How can I unambiguously differentiate between universals and particulars?

Question

I am posting this question here as the question is philosophical at its core, but is connected to formal ontologies (e.g. DOLCE) used in computation. My background is more in computation than philosophy, so please forgive me for the potential misuse of terms such as classes, instances etc. So first, a couple of premises:

1. A concise layman definition of universals vs particulars I've gathered is: "particulars are entities that cannot have instances; universals are entities that can have instances".
2. In the DOLCE ontology, the topmost class containing everything is a particular, under which endurants and perdurants have been located. Under endurants there is a class called "Physical Object".

Thus, my question becomes:

Isn't the class (or category in the taxonomy?) "Physical Object (as perdurant particular)" in itself already an universal from which every instance of a physical object "spawns"?

Due to my background I have a temptation to read the class "Physical Object" as either a set that collects all individuals falling under its definition, or as a template that defines the common features for individuals falling inside such set. Thus my intuition tells me that this class should be an universal.

The only solution I've come up with on how to possibly interpret this "correctly": I should think about the "target" of the class: every physical object is by definition already an instance/individual, thus it cannot be an universal that spawns instances. I.e. whether a class is a particular is defined by what "it contains", not by its platonic nature?

Could anyone give me a hint on whether I'm at all on a right track?

I found this thread talking about roughly the same question: On Universals and Particulars but unfortunately the answers did not clarify it.

Also, this source (https://plato.stanford.edu/entries/nominalism-metaphysics/#Uni) states: "Thus while both particulars and universals can instantiate entities, only universals can be instantiated." which would speak against my previous understanding.

Getting a concrete tangible example of an "instantiated universal" would clarify this a lot so that it would be easy to differentiate it from "an entity by an universal/particular".

Answer 1

Part of the reason that this question is hard is because there are a couple of potentially confusing issues involved. First, there is the difference between a universal and a set. Second, there is the difference between a species and an instance.

So, when you say "particulars are entities that cannot have instances; universals are entities that can have instances", you need to know the difference between a universal and a set (which a also kind of has instances) and between an instance and a species.

The notion of universal is very old, and it has been discussed and analyzed for so long that there is little agreement on what it is. However, there seem to be a couple of things that are generally agreed on: universals have instances, and universals are not extensional.

If universals were extensional, they would be sets. What is the defining characteristic of a set? That if two sets have exactly the same elements, then they are the same set. A set is defined entirely by its members--that's what extensional means in this context. A universal, by contrast is defined by what concepts it includes. Consider the following two univerals:

1. An odd number greater than one and less than nine.
2. A prime number greater than two and less than eleven.

The extension of a universal is the set of instances of that universal. Both of the above universals have the same extension; they both have the same set of instances: {3, 5, 7}. Yet they are different universals because (1) includes the concepts "odd number" and "number between one and nine", while (2) includes neither of those concepts; it includes the concepts "prime number", "number between two and eleven".

Just as the set of instances of a universal is its extension, so the set of concepts that characterize a universal is its intension. For example, the intension of (1) is {"odd number", "number between one nine"}.

You may have noticed that "odd number" and "number between one and nine" are both universals, so I should confess that given this very generic notion of universal, a universal is no different than a very generic notion of a concept, so I've been using the words interchangeably. In other words, universals can have other universals as components.

When one universal, A, has another universal B in its intension, then A is said to be a species of B and B is said to be a genus of A. If A is a species of B, A's extension is a subset of B's extension and B's intension is a subset of A's intension. The set consisting of the intension of A minus the intension of B is said the be the difference of A with respect to B. (I should note that I'm using set language here for brevity, assuming my readers are familiar with it; the traditional literature does not use set language).

In the modern terminology of concepts, when A is a species of B, B is often said to be more abstract than A, and A is said to be more concrete than B. Suppose that someone tells you that they have a fruit in a paper bag. There is a broad set of things that it might be, what they have told you is very abstract. But if they tell you they have an apple in the bag, you know a lot more. What they have told you is more concrete.

However, this language is prone to confusion because people sometimes confuse "more abstract" with "higher order". I've done this myself. So, what is higher order? It is the intensional version of what is called a type in set theory. In typed set theory, if a set A has a set B as an element, then set A has a higher type than B. There is an importance difference between A having B as an element vs. A having B as a subset. The difference between more abstract and higher order is parallel to this difference.

I don't know if the Medievals actually talked about higher order universals, so I'm adapting this from the modern theory of concepts. A higher order universal has other universals as instances. Going back to my examples above, notice that "an odd number" does not have universal (1) as an instance (a set member); it has (1) as a species (a subset). However, "a classification of numbers based on factors" does have "an odd number" as an instance. It's a bit easier to see this in the extensions. The extension of "a classification of numbers based on factors" is A, the set of all sets of numbers that can be described as having or not having certain factors. The extension of odd numbers is B, the set of numbers not having 2 as a factor. B is an element of A.

For another example: the concept apple is a species of the concept fruit, it is an instance of the concept "classification of fruit". To help avoid confusion, try the phrase "is a". You wouldn't say that the concept apple is a fruit. A concept isn't a fruit. An apple is a fruit, but the concept of an apple isn't a fruit. Therefore, the concept apple is not an instance of the concept fruit. However, the concept apple is a classification of fruit. "Classification of fruit" is a higher order concept that includes the concept apple. The concept apple and the concept fruit are both first order concepts that have individuals as instances.

So, with that background, you should be able to tell whether something is a universal or a particular. Does it have instances (or is it the kind of thing that might have instances if any existed)? If so, then it's a universal or a set and not a particular. Does it also have an intension? If so, then it is not a set, so it must be a universal.

It doesn't matter if it is an instance of a higher-order universal. You still decide whether it is a universal or not based on whether it is the kind of thing that might have instances of its own.