JP Moreland (Universals)

1. Attribute-Agreement
   1. Thesis: In what manner do two entities possess the same attribute?  If Socrates is white and Plato is white, how are they both “white?” (see 1.3.1).  Moreland writes, “Qualities are universals and not particulars and quality instances–like red are complex entities with at least three constituents in them–a universal, an individuator, and a tie of predication” (Moreland 192).
      1. Nominalism:  acknowledges the existence of qualities but denies they are universals.  Will use terms like trope, abstract particulars, perfect particulars, property-instances, etc.  
      2. realism: when an attribute-agreement obtains, it does so by universals.
   2. Nature of universals
      1. Kinds are universals to which instances belong.  They are similar to sets in that examples of a kind are members of a kind.
      2. intension: distributive unity (something each member of the universal has)
      3. extension:
   3. The relationship between redness and the abstract particular red:
      1. Realism: both the universality and particularity of an abstract entity must be given an ontological ground (Moreland 12; see 1.1)
      2. Nominalism: the relation between red and redness is the ∊ of set membership.
   4. An assay of the abstract particular
      1. trope: a simple entity that has no other constituent outside the infimae species that grounds its exact similarities with other tropes in the same set.
         1. it grounds exact similarity with other tropes.
         2. individuates them.
2. Tropes
   1. Individuation of concrete particulars
      1. Identity of indiscernibles
         (Ф) (Фa    Фb ) (a=b)
         Ф ranges over pure properties, not impure ones
   2. A problem for the realist: how can Socrates’ redness and Plato’s redness be the same if they are in different locations, or if one is round and the other square.  The tropist assumes that phrases referring to the qualities-of-things must refer to the 
      1. Realist response:  we can hold that the “f-of-a” is a state of affairs.  This is the having of a quality by a particular.  It is a particular and a universal standing in a relation of exemplification.
      2. The universal is different from the having the universal.  
3. Tropes and Individuation
   1. How do you account for grounding numerical differences between two entities that share all their pure properties in common?  What is it that grounds the “thisness” of Socrates and the “thatness” of Plato? If red₁ and red₂ are two exactly similar tropes, then how are they not the same thing?
   2. Suarez and Distinciton of Reason
      1. real distinction: two entities, A and B, are not the same thing and can be separated.
      2. distinction of reason (distictiones rationes): purely mental distinction.  God’s being and is simple, so we make a mental distinction between his mercy and justice.
      3. If A and B are distinguished by a distinguished by a distinction of reason, then A is identical to B.  
      4. modal distinction: obtains between quantity and inherence of quantity in a substance.  There is a distinction between six inches and the inherence of six inches in a pen.
   3. Hume’s distinction of reason
      1. shape and color of an impression are actually identical and are distinguished by a distinction of reason.
   4. Summary: trope view cannot account for individuation because its criterion of existence is independent existence. It makes the trope’s nature identical to a place. We have nothing then but bare particulars.
4. The trope view and abstract reference
   Thesis: most people grant that certain sentences are true that appear to refer to universals (85).  “Red is a color.” This sentence accurately describes a state of affairs that obtains in this world. 
   1. a trope nominalist would say “the set composed of red” matches the set composed of color at instance a. 
      1. However, membership in a set of tropes is arbitrary (see previous chapter).
      2. Universal qualities are not sets.  Sets do not resemble the way colors resemble.
5. The trope view and exact similarity
   argument:  trope nominalists use the argument of “exact similarity” to avoid the realist construction.  By contrast, the realist argues that cases of exact similarity (ES) are grounded in universals (110).
   1. Trope account of ES
      1. Two red balls (A and B) resemble each other because they have red₁ and red₂ constituents.
      2. The copula “is” in question is neither of predication or identity, but set membership.
      3. Rejoinder:  why red and not green?  Red tropes resemble each other in a different way than green tropes?  Why?
   2. If two tropes, Red and Sweet, are in the same location, how are they not identical on the Trope Nominalist view.
   3. Three Infinite Regress arguments
      1. The trope nominalist will try to avoid the universal red by introducing the universal “exact similarity.”  It is a relational universal that holds between all pairs of red tropes.
         1. potential infinite: something that can increase indefinitely but is always at every point finite in number.
         2. actual infinite: unattained, indefinite goal of a potential infinite.
            symbolized . It is a set such that each of its members can be put in a one to one correspondence with one of its parts.  
      2. If one accepts the existence of an actual infinite, certain paradoxes arise:
         1. “Imagine a library with an infinite number of books. Each book has a different natural number.  Further, there are an infinite number of red books and an infinite number of black books such that each even number is on a red book and each odd number is on a black book. 
            Problem: there could be no red or black book added to the library because there would be no natural number for its cover.  Further, if one took away all the red books, one would diminish the library by an actual number of infinite books. Yet one would still have the same number of books in the library.
      3. Medieval regresses
         1. per se regress: a causal regress like a’s being moved by b, and b’s being moved by c, and so on, cannot go on to infinity. The second cause depends on the first cause, the third on the second, and so on, precisely in its act of causation. 
            A causal series is per se iff it is of this form: w’s being F causes x to be G, x’s being G causes y to be H, and so on. 
            The relations between the members of a per se regress are transitive.  If x moves y, and y moves z, then x moves z.
         2. per accidens:  if x begets y, and y begets z, then x does not necessarily beget z.
6. Realism and Quality Instances
   1. Wolterstorff: universals as kinds
      1. universals are kinds or types with examples or tokens as their instances.
      2. cases as simples: 
      3. Socrates is an exemplification of wisdom and the case “Socrates’ wisdom is an instance of wisdom.
7. Seven Theses
   1. Universals are multiply exemplifiable entities.  They are ones-in-many (194). They are numerically identical constituents in non-identical entities.  Universals exist and the qualities of objects are universals.
8. Concluding notes:
   1. Nominalists hold to a bundle-theory (Hume?).
9. Terminology
   1. entity: any existent whatsoever (17).
   2. existent: anything that has properties or can be a property of another thing
   3. predication: primitive, intransitive, non-linguistic relation that obtains in cases like Socrates’ being white.
   4. universal: an entity that is capable of multiple exemplification.
   5. Third man argument (Plato): Let’s say that A, B, and C, partake of Largeness (L₁).  By self predication L₁ is also large. There is now a new plurality: A, B, C, and L₁.  Given the One-over-many principle, there is a form of largeness in which all of the above partake.  We will call it L₂.  
   6. impure property:  makes essential reference to a particular
   7. Pure property: makes no such reference
10. Critique of Hume: 
    1. Hume sought to reduce the universal to an abstract idea. 
    2. Hume failed to note that words and ideas manifest type/token phenomena
       1. a type is a general sort of thing.  A type is close to a universal.
       2. a token is a particular instance

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