"Resemblance between particulars requires the existence of a universal,
so there is no way to eliminate universals from our ontology."
How convincing is this argument?

In order to understand just what the title quote is claiming about things called "universals", I will have to explore in some depth the nature of "particulars".  I will demonstrate that the argument in the title quote is not at all convincing because it is based on presuppositions about what "particulars" and "universal" actually are that are not accepted by many philosophers.

Particulars

"Particulars" is an ontological category for entities that have attributes.  (I mean attributes other than "existence" - if "existence" is indeed an attribute.)  An attribute is a quality, character, characteristic, or property that is or can be attributed to a thing.  It is part of the definition of a "particular" that particulars have some sort of relationship with attributes, or characteristics.  Exactly how that relationship is described depends on the metaphysical theory one adopts.  For the time being, however, I am going to use the terminology that particulars "have" attributes.  But by this I mean to be neutral as to just what the relationship is between the particular and the attributes associated with it.

Some ontologies divide particulars into concrete particulars and abstract particulars.  The most common position is that concrete particulars exist in space and time and undergo change, while abstract particulars do not exist in space and time (and so lack physical extension) and do not undergo change.  Abstract particulars, on this view, lack causal powers and are incapable of entering into causal relations with other entities. 

Concrete particulars are generally considered to include such things as the normal "furniture of the world" - stick and stones, tables and chairs, and what not.  Concrete particulars are the things that we perceive when we perceive the world.  Abstract particulars are generally considered to include such things as numbers and geometrical shapes. 

The three most widely discussed theories of particulars are the substratum theory, the substance theory, and the bundle theory. The substratum theory maintains that what a particular actually is, is something that underlies the attributes it "has" - something to which the attributes are "attached" in some fashion.  This means that we could conceptually remove all of the attributes of a particular to be left with nothing but a "bare" particular.  Of course, there would be nothing left by which we could perceive the particular.  Hence, on this theory, a "bare" particular is something that is unperceivable, indescribable, and unknowable.  Most philosophers regard it as a disadvantage if an ontology requires us to grant existence to something that is unperceivable, indescribable, and unknowable

The substance theory dates from Aristotle.  It proposes that a particular has some attributes essentially, while all others it has contingently.  We could not remove an essential attribute of a particular without changing the kind of thing it is.  But any of its contingent attributes we could remove without changing the kind of thing it is.  For example, Aristotle is essentially a man.  We could not remove the attribute of being a man from Aristotle without changing it/him into something that is not a man.  But Aristotle also had a beard.  We could remove the beard without changing Aristotle into something that is not a man.  Unfortunately, it is not at all clear what distinguishes essential from contingent attributes for any given particular.  For example, suppose we are considering Aristotle as an example of a "bearded man".  If we then remove his beard, he is no longer a bearded man.  So by removing an attribute, we have changed Aristotle into something else.  It is not obvious that this sort of change is significantly different from the previous one.

The bundle theory of particulars proposes that a particular is nothing other than a collection of attributes.  If we were to remove all of the attributes of a particular, there would be nothing left.T  he bundle theory of particulars is maintained by those metaphysicians who argue, contrary to the implications in the essay's title, that particulars are not a fundamental category of existents.  They are derivative, and based on the existence of attributes (or more precisely, universals).  The problem that bundle theorists have inadequately addressed, is the nature of the relationship between the attributes that are bundled together as a specific particular - what it is that keeps the bundle together as a unit; and why this specific bundle of attributes rather than another.

What all these theories accept as given is that particulars exist independently of how we think about them, and that it is the function of ontology to describe how they exist.  But one of the difficulties that this approach creates, is the problem of boundaries.  How is it that we draw the boundaries we do around the particulars we identify.  What is it that renders particular A numerically identical (exactly the same one) as particular B?Ontologists have come up with all sorts of explanations, the most famous of which is the theory of natural kinds.  This theory maintains that there are "natural kinds" of particulars out there for us to discover, and it is up to us to discover what natural kinds actually exist in the world.  And it is up to the ontologists to provide descriptions of what it is that makes one natural kind different from another.What is it that makes that grand oak the same thing as the acorn?  And what is it that makes a heap of sand different from a collection of individual sand grains?

