Constituent Versus Relational Ontologies

Since the relationship between God and universals is one factor in the controversy over divine ultimacy lurking behind the classical theist versus theist personalist dispute I discussed here, here and here, it seems fitting to review this old entry. 

Debates over the difference between Platonism and Aristotelianism, and the respective merits of each position, are likely to continue for as long as Man philosophizes. This post does not seek to take a stance on which position is correct but to provide clarification on an issue which is too often lumped into this debate, that is the way in which particulars are related to their universals.

I contend that many of the superficial charges Platonists and Aristotelians, particularly those who adopt such position in virtue of the role they play in wider philosophical systems, lay at one another's feet really relate to the alternative and more fundamental differences between constituent and relational ontologies. This entry is intended to give a brief run-through of these two approaches to ontology. To do so I will look at two claims attributed to each position, at least in popular presentations (let us call their proponents the ‘pop-Platonist’ and ‘pop-Aristotelian’ respectively).

Origin Essentialism and Disappearing Possibilities: A Problem for S5

In the spirit of continued self-criticism I will turn to a problem for a specimen of my favourite family of theistic proof, that it is Plantinga’s formulation of the modal ontological argument.

Axiom S5 states that if something is possible then necessarily it is possible¹. If Socrates is a possible being then this fact could not be otherwise; it is always and forever true that Socrates is a possible being. Possibilities do not change or pass away—they are a necessary part of the ‘deep’ ontological structure of reality and thus are set throughout all possible worlds.

An Introduction to Tropes

Since they have cropped up in a number of discussions before and arguably form an indispensable part of the metaphysics of 'Classical Realism', Scholastic Realism very much included, I thought it would be worth doing an all-round intro post on the subject of tropes. First of all a terminological distinction: the term 'tropes' and 'property-instance' will be used synonymous throughout this post, though the former is often used in the context of a certain kind of Nominalism it is in fact neutral as to whether one also includes universals in one's ontology. The term property-instance on the other hand might imply a realist commitment with said entities being instances of something above them. The phenomenologically inclined will of course also recognize tropes/property-instances as being equivalent to Husserl's 'moments'.

Word-making isn't World-making

Properties don't stand in one-to-one correspondence with predicates, and predicates don't stand in one-to-one correspondence with properties.

Arguing in the first direction, there are probably properties for which human language has no terms. So, there are probably properties that don't stand in one-to-one correspondence with predicates.

And even if there aren't any properties for which human language has no terms, rocks, cabbages, trees and things had properties before man and would have had he never risen from the ooze at all.

Infinities and Infinities and Infinities

Arguing in the second direction, by following accepted predicate formation rules, predicates can be gratuitously generated from other predicates. They can, for example, be generated from disjunctive predicates like “—is red or yellow”, “—is red or shiny”, and “—is red or aquatic”, and negative predicates like “—is not yellow“, “—is not shiny”, and “—is not aquatic”. If predicates stand in one-to-one correspondence with properties, each of those predicates corresponds to a unique property. So, if predicates stand in one-to-one correspondence with properties, there is some indefinitely large number of properties in the world¹.

The one-to-one correspondence also leads to infinite regresses. For instance, “a is self-identical” would correspond to a property of self-identity. If, however, a has the property of being self-identical, it also has the property of being self-identical with itself-with-that-property-of-self-identity. And if a has the property of being self-identical with itself-with-the-first-self-identity-property, it also has the property of being self-identical with itself-with-the-self-identity-property-for-itself-being-self-identical-with-itself-with-the-first-self-identity-property. And so on, ad infinitum.

There is another regress. If predicates stand in one-to-one correspondence with properties, the truth of “a is red” necessitates that a has the property of being red. If, however, the truth of “a is red” necessitates that a has the property of being red, the truth of “a has the property of being red” necessitates that a has the second-order property of having the property of being red. And so on, ad infinitum.

There are more regresses. If predicates stand in one-to-one correspondence with properties, the previous argument applies to every property we can generate from a base predicate (e.g. red). So, if predicates stand in one-to-one correspondence with properties, there is an infinity of properties of having properties for every base predicate.

There are, however, probably not infinities of odious properties like the above. So, predicates probably don't stand in one-to-one correspondence with properties.

Contradiction

There are also paradoxical predicates like “—is a property to which no predicate corresponds”. So, predicates don't stand in one-to-one correspondence with properties, and we can abandon the disastrous conflation of predicates and properties, of language and reality, once and for all.

You will see why all this matters, if not now, in future posts.²


1. I take Ellis's word for it when he says that there is at least one infinite set corresponding to each generative operation.
2. Most of this post's arguments, as well as its title phrase, can be found in George Molnar's Powers.

Tropes or God, II: Relata-specificity

This post assumes familiarity with Tropes or God, I.

Rejecting (1)

In Relata-specificity: A Response to Vallicella, Betti argues that we can resist (5) by rejecting (1).

Betti begins her argument by distinguishing relata-specific and relata-unspecific relations. A relation is relata-specific if and only if it's in its nature to relate specific relata; in contrast, it's relata-unspecific if and only if it isn't in its nature to relate specific relata. Relata-specific relations are unsaturated entities into which only specific objects fit; relata-unspecific relations aren't unsaturated entities into which only specific objects fit.

Betti then argues that if R in aRb can be construed as the relata-specific _a_R__b, aRb can be identified with the sum a + _a_R__b + b; R in aRb can be construed as the relata-specific _a_R__b; hence, aRb can be identified with the sum a + _a_R__b + b; hence, there isn't necessarily a real difference between aRb and the sum a + R + b. In other words, she argues that relata-specific relations can be used to reject (1).

