Three Cats

          In the debate between realists and nominalists, one of the most noteworthy arguments that realists have employed is known as the Formal Cause Argument.  This argument takes its name from one of the four causes that Aristotle listed as accounting for the reasons why a certain thing exists.  Among these four causes, the formal cause can be thought of as the exemplar for something else.  Take, for example, a statue of Socrates.  The formal cause for this statue would be Socrates, himself, since the sculptor is seeking to copy the form of Socrates in stone.

            The Formal Cause Argument can be given like so:

  • 1. Felix is a cat, Garfield is a cat, and Morris is a cat.
  • 2. There must be something about Felix, Garfield, and Morris that accounts for all of them being cats.
  • 3. This “something” can only be their felinity or “catness”.
  • 4. Therefore, the universal, “catness”, exists.

            The above argument is valid; therefore if the nominalist desires to counter it, he must attack one of the argument’s premises.  Since the nominalist would have to agree with the first premise, the only premises that remain are premises two and three.

            In rejection of premise two, some nominalists assert that there is no explanation for why Felix, Garfield, and Morris are cats: this is simply a brute fact.  While this is certainly a position that an individual can take, it tends to be quite an undesirable one because of the need to appeal to a brute fact.  Most philosophers desire to be able to explain as much as possible about the universe, but brute facts deny the possibility of explanation.  Therefore, whenever possible, it is better to give a reasonable explanation for something than no explanation at all.

            Thus the nominalist is left to counter the third premise of the Formal Cause Argument.  One such attempt is the Verbal Definition theory of universals.  This view was popularized by the medieval monk, Roscelin, who asserted that universals are nothing more than flatus vocis or “puffs of air”.  In essence, Roscelin was asserting that what are often mistaken for universal properties are nothing more than verbal definitions.  For example, the property of “catness” can be reduced to the technical definition of “cat”.  Therefore, Felix, Garfield, and Morris are all cats in virtue of the fact that they all conform to the definition of “cat”.

            The problem with this theory is that it is not so easy to define things as one may think.  While it may be a somewhat simple matter to define a basic element like gold or iron; just how do we define the word “cat”?  Perhaps we may say that a cat is a four-legged mammal with whiskers and a tail; however this very same definition applies to thousands of other species of animals (and perhaps some species that have not been discovered as of yet).  And what are we to do with a cat that is born with only three legs?  Is this animal no longer a cat?  Our base intuition would say that it is, but according to the above definition it could not be.  In short, the problem with the Verbal Definition theory of universals is that it requires something that we cannot give; in this case, a perfect and exhaustive definition for “cat”.

            Another objection to the third premise of the Formal Cause argument is the Causal Theory.  This theory seeks to dismantle the Formal Cause argument by appealing to another one of Aristotle’s four causes: the efficient cause.  The Causal theory would assert that Felix, Garfield, and Morris are all cats based upon the fact that each one of them had another cat as its efficient cause.  In other words, we know that a creature is a cat because it came from a cat. 

            The problem with this theory, however, is that it is based upon the assumption that “like begats like”.  This means that each cat would have to be produced by another cat ad infinitum.  There could never come a point in which a cat was formed by something that was not a cat (such as Darwinian evolution or Divine creation).  The problem here is that this theory requires that every kind of concrete particular be eternal.  In other words, cats would have always existed and will always exist.  There are not too many individuals who would be willing to accept this as a fact.

            A final and more promising alternate theory offered by nominalists is called Trope Nominalism.  In this theory, nominalists introduce the concept of tropes.  Tropes are asserted to be the particular, non-sharable, concrete aspects of a certain concrete particular.  For example, if two squares are the same shade of blue, the realist would say that both of these squares exemplify the universal “blueness”.  However, the trope nominalist, while stating that the two squares resemble one another, would assert that neither one of these squares share a universal property but that each one of them exhibits a particular shade of blue that is unique to that square (a trope). 

            Indeed the very idea of “resemblance” is crucial to this form of nominalism (trope nominalism is sometimes referred to as resemblance nominalism).  A trope nominalist explains their position as such:

X, Y, and Z belong to a kind F iff X, Y, and Z each have a particular F-ness and these F-nesses form a circle of similarity (or resemblance).

            Applying the above definition to Felix, Garfield, and Morris would yield the following result:

Felix, Garfield, and Morris are all cats iff all three of them have a particular “catness” and these “catnesses” form a circle of similarity.

            Some realists would argue that this brings the trope nominalist perilously close to realism due to the fact that the relation of resemblance between each concrete particular appears to be a universal itself.  However, the nominalist reply is that each resemblance relation is a particular resemblance relation (just as each trope is a particular aspect) based upon its resemblance to other resemblance relations.  While some realists would (correctly) argue that this leads to an infinite regress in resemblance relations, the nominalist can easily defend himself by pointing out that realism, itself, is dependant upon an infinite regress of shared qualities.

            Therefore, it appears that the concept of tropes provides the nominalist with an effective counterexample to premise three of the Formal Cause Argument.  One can accept either the existence of universals or the existence of tropes to give an account of the “something” that causes Felix, Garfield, and Morris to all be cats.  And in the case of this particular argument, it seems that the nominalist (with Ockham’s razor in his corner) would be in a better position with his theory of concrete tropes then the realist with his theory of universals.

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