One of the theories that is neglected in modern ontology, is the Conceptualist theory of particulars.  The Conceptualist theory posits that what marks the boundaries of a particular (in space or time) is our current cognitive purpose.  Contrary to the standard approach, particulars do not exist independently of how we think of them.  If one is a metaphysical realist (as I am), then one can accept that the world as a whole exists independently of how we think of it.  But the boundaries of any given particular are drawn to suit our cognitive convenience.  They are not given by the world for us to discover.  The boundaries of a particular can change as our cognitive purpose changes.  The conceptualist approach renders the differences between the substratum theory, substance theory, and bundle theory of particulars into questions of different cognitive purposes. 

One of the corollaries of the conceptualist theory, however, is that it views particulars as derivative rather than fundamental entities.  The fundamental entity that exists is the world (or the space-time continuum, if you will).  The existence of any specific particular is dependent on our cognitive purpose in establishing its boundaries.  But it does render moot the problem of establishing whether the most fundamental existent is a quark, an atom, a molecule, a cell, a heap, an organism, an ecology, a biome, or what have you.

From the perspective of a conceptualist, then, "particulars" are parts of the world around which we choose to draw boundaries to most economically meet our need to understand and predict how the world is going to react to our efforts.  In a realist/conceptualist ontology, then, "particulars" are not fundamental mind-independent entities.  The entity known as "The world" is a fundamental mind-independent entity (assuming a realist metaphysics).  But "particulars" are derivative and somewhat mind-dependent entities.  They exist because and only when we create them by drawing suitable boundaries around parts of the world that interest us.  As a consequence, it becomes a matter of debate over the meaning of "existence" as to whether "particulars" ought to be acknowledged as a proper part our ontology.

Universals

Every individual particular "has" attributes.  (Remember, to this point I am being neutral to the exact nature of this "has" relationship.)   And some particulars have attributes that we would recognize as similar.  For example two different mats, each being a particular, share the attributes of being mats, being flat, being on the floor, being manufactured by the same manufacturer (according to their respective labels), and being (according to the manufacturer's label, say) green in color. 

In metaphysics a "universal" is the term used to refer to what individual particulars have in common when they exhibit some resemblance in their respective attributes.  The term "universal" is used, in contrast with the term "particular", because universals can be instantiated or exemplified by many particular things (ie. universally), whereas particulars can be instantiated only once - each particular is unique.  Universals are employed to explain why it is that we judge many particulars similar with respect to some attribute.  The two mats I referred to have in common that they are "Green" according to their labels.  And we can observe that they are very similar in color, even though one of the mats has been washed several times and is a distinctly more faded green.  Presumably, there will be any number of other particulars in the world that we would also judge as being very similar in color to our two mats.

The issue raised by the argument in the essay's title quote is how to account for the general agreement that our two Green mats have a certain similarity in their respective color attributes.  (Or a certain similarity in any other property we might judge they have in common.)   Metaphysicians fall into two main camps on this issue: Realists endorse universals, while Conceptualists and Nominalists deny they are needed.  Realists maintain that universals (like our Green color) have real mind-independent existence, and hence properly belong in our ontology.  It is the relationship between the particular and the universal that explains why we perceive the two mats as having similar color.  Nominalists and Cnceptualists deny that universals have real existence and hence do not properly belong in our ontology.  They claim that independently existing entities are not necessary to explain the perceived similarity in color (or other properties we judge they share).

One of the arguments of the Realists is essentially linguistic.  Consider the statement "Green is a color."  A name like "Green" wouldn't be a name if there weren't something for it to refer to.  Since many philosophers maintain that the meaning of a name just is its referent, the realists can argue that there must be something that is the referent of "Green".  If general words are in fact names, and the meaning of a name is the referent of the name, then there must exist something that is the referent of names of attributes.  According to the realists, "universals" is the category of existing entities that are the referents of general terms.

