Universals

1. Universals

2. The question as to whether there is any general explanation for the pre-philosophical truism that things agree in attribute is an old metaphysical question, dating at least to Plato, and continues to be a subject of debate in metaphysics.

3. Objects in the world have real properties and there are objective similarities among the world’s objects. If we didn’t classify things the way we do, the objects of the everyday world would still agree or disagree in their characteristics, features, or attributes; and because objects really have attributes, we can be incorrect in our classification.

4. “It is not as if we just arbitrarily choose to call some things triangular, others circular, and still others square; they are triangular, circular, and square. Likewise, it is not a mere consequence of human thought or language that there are elephants, oak trees, and paramecia. They come that way, and our language and thought reflect these antecedently given facts about them.” – Loux, Problem of Universals I, p. 18.

5. The issue of attribution becomes philosophical when we ask if there is some fundamental fact that explains attribute agreement. • Take, for example, “Moonlight Sonata” by Beethoven, “Starry Night” by Van Gogh, and “Meditation at Lagunitas” by Robert Hass. • What makes these different things beautiful?

6. Philosophers since Plato have argued that attribute agreement can be explained by the instantiation of universals – entities that can be simultaneously exemplified by several different objects, and which encompass the properties things possess, the relations into which they enter, and the kinds to which they belong.

7. Philosophers that explain attribute agreement in this way are called realists, and explain the attribute agreement of our photograph, poem, and sonata by saying that the universal “beauty” is exemplified by each of them.

8. The phenomenon of attribute agreement gives rise to the debate between realists and nominalists. Again, realists claim that where objects agree in attribute, their commonality can be explained by exemplifying the same universal; nominalists deny this claim. • The debate between realists and nominalists is the longest sustained debate in metaphysics.

9. Universals and Many-Worlds Metaphysics So why do we care about universals anyway? • Distinguishing between realists and nominalists will help us understand what it means to call Lewis’ many-worlds thesis a “reductive nominalism” and similarly to understand why his thesis was confusingly dubbed “Modal Realism.”

10. Distinguishing between realists and nominalists will enrich our understanding of Plantinga’s “Modal Actualism”

11. Lewis claims that the many-worlds thesis is useful in talking about properties (section 1.5 in On the Plurality of Worlds; the short version is that we can think of properties as sets of possibilia), and thus the usefulness of the thesis may be diminished if we believe in universals.

12. On a related note, modal “ersatzism” is in opposition to Lewis’ thesis, and relies on thinking about possible worlds as being somehow constructed out of this-worldly universals.

13. The existence of universals would complicate Lewis’ denial of trans-world identity.

14. A strict Platonist would insist that universals are necessary beings; if this is true, then we have some idea about what would constitute necessary truth (or, truth in all possible worlds; □ A).

15. The Utility of Realism So, a great deal hinges on whether or not there be universals. In considering whether or not we ought to believe in universals, it might aide us to consider why realists think the concept is useful.

16. Realists claim that unless we posit universals as the referents of predicate expressions, we cannot explain how subject predicate sentences can be true. • Realists claim that we can only explain the truth of sentences incorporating abstract referential terms if we take universals to be things identified by use of those terms.

17. Plato and Universals These claims put the debate about universals in modern terms, but, again, talk of universals began with Plato. What was his motivation for arguing the existence of universals, what he calls the “Forms?” Plato had two main reasons for arguing the existence of universals:

18. Universals allow humans to live a fulfilling, happy life in a contingent, changing world where every thing they attach themselves to can be taken away. Reason gives us access to the unchanging world of forms, invulnerable to the pains and changes of the material world. By detaching ourselves from the material world and our bodies and developing our ability to concern ourselves with the forms, we find a value which is not open to change or disintegration.

19. Universals allow us to understand the world as both permanent and changing. The world we perceive through the senses seems to be always changing. The world that we perceive through the mind, using our concepts, seems to be permanent and unchanging. The question arises as to which is most real and why it appears to be both ways. Splitting existence up into two realms solves the problem of permanence and change. We perceive a different world, with different objects, through our mind than we do through the senses. It is the material world, perceived through the senses, that is changing. It is the realm of forms, perceived through the mind, that is permanent and immutable. It is this world that is more real; the world of change is merely an imperfect image of this world.

20. Plato mentions universals in Phaedo,Parmenides, andin Books VI-X of the Republic.

21. Universals and Modern Realists • While Plato speaks of things “participating in” or “ partaking of” forms or universals, modern realists say that things instantiate, exhibit, or exemplify a property, quality, or attribute.

22. Informally, the claim of modern realists is that different things are qualified or characterized in some way by virtue of their all standing in a relationship to the quality or characteristic in question. Attribute agreement gets grounded in a characteristic or quality common to or shared by the agreeing objects.

