Ch. 1: The Problems of Universals I

 page 17-30  19-20 Dec, 2010
"X is real". [X= a concrete object, a property, a person .... ]
There are two components in such a claim.
  1. X is not fictitious, or a mental product; not something depending on my/our consciousness.
  2. X is ontologically significant; X is ontologically basic — X cannot be reduced to some other basic entities.
So when Lalon is a realist with respect to human individuals, he takes human individuals to be ontologically basic, but all those entities like classes/communities are either dependent on the basic entities or fictitious (in fact Lalon takes the latter option).

Realism :
Usually one is a realist with respect to something; that is he/she believes that that very something is real.
Bear in mind that one is not — perhaps cannot be a  realist with respect to everything. Like Lalon Fakir you might be a realist with respect to human beings claiming that each human individual is real; but you may not be a realist with respect to nations/communities or জাতি.

Metaphysical Realism :
Universals are real. They (which are repeating entities) are no less real than the particulars (which are non-repeating entities)
  • Platonists are considered to be metaphysical realists.
  • A distinction between a particular and a universal is assumed in the Platonist account. A particular is, initially, non-repeating, whereas a universal is repeating. In his Parmenides [131b] Plato suggests a notable criterion. Here is what Plato writes originally:
“Then while it is one and the same, the whole of it would be in many separate individuals at once, and thus it would itself be separate from itself.”

“No,” he replied, “for it might be like day, which is one and the same, is in many places at once, and yet is not separated from itself; so each idea, though one and the same, might be in all its participants at once.”

“That,” said he, “is very neat, Socrates you make one to be in many places at once, just as if you should spread a sail over many persons and then should say it was one and all of it was over many.

            Louxe spells out the criterion as follows:

what is peculiar to particulars is that each occupies a single region of space at a given time. Universals, by contrast, are construed as repeatable entities. At any given time, numerically one and the same universal can be wholly and completely exhibited or, as realists typically put it, exemplified by several different spatially discontinuous particulars.    [p.19]

  • Exemplification or tie :: Relation between a universal and a particular. A universal U is said to be exemplified by a particular P; or P is said to exemplify U; U and P are said to be tied together.                                                                                                                                                  [Caution: This relation, which we call "exemplification" or "tie" is very special; it is quite unlike the relation "Love". We will soon see that how metaphysicists tackle the problem pertaining to this relation.]
Nominalism :
A position contra metaphysical
realism. Nominalists will, generally, consider a universal as not real; along with that they will reject the notions of exemplification

Loux seems to be a metaphysical realist; in fact he seems to be an Aristotelian.
[Caution: Aristotelianism is often regarded as nominalism, which opposes Platonism. But in this context we consider Aristotelianists as metaphysical realists. In fact historically there had been Neo-Platonism, which saw Aristotelianism as a version of Platonism.]   

Attribute-agreement: (সমগুণবন্ধন) [p.20]
A common attribute is shared by different particulars.
Mind it that a metaphysical realist will take this common attribute to be a single attribute pervading over all those particulars.


Loux talks about attribute-agreement, which is a little ambiguous. Most often it means  inter-particular agreement: various particulars share a common attribute. More familiarly this is also called ONE OVER MANY. Example: You, me, she, we all are  men. The universal MAN pervades over many of us. 

There is also intra-particular agreement : various attributes share a common particular. More familiarly it is called MANY OVER ONE. Example: I am tall, funny, and brown. Many qualities —  being tall, being funny, being brown — are exemplified by me.

 So we will use  the word "attribute-agreement" ambiguously. In narrow sense it means inter-particular agreement, and in broader sense it means either inter-particular or  intra-particular agreements.]

We will later see that there are three schools of thought splitting over the issues on attribute-agreement.
  • Bundle Theorists :: a particular is just a bundle of attributes
  • Substartum Theorists :: a particular has an attribute-less substratum as its constituent
  • Aristotelians :: a particular itself is a unified entity having essence and accidental properties; it is neither  a bundle nor a result of substratum.
Metaphysical Realists have some further details to add about universals

  • There are two types of universals

  •      (a) Properties [ we say that a particular has/possesses a property; red and courageous are properties        
         (b) Kinds [ we say that a particular belongs to the relevant kinds; man and birds are kinds]

  • Not only that universals can be related with particulars. They can also be related with other universals with the help of some other (higher) universals. Examples :    

  • a) Cherry red is brighter than cream white.

    b) Running is better than walking.

    In b) we see that the universal Running is related with the universal Walking with the help of a (binary) relation Better. Better in this example is a higher universal than the universals Running and Walking.
    Platonists then claim that this further relation involving a higher universal with two universals is also real; ontologically no less significant than the relation between a universal and a particular.

  • However, Platonists claim that attribute-agreements happen in various degrees.
  • Consider this situation.Don and Dona are dogs. Parallelly, Cam and Camey are cats. Don, Dona, Cam and Camey are all mammals; they all are in an attribute-agreement — being mammal. In particular Don and Cam are mammals — sharing the attribute being mammal. We will indicate this by writing  DonMammal Cam. Similarly,  DonDog Dona. In other words Don shares mammalhood with Cam; and doghood with Dona as well. But ( here comes  the matter of "various degress") Don's sharing doghood with Dona is stronger than Don's sharing mammalhood with Cam. In other words:

    Dog Dona  >   DonMammal Cam

    Put differently, Don's being a dog has higher degree of exemplification than Don's being a mammal. This degree of exemplification becomes manifest in determinant-determinate relation. A particular's exemplifying the determinate is more determinate than its exemplifying the determinant; being circular of 2" dia is more determinate than just being circular.