If Betti is right, we can resist (5) by rejecting (1).

Simple or Complex? Vallicella's Reply

In his review of Betti's Against Facts, Vallicella argues that, one, R can only be relata-specific if it's identical to aRb and incorporates its relata; two, if R is identical to aRb, it can't account for the unity of aRb; thus three, if R is relata-specific, it can't account for the unity of aRb; thus four, relata-specific relations can't be used to reject (1).

But why accept that R can only be relata-specific if it's identical to aRb? Construing relata-specific relations as unsaturated entities into which only specific objects fit provides a seemingly fine explanation for why they're relata-specific, and doesn't obviously make R into aRb.

We can go a step further than Betti herself does and bolster her explanation by turning Brentano on his head and making primitive directedness a mark of non-mental entities either instead of or as well as mental entities.

I wrote this article about a year ago and, at the time, I was keen to uphold something like Martin's naturalism. I no longer find naturalism convincing. I still, however, think that we must admit primitive directedness into our ontologies somewhere, and can find no real objection to admitting it in the non-mental world.

I would be interested if anyone can.

Further reading:

“Intentionality and the Non-Psychological”

The Mind in Nature

“Intentionality, Potentiality, and Dispositionality: Some Points of Analogy”

Tropes or God, I: Bradley's Regress

In Relations, Monism, and the Vindication of Bradley's Regress and Bradley's Regress and Relation-Instances, Vallicella argues:

(1) There is a real difference between the sum a + R + b and fact aRb.

(2) This difference isn't brute¹. That is, it must have an ontological ground.

(3) This ground is in (i) constituents a, R, or b; (ii) one or more additional constituents in aRb; (iii) aRb itself; or (iv) something outside aRb.

(4) The ground isn't in (i), (ii), or (iii).

(5) From (1) – (4), something outside aRb grounds its difference from a + R + b.

His argument implies that without God the world would fall apart.²

I begin my attempt to exorcise Bradley's ghost by supporting Vallicella's premises.

Premises (1), (2), and (3)

Vallicella starts by distinguishing the sum a + R + b from the fact aRb. The sum exists as long as a, R, and b exist; in contrast, the fact only exists if a, R, and b are unified or “together”. The sum of John, a tea cup, and the two feet from relation exists as long as John, the tea cup, and the relation exist; the fact of those constituents only exists if John is two feet from the tea cup. In short, since John + the tea cup + the two feet from relation can exist without its corresponding fact existing, sums are different from facts.

Vallicella argues that this difference has an ontological ground. He argues that, one, if the difference between a + R + b and aRb is brute, they're both composed of nothing more than a, R, and b; two, if a + R + b and aRb are both composed of nothing more than a, R, and b, they're identical; three, since aRb is the unity of a + R + b's constituents, a + R + b isn't identical to aRb; thus four, if the difference between a + R + b and aRb is brute, a + R + b both is and isn't identical to aRb; thus five, the difference between a + R + b and aRb has an ontological ground. It follows from the last two paragraphs that the difference between sums and facts has an ontological ground.

The foregoing and some analysis entail that the difference between a + R + b and aRb is grounded in (i) the constituents a, R, or b, (ii) one or more additional constituents in aRb, (iii) aRb itself, or (iv) something outside aRb.

Premise (4)

Vallicella argues that this difference isn't grounded in (i), (ii), or (iii). First, he argues that a + R + b and aRb are both composed of a, R, and b; if a + R + b and aRb are both composed of a, R, and b, they're identical in respect of a, R, and b, and neither a, R, nor b can ground their difference; thus, neither a, R, nor b can ground the difference between a + R + b and aRb. In other words, he argues that assumptions behind the sum-fact distinction rule out (i).

Second, Vallicella argues that aRb can only ground its own unity if it exists logically prior to its existing; it therefore can't ground its own unity; the difference between the sum and its fact is that the sum isn't relevantly unified and the fact is; therefore, since aRb can't ground its own unity, it also can't ground the difference between a + R + b and itself. In brief, he argues that (ii) is incoherently circular.

Third, Vallicella argues that if one adds a constituent (C) to aRb to try grounding aRb's unity, this results in a further fact (aRCb) that needs its unity grounded. And if one adds another constituent (C*) to that fact, this results in another fact that needs its unity grounded, and so on with each new constituent ultimately failing to ground its corresponding fact's unity. In fewer words, he argues that (iii) leads to a vicious, infinite regress. It follows from the last three arguments that the difference between a + R + b and aRb isn't grounded in (i), (ii), or (iii).

If the foregoing arguments are right, (5) follows. In future posts, I shall argue that some of them are wrong, and build an ontology that grounds the unity of facts in particularized relations.

1. I use brute, here, to mean "lacking an ontological ground".

2. Or, if you're truly brave, you can accept fact infinitism. I won't be developing the inference from external unifier to God in this post, though I think it right.

Bibliography

Betti, Arianna. Against Facts. The MIT Press, 2015.
Betti, Arianna, and Jan Willem Wieland. “Relata-specificity: A Response to Vallicella”. Dialectica, vol. 62 no. 4, 2008, pp. 509-524.

Vallicella, William F. A Paradigm Theory of Existence: Onto-Theology Vindicated. Kluwer Academic  Publishers, 2002.

---. “Bradley's Regress and Relation-Instances”. The Modern Schoolman, LXXXI, 2004.

---. “Relations, Monism, and the Vindication of Bradley's Regress”. Dialectica, vol. 56 no. 1, 2002, pp. 3-35.