External Relations and Bare Particularism

K. V. writes,

I am a first year Jesuit novice of the USA Midwest province. I'm from Cincinnati, OH. I have interests in philosophy. I know Thomism well. My hope is to do metaphysics and philosophical logic within the analytic tradition. 

 

I saw that you wrote a paper on external relations and Bradley's Regress. Can I ask you a couple questions regarding external relations? Do you think that first order logic is ontologically committed to external relations? Also, if all relations are external, would this entail a sort of bare particularism about objects? In other words, would all necessary properties be conceived of as something added, rather than as the essence?

It is good to make your acquaintance, K. V. Best wishes for your studies.

 

First we need to clarify 'internal and 'external' as applied to relations.  

 

External Relations. My coffee cup rests on a coaster which rests on my desk. Consider first the dyadic on top of relation the relata of which are the cup and the coaster. This is an external relation in the sense that both the cup and the coaster can exist and have the intrinsic (non-relational) properties they have whether or not they stand in this relation. Removing the cup from the coaster need not induce an intrinsic change (a change in respect of an intrinsic property or change in existential status) in the cup or in the coaster. One could also put the point modally. In the actual world, the cup is on the coaster at time t. But there is a merely possible world W in which the cup is not on the coaster at t. In W, cup and coaster both exist and possess the same intrinsic properties they have in the actual world, but the cup does not bear the external on top of relation to the coaster.

Now consider the triadic between relation that relates the members of the ordered triple <coaster, cup, desk>. This relation is also external. The terms (relata) of the relation can exist and have the intrinsic properties they have whether or not they stand in the relation.

A-Internal Relations. If a relation is not external, then it is non-external. One sort of non-external relation is an A-internal relation, where ‘A’ honors David M. Armstrong:

Two or more particulars are internally related if and only if there exist properties of the particulars which logically necessitate that the relation holds. (Universals and Scientific Realism, II, 85)

Consider two balls, A and B. Each has the property of being red all over. Just in virtue of each being red, A and B stand in the same color as relation.  Each ball's being (the same shade of) red logically suffices for them to stand in the relation in question.  This relation is internal in that the non-obtaining of the relation at a later time or in a different possible world would induce an intrinsic change in one or both of the balls. In other words, the two balls could not cease to be the same color as one another unless one or both of the balls changed color. But the two balls could cease to be ten feet from each other without changing in any intrinsic or non-relational respect. Spatial relations are clear examples of external relations.

 

In a theological image, for God to bring it about that Mt. Everest is higher than Mt. Kiliminjaro he need do only two things: create the one mountain and then create the other. He doesn't have to do a third thing, namely, bring them into the higher than relation. 

A-internal relations can be said to be founded relations in that they are founded in intrinsic (non-relational) properties of the relata. Thus the relational fact of A’s being the same color as B decomposes into a conjunction of two non-relational facts: A’s being red & B’s being red. These non-relational facts are independent of each other in the sense that each can obtain without the other obtaining.  A-internal relations reduce to their monadic foundations.  They are thus an "ontological free lunch" in Armstrong's cute phrase.   They do not add to the ontological inventory. They are no "addition to being." So if every relation were A-internal, then the category of Relation, as an irreducible category of entities, would be empty.

B-internal relations. To say that two or more particulars are B-internally related, where ‘B’ honors Bradley and Blanshard, is to say that there is no possible world in which the particulars exist but do not stand in the relation in question. Thus two B-internally related particulars cannot exist without each other. Each is essential to the other. Here is an example. Set S has five members essentially (as opposed to accidentally) , while set T has seven members essentially. These essential properties of S and T found the relation larger than (has a greater cardinality than) that obtains between them. Although there are possible worlds in which neither set exists, there is no possible world in which both sets exist but fail to stand in the relation in question.  So S and T are B-internally related.

 

Here is a simpler example, Socrates and his singleton {Socrates}.  The first is an element of the second, and cannot fail to be an element of the second. And the second cannot fail to have Socrates as its sole element.  So Socrates and his singleton stand in a B-internal relation.  

 

Go back to the cup and the coaster. The first is on top of the second.  If they were B-internally related, then that very cup could not have existed without that very coaster, and vice versa. In every possible world in which the cup exists, the coaster exists.  That strikes me as preposterous. So while I grant that there are B-internal relations, not all relations are B-internal. There are external relations.

In sum, external relations are not founded in the non-relational properties of their relata. A-internal relations are founded in accidental non-relational properties of their relata. B-internal relations are founded in essential non-relational properties of their relata.

My reader asks a question that I will precisify as follows: Is standard first-order predicate logic with identity ontologically committed to external relations?  I should think so. The quantifiers range over a domain of existents.  If that were not the case, 'Cats exist' could not be replaced salva veritate with 'For some x, x is a cat.' For the particular quantifier to be an existential quantifier, the domain of quantification must be a domain of existents.  

 

So modern predicate logic includes a commitment to ontological pluralism, to a plurality of numerically distinct individual existents.  This is a totality of "independent reals" (to borrow a phrase from Josiah Royce). Each of these independent existents has no need of any other one for its existence.  In Humean terms, they are "distinct existences," i.e., numerically distinct existents.   No doubt they stand in external relations. The cat is on the mat but it has no need of the mat to exist and the mat pays the same compliment to the cat.  The relation that connects them is external.   

 

The reader's second question is none too clear.  He may be asking this: If all relations are external, does it follow that concrete particulars that stand  in such relations are bare particulars? First of all, what is a bare particular?

 

A bare particular is not a particular without properties. As a matter of metaphysical necessity, everything has properties. What make a bare particular bare is not its lack of properties, but the way it has the properties it has. It has them by exemplifying/instantiating them, where (first-order) exemplification is -- or is modelled on -- an asymmetrical external relation.  Thus the bare particular in a red round spot -- to use a typical Bergmannian, 'Iowa,' example -- stands in an external relation to the property of being red and the property of being round in the same spot.   A bare particular is not an Aristotelian primary substance; it is not an individual essence or nature.  It has properties but they are all accidental properties.  It cannot not have properties, but there is no necessity that it have the very properties it has. So, from 'Necessarily, every bare articular has properties' one cannot validly infer 'Every bare particular has the properties it has  necessarily.'  By contrast, an Aristotelian primary substance (prote ousia) is an individualized essence or nature.

 

The answer to the second bolded question, I think, is in the affirmative. But to explain this with any rigor would take more time than I presently have to invest.

Comments

[KV]

Thanks, B.V. You answered both of my questions. If bare particulars don't have properties necessarily, then I wonder how they can be characterized at all. Isn't "necessarily having properties" itself a property that bare particulars have? If this is the case, then do they have this property with necessity? This would undermine a "totality of independent reals," taking first order logic down with it.

Thanks,
KV

[BV]

>>If bare particulars don't have properties necessarily, then I wonder how they can be characterized at all.<< Two points.

First, 'essentially' is the right word, not 'necessarily.' Socrates is essentially human -- human in every possible world in which he exists --but not necessarily human: he does not exist in every possible world. God is both essentially and necessarily omnipotent.

Second, BPs have accidental properties and they are characterizable in terms of them.

[BV]

>>Isn't "necessarily having properties" itself a property that bare particulars have? If this is the case, then do they have this property with necessity?<<

This argument is plausible but not compelling. Bergmann could say that while it is true that every BP has properties, this truth does not require that there be a property of having properties that every BP instantiates.

[KV]

Thank you for answering my questions. I still have many more, but I see that Bergmann is a good place to start for reconstructive metaphysics.