  • "So particulars exemplify different sorts of universals of varying degrees of generality" [p. 21]. Further down Loux writes at page 21, 
    Particulars and n-tuples of particulars exemplify universals of different types: properties, kinds, and relations. Those universals, in turn,possess further properties, belong to further kinds, and enter into further relations; the same is true of these further properties, kinds, and relations; and so on, seemingly, without end. And the seemingly endless series of universals that have come on the scene enter into complicated hierarchies of generality inducing thereby complex patterns of attribute agreement of varying degrees of generality. What began, then, as an apparently innocent extension of common sense has blossomed into a full-scale metaphysical theory, an ontology, that is a long distance from common sense.
  • So, as it becomes evident in the above quote, for Platonists the complex structure involving and including particulars and universals of various degrees and levels are real. Bear in mind that this complex structure is very abstract.

    Consider the following diagram

    Diagram 1

    Realists take that parallel to predication, which is a linguistic relation, there is the metaphysical relation of exemplification or — more familiarly — instantiation; and parallel to the semantic relation of referring or naming there is also the metaphysical relation of expressing/connotation. We refer a particular by using a name; likewise we connote or express a universal by using predicate. "[W]here we have a true subject-predicate sentence, the universal expressed by the predicate is exemplified by the referent of the sentence’s subject term" [p. 26]. Language and Reality are, then, isomorphic. An isomorphism is manifest between predication and exemplification; and note there is expressing parallel to naming.

    Nominalists are not happy with those metaphysical notions (in Diagram 1, the bottom right corner, the red portion). They would rather invoke new notions: 
    • true of  
    • satisfy
    [each of these two relations is converse of the other]

    a predicate is said to be true of a particular which satisfies the predicate                                                 (the blue dashed arrows). 
    They think all those are extravagant notions: universals, exemplification and expressing. We can get rid of those notions, at least we can define away those notions.

    But now we are puzzled what Loux says at the beginning of p. 26.
    There is,then, a referential relation here, one weaker or less direct than, but parasitic on the naming relation.

    This, what is claimed in the quote, seems to be a nominalistic program; whereas Loux put it as a realistic program. For if referential relation is parasitic on the naming relation and thus it is weaker or less direct, then this can mean that referential relation (i.e. the expressing/connotation relation) can be explained away; this is exactly what nominalists try to do.

    the general term that marks a given case of attribute agreement expresses or connotes precisely the same universal that supports or grounds that case of attribute agreement
     [p. 26, emphases added]

    Predication and as well as attribute agreement are supported by or grounded in exemplification; not the other way round. [ Nominalists take the opposite view: it is because of predication we tend to think that there is exemplification, the latter is grounded in the former]

    Metaphysical realism provides us an intuitively satisfying — though it sounds naive to nominalistic ears — account for the truth conditions of sentences involving abstract terms. Consider these sentences (from p. 27)

    (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 the philosophic life.

    All these sentences involve abstract terms; and those abstract terms — according to metaphysical realists — are not empty; they denote or connote some entities, albeit the connoted entities are abstract — beyond our perception. The nominalists' main objection lies here: those abstract entities lie beyond our perception. But where is the problem if the abstract terms are beyond our perception? The nominalists have a model  of human cognition. The model is: we the human beings are concrete, and we are entangled in a causal network which itself is concrete — in the sense that causal interaction is possible only among concrete entities.  Our cognition happens only through this causal network; we have no chance to interact with abstract entities through the causal network.

    page 30-45  21-22 Dec, 2010

    Metaphysical Realism does have some problems, unless we put some restrictions.

    Version of Russell's paradox

    Any predicate cannot connote/express an abstract entity — a universal. Otherwise we will have paradoxes à la Russell. How?
    Note, any predicate can be

    • non-self-exemplifying : when the predicate cannot be predicated over itself; for example the predicate “ ... is a table” is not itself a table. F is non-self-exemplifying if ¬F(F)
    • self-exemplifying : when the predicate can be predicated over itself; for example the predicate “... is incorporeal ” is itself incorporeal. F is  self-exemplifying if  F(F)
    Now consider the following sentence, a simple sentence with a subject along with a predicate

    Non-self-exemplifying is self-exemplifying                          [Σ]

    Along with the laws of logic [Σ] generates a paradox. These two laws of logic are relevant for generating the paradox

    [LEM]    Law of Excluded Middle

    With respect to a  predicate P for any subject S we have either S is P or S is not-P


    Any sentence is either true  or  false                               

    [LNC]   Law of Non-contradiction

    With respect to a  predicate P for any subject S we have either S is P or S is not-P

    No sentence is both true and false                            

    Now Σ is either true or false (according to LEM).                                                                                             If it is true ( i.e. if Non-self-exemplifying is self-exemplifying) it becomes false ( for the truth of Σ implies that Non-self-exemplifying is non-self-exemplifying, which further means that Non-self-exemplifying is not self-exemplifying). That means Σ is both true (in our assumption) and false (at the consequence) — a clear violation of LNC.                                                                                                                                    Now suppose the other alternative, that Σ is false. This means that Non-self-exemplifying is not self-exemplifying, which further means that Non-self-exemplifying is non-self-exemplifying. But that actually means Non-self-exemplifying is self-exemplifying, i.e. Σ is true.                                                        We cannot, thus, escape the contradiction.