “blueberry” cannot be grounded in an infinite regress of terms, can the existence of an actual blueberry be explained by infinite regress? To clarify, the word “explain” can mean “analyze” or it can mean “ground the existence of”. If we use “explain” to mean “analyze” then we are again talking about definitions, which are linguistic and conceptual, not mind-independent things. But let’s say that by “explain” we mean “ground the existence of”. Now we’re talking about which existing things depend on which other existing things. If I ask “how do you explain man?” this could mean one of two things. First, it could mean “how do you define what ‘man’ means?” which can be answered by appeal to a definition which analyzes the meaning of “man” (perhaps the definition would be “man is a rational animal”).

A second possible meaning for the question “how do you explain man?” is “what kinds of objects ground the existence of a human?” An explanation for man in this sense would require talking about the parts of man (“in order for a human to exist, you need a specific kind of body, with this kind of skeleton, and that kind of brain, and perhaps a rational soul…”) and the causes of the existence of man (“humans are conceived by sexual reproduction, and the first human was either created, or evolved from a lower life form…”). It is interesting to note that an explanation in the first sense (definition) is a sub-set of explanation in the second sense (ontological grounding). After all, when we seek a definition, we are trying to ontologically ground a specific kind of mental state: understanding.

So let us return to the question. Can an infinite regress ground the existence of something? We know that at least sometimes, such infinite regresses cannot ground things. For instance, we’ve already seen that because an infinite regress of ungrasped concepts cannot help you to understand an ungrasped concept, it follows that infinite regresses of ungrasped concepts cannot ground understanding. But can infinite regresses ground mind-independent things?

Not if we think that philosophical explanations match up to some extent with ontological grounding. Typically when we ask for a philosophical explanation, we’re not just having a chat about concepts. Instead we’re trying to see how concepts match up with reality. We’re trying to get in touch with reality, and thus we are also looking for the ontological grounding of a thing. So we assume there is a match-up (not necessarily a one-to-one correspondence, but some kind of close relationship) between explanations (analyses, definitions) and explanations (ontological groundings). Thus, if our goal is understanding, and understanding cannot be achieved with an infinite regress of concepts, then we must either give up on the idea that philosophical explanations can succeed, or we must abandon the possibility of an infinite regress of beings. If we say “we cannot have infinite regresses of ungrasped concepts to ground understanding, but there can be infinite regresses of beings that I don’t understand in order to ground the existence of other things” then we can never actually succeed in understanding beings which are grounded by an infinite regress.[2]


In conclusion, to bring this back to the issue of universals and particulars, when the answer to the question “in virtue of what does a particular have that universal?” ends up being “because the particular has the universal ‘having’”, this invites the same question: “in virtue of what does a particular have that universal?” This will get us only wullumps, fishfakers, and gorpulshrunkle—an infinite regress of things. It certainly won’t give us a philosophical explanation. Infinite regresses are not the answer.[3] Because infinite regresses cannot provide satisfying explanations (definitions, analyses) it follows that infinite regresses cannot provide satisfying explanations (ontological grounding).

[1] Notice that I’m not affirming foundationalism about epistemic justification here. I’m just affirming some kind of foundationalism about definitions. What I mean is this. Foundationalism about epistemic justification says that there are non-inferrentially justified beliefs. Perhaps foundational beliefs include “1+1=2” and “I’m being appeared to as though a wall is in front of me”; neither of these beliefs seem to be inferred from other beliefs. Instead they are reasonable to hold based on experiences. But in asking the question “what is x?” we’re not trying to look for the evidence for or against the existence of x. We’re not trying to justify belief that x exists, whether by appealing to an experience or another belief. Instead, we’re just trying to understand what is meant by the word “x”.

So to demand a “foundation” as a starting point for understanding what “x” means, we’re really looking for something that we understand the meaning of. If we’re wondering how to answer the question “what is justice?” our answer needs to consist of words that we have a decent understanding of. “Justice is giving each man his due” is a false answer to the question “what is justice?”, but it is at least an understandable answer. Why? Because the starting point for explaining “justice” is “giving”, “each man”, and “his due”—all of which are terms we understand better than the term “justice”. Perhaps once we offer this suggestion, it leads to the question “what is a man’s ‘due’?” But if we can get decently clear about what “due” means, then we’re okay to use the word in order to offer an explanation.

[2] If someone replies “I only propose to offer an infinite regress to ground things which invokes concepts I can define at this moment—not a regress which requires the existence of things which I cannot grasp at this time” then it can be replied that this is unsatisfying. Forget whether you are presently invoking concepts you can define. For if it is even possible for there to be an infinite regress which consists of an infinite number of as-of-yet-undefined things, it would still follow that we can never succeed at grasping or understanding those things; thus, philosophy is still in trouble.

A strange reply may occur to someone at this point: “perhaps the only kinds of infinite regresses which can exist are the kinds that I can understand right now”. But although this saves philosophy and ensures that understanding is possible, it comes at the price of requiring some kind of anti-realism. If we say “it isn’t possible for there to be infinite explanatory regresses with members that I cannot presently understand” then we must wonder why our present state of understanding is constraining reality in that way. If the mere fact that I cannot at present understand what a fish is prevents fishes from existing, then that seems to mean that my mind creates reality. For if I somehow came to understand “of course—a fish is a thing with fins, and gills, that lays eggs…” then suddenly reality would change, and it would become possible for fishes to exist. Aside from the fact that this is an implausible story (how could you come to understand what a fish is if it did not exist already?) it seems to imply that our concepts create reality, instead of reality existing first and our concepts latching onto reality. This is false.

[3] Perhaps someone could reply to my above point by saying “If we do not have to understand a thing’s source in order to understand what the thing is, then why can’t an infinite regress of causes exist to ground the existence of x? Surely this would not get in the way of the claim that we can understand x. Thus, there is no problem in postulating an infinite regress of universals that cause a particular to exist.” Two replies are in order. First of all, at most this reply works against infinite causal chains. It would not show that there can be an infinite regress of things which constitute the existence of x. Thus saying “there are infinitely many universals which depend on each other, and together they constitute the particular x” will still not work. They are constituting, not causing, the particular. Second, perhaps causal chains are entities which are made up of causes. If so, then the argument of this post again applies: if it is possible in principle to understand what a causal chain is, then causal chains cannot be made up of an infinite number of members.


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