Realists maintain that we judge the two mats mentioned above as both being a similar color because they both share a common relationship to the universal "Green".  The reason why we recognize a similarity of attribute across two or more particulars is because those particulars share a common relationship to the universal that is the attribute in question.  However, one of the challenges facing realists is describing precisely what this relationship is between the particulars that exemplify universals, and the universals that they exemplify.  Modern Realists about universals are generally less than clear about precisely what they mean when they claim that particulars "exemplify" universals, or "instantiate" universals, or "manifest" universals.  And they are less than clear on just how it is that we come to some awareness of that "manifestation", "participation", "exemplification", or "instantiation".

Nominalists, by comparison, deny that the referent of the general term is an existing entity.  Instead, the Nominalists argue that what the word refers to is the class of particulars that "fit" the general term.  In the view of Nominalists, all that exists are particulars and the words we use to talk about them.  Critics of nominalism challenge this view by claiming that it does not resolve the problem of universals, rather it ignores the problem.  Predicate nominalism leaves as unexplained just why it is that some predicates (in this case, "is Green") correctly apply to given particulars while others (say "is red") do not.  Resemblance nominalism leaves as unexplained why is it that our two mats are members of that particular resemblance set, rather than some other set (like the set for "is red").  Trope nominalism leaves unexplained just how it is that we can recognize that some tropes are similar while other are not.

According to Conceptualism, the relation of resemblance or similarity is the consequence of a combination of our cognitive convenience and our bio-psychological reaction to the inputs of our senses.  We recognize that our two mats are similar in color because the inputs to our visual cortex result in a similar cortical response to the sight of the mats.  We judge that the two mats are similar in color because the cortical responses are similar, and the classifications of colors that we have created contains a classification called "Green" within which both those cortical responses fall.  Or in briefer terms, the two mats are both Green because the concept of Green covers both colors.  The same reasoning applies to all general terms.  So for Conceptualists, like for Nominalists, all that exists are the particulars and the words we use to describe them.  But unlike for Nominalists, Conceptualists regard the referent for the word as a concept that we create, rather than a mind-independent entity called a "universal".

One of the corollaries of the conceptualist theory of universals, however, is that it views universals as derivative rather than fundamental entities.  The fundamental entity that exists is the particular.  The existence of any specific universal is dependent on our cognitive purpose in establishing its boundaries.  From the perspective of a conceptualist, then, "universals" reflect how we react to the world around us, and how we choose to draw boundaries to most economically meet our need to understand and predict how the world is going to react to our efforts.  In a Realist/Conceptualist ontology, then, "universals" are not fundamental mind-independent entities.  The entity known as "The world" is a fundamental mind-independent entity (assuming a realist metaphysics).  But "universals," like "particulars," are derivative and mind-dependent entities.  They both exist because and only when we create them by drawing suitable boundaries around how we react to the world around us.  As a consequence, it becomes a matter of debate over the meaning of "existence" and "fundamental" as to whether "universals" ought to be acknowledged as a proper part our ontology.

Conclusion

So now we have reached a point where we can understand what the argument in the title quote is saying.  The first part of the argument is "resemblance between particulars requires the existence of a universal".  This is non-problematic.Regardless of one's theory of particulars, or one's theory of universals, it is readily acceptable that there are indeed resemblances or similarities that we acknowledge between particulars.And in a very noncommittal way, "universals" is just the name that we give to these similarities.

The second part of the argument is "There is no way to eliminate universals from our ontology".  This part of the argument must be read as a conclusion that because we acknowledge resemblances between particulars, we must therefore accept that universals have real fundamental existence.

This is clearly a basic realist argument.And as we have seen, both nominalists and conceptualists would deny that this argument carries any weight.  So I must conclude that the argument is not at all convincing.

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