23. Formally, universals give us a schema for attribute agreement as follows: “where a number of objects a…n agree in attribute, there is a thing, 𝝓, and a relation R, such that each of a…n bears R to 𝝓, and the claim is that it is in virtue of standing in R to 𝝓 that a…n agree in attribute.” Loux, Problem of Universals I, p. 18

24. The Ontology of Metaphysical Realism Realists draw a distinction between two general groups of things: • Particulars—things; familiar concrete objects like human beings, animals, plants, and inanimate material bodies. Each particular occupies a single (contiguous?) region of space at a given time. • Universals – repeatable entities; numerically one and the same universal can be wholly and completely exemplified by several spatially discontinuous particulars at any given time.

25. Attribute Agreement • Particulars agree in attribute by jointly exemplifying a single universal. Particulars are non-repeatable entities standing in a special relation to repeatable entities, and this special relation grounds attribute agreement.

26. Monadic and Polyadic Universals There are different kinds of universal: • One-place/monadic universals (e.g., beauty) • Many-place/polyadic universals (e.g., relations). These may be: • Symmetrical, or • Asymmetrical Monadic universals can be exemplified by only one particular (e.g., beauty, red, justice); a particular can exemplify the universal without the involvement of any other particular.

27. Polyadic universals involve more than one particular (universal relations like “being next to,” ”being taller than,” etc. require two particulars for their exemplification). Symmetrical relations are such that if A bears a relation to B, B also bears a relation to A. So if Towson is 18 miles away from Catonsville, Catonsville is similarly 18 miles away from Towson. Asymmetrical relations are those in which pairs of objects only enter into the relation specified when we order the objects appropriately. For example, if Darth Vader is the father of Luke Skywalker, Luke Skywalker is not similarly the father of Darth Vader.

28. Properties and Kinds In addition to distinguishing between different relations, we can also distinguish between properties and kinds. • properties – objects exemplify properties by possessing them (red, courage, beauty) • kinds – things exemplify kinds by belonging to them (human beings, mammals, clouds) In regard to kinds, there are hierarchies of generality such that a dog and a cat both belong to the kind “mammal” but two dogs are more closely related by virtue of belonging to the kind “canine.” These hierarchies terminate in fully determinate universals such that no less general or more determinate universals are under them; particulars that belong to kind described by a fully determinate universal will agree exactly in attribute.

29. Summary of Realist Ontology • Particulars exemplify different sorts of universals of varying degrees of generality. Universals that serve to explain attribute agreement among particulars can themselves agree in exemplifying universals, e.g., blue and red belong to the kind “colors,” they enter into relations like “lighter than” or “darker than,” and the universals exemplified by color can be more or less determinate, which explains why yellow is closer to orange than blue is.

30. What we have is a very complex picture; an inflationary ontology that seems counter-intuitive and contrary to experience. But the realist says the structure has theoretical payoff in giving us the ability to establish the truth of subject-predicate discourse and to help us make sense of abstract reference.

31. Subject Predicate Discourse What is subject-predicate discourse? All the following are examples of subject-predicate sentences: 1. Socrates is courageous. (the universal is a monadic property) 2. Plato is a human being. (the universal is a kind) 3. Socrates is the teacher of plato. (the universal is an asymetrical relation) In 1 we pick out the particular “Socrates” and say something about him. But the realist says that the term “courageous” also has a referent, and that it must in fact refer to something of the sentence is going to be true.

32. The truth of 1 involves a linguistic structure and a non-linguistic structure; it’s truth depends on things being related in the sentence and things being so related in the world. That is, it is true if the linguistic structure mirrors the non-linguistic one.

33. With the repeatable entities of universals and a relation of exemplification tying them to particulars, we have an ontological framework that can provide truth conditions for subject-predicate discourse.

34. As noted above, different kinds of unievrsals can be the referents of predicate terms. In 1 and 4 where we characterize an object, the predicates are taking properties as their referents. 2 takes a kind as its referent, and 3 takes a relation as its predicate.

35. The Nature of Referential Relations What is the referential relation that ties predicates to properties, kinds, and relations? Is it that between a name and its bearer? This seems to work for: 4. This is red but it doesn’t work for 1 because courageous is not a noun, but an adjective – it is not grammatically suited to occupy the subject position. We want to say that the word “courage” plays the referent role we’re looking for, but it is not suited to play the predicate role.

36. Other examples will serve to illustrate this problem: 5. This coin is circular 6. Plato is wise 7. Alcibiades is exhausted

37. In each case, the predicate doesn’t grammatically pick out an entity, and substitution of words that could fail to serve as proper predicates. For example, in 6 we want to say “circularity” is the property the word picks out, but this can’t be a predicate term. So, as we can see there are grammatical obstacles to conceiving of the relation that ties predicates to properties, kinds, and relations as a naming relation.

38. The realist attempts to get out of this problem by saying that predicate terms “express” or “connote” universals. In this way, applying a predicate term to an object indicates that the object is a member of a set of objects, and also indicates the universal itself.

39. Realists argue that this is the case on the basis that sentences like 1 can be paraphrased as: “Socrates exemplifies courage.” In such a paraphrasing, we get the naming relation between predicate and universal we’re looking for, and realists claim that the possibility of paraphrases is general – any sentence “x is F” can be paraphrased as “x exemplifies F-ness.”

40. Thus, even though we don’t directly get a naming relation between predicates and univerals, we get a referential relation called expression or connotation whereby we pick out the universals to which predicates refer.

41. Summary of the Realist Account of Subject-Predicate Discourse • In a true subject-predicate sentence, the universal expressed by the predicate is exemplified by the referent of the subject term. • The realist claims that this correspondence between subject-predicate sentences is natural. • It’s natural because of the way it meshes with the realist’s explanation of attribute agreement. • To wit: General terms mark cases of attribute agreement, and a general term connotes/expresses the same universal that supports a case of attribute agreement.

42. Realism and Abstract Reference Realists assert that their ontology gives us an intuitively satisfying account of the phenomenon of abstract reference. What is abstract reference? One place we can find the phenomenon is in “abstract singular terms.” abstract singular terms – terms that can play the subject role and also pair off with general terms that play the predicate role, e.g. triangularity/triangular, wisdom/wise, mankind/man, courage/courageous, and red(noun)/red (adjective)

43. The abstract singular term (triangularity) is a device for picking out a certain property or kind and the general term (triangular) is an expression true of or satisfied by all and only the objects that exemplify that property or kind.

44. The realist claims that only by taking abstract singular terms to be devices for referring to universals can we provide a satisfactory account of the sentences in which abstract referential terms appear: 9. Courage is a moral virtue 10. Triangularity is a shape 11. Hilary prefers red to blue 12. Mankind is a kind 13. Wisdom is the goal of philosophic life Here, the realist says that abstract singular terms (e.g., courage) are functioning as names of universals, and thus the sentences can only be true if the universals in question exist.

45. There are other types of sentences involving reference to things like properties, kinds, and relations that do not incorporate abstract singular terms: 14. That tomato and that fire engine have the same color. 15. Some species are cross fertile. 16. There are undiscovered relations tying physical particles to each other. 17. He has the same character traits as his cousin. 18. That shape has been exemplified many times. None of these sentences includes a singular term that names a universal, but the universalist says they are all sentences that could not be true unless the universals in question actually exist; claims about colors, character traits, shapes, biological kinds, relations are all claims about universals, says the realist. The truth of each of these sentences presupposes the existence of at least one multiply exmplifiable entity.

46. CRITICISM OF REALISM For the realist account to be correct, alternative analyses of these sentences, that is, analyses that use some device in explaining abstract reference that does not posit the existence of universals, must fail. Thus, if the nominalist account of subject-predicate discourse and of abstract reference gives us truth-conditions for the preceding statements, we need not commit ourselves to the extravagant ontology of realism. Moreover, full-on, unrestriced Platonic realism leads to problems that force the realist to revise their account.

47. The Paradox of Self-Exemplification Not every predicate term can connote a universal. What are the consequences of this? Either sentences in which the predicate term does not connote a universal are false, or realist metaphysics cannot provide us with a framework adequate to determining truth-conditions of all subject-predicate discourse.

48. For example, consider “does not exemplify itself.” If we have this phrase serve as a general term in a sentence, it would look like this: • My finger does not exemplify itself. If the realist notion that predicates express universals is correct, we can say that “does not exemplify itself” connotes a property of non-selfexemplification, and paraphrase the above statement as follows: • My finger exemplifies non-selfexemplification.

49. It is true that my finger is non-selfexemplifying. But the property of being incorporeal, like a ghost, is self-exemplifying, thus the following statement is false: • Incorporeality is non-selfexemplifying On the surface it seems that “non-selfexemplifying” is suited to serving as a predicate referent of a universal in a way that meshes with the realist ontology.

50. However, the assumption that there is a property of self-exemplification leads to paradox. As Loux says: • “Suppose it [the property of self-exemplification] does exemplify itself; then, since it is the property a thing exemplifies just in case it does not exemplify itself , it turns out that it does not exemplify itself. So, if it [the property of self-exemplification] does exemplify itself, it does not exemplify itself. Suppose, on the other hand, that it does not exemplify itself; then, it turns out that it does exemplify itself; for it is the property of being non-selfexemplifying. So if it [the property of self-exemplification] does not exemplify itself, it does exemplify itself. But, then, it [the property of self-exemplification] exemplifies itself just in case it does not, a deplorable result.”