(1, 2, S5)
If an infinite thing causes another infinite thing, then they have the same nature (S6).
No infinite thing can cause an infinite thing. (4, S5)
No finite thing can cause an infinite thing. (S5, S6)
Only finite things can be caused by another. (5, 6)
Everything that is caused is caused (ultimately) by a self-caused thing. (S8)
If one thing causes another, the second thing is a finite thing caused by an infinite thing. (7, 8, 1)
An infinite thing cannot cause a finite thing. (S6, S7)
Nothing is caused by something else. (9, 10)
Everything is self-caused. (S2, 11)
There is at least one thing. (S1)
There is exactly one thing. (3, 13)
The argument up to step 9 is one that could have been endorsed by many ancient, medieval, and early modern philosophers who engaged in what is known as natural theology. This would include Plato, Aristotle, Plotinus, Anselm, Thomas Aquinas, Duns Scotus, Leibniz, or Samuel Clarke. All would agree that we can establish the existence of a First Cause of the world that is infinite and unique. (We will consider such First Cause arguments in more detail in Section 26.2.) However, at step 10 Spinoza moves in a surprising and new direction: he attempts to show that this First Cause (“God”) is incapable of causing the existence of anything else, since It could only cause things having the same nature (S6), but nothing else with the same infinite nature could possibly exist (S5).
Philosophers in the natural theology tradition would challenge step 10, which resulted from the combination of S6 and S7. Why can't an infinite thing cause a finite thing? Thomas Aquinas would have rejected S6, claiming that an infinite cause can have the nature of its finite effect “eminently”. (Thomas Aquinas, Summa Theologiae I, Q4, A2) Concerning S7, we could ask. Why can't finite and infinite things have the same nature, in the relevant sense? John Duns Scotus, for example, would have rejected S7, arguing that God (an infinite thing) shares many natural features with many finite, created things (such as existence, goodness, life, knowledge, and consciousness) (Ordinatio 1.3.1, 1–2; see Cross 1999: 38–41).
Spinoza has a number of additional arguments for step 10. One such argument is based on the supposition that God, the infinite being, would not create a mere finite being, since the product would fall so far short of God's own excellence (see pages 51–52 of the Short Treatise, Spinoza 1677b/1958b).
11.2.3 Bradley's Monism
F.H. Bradley was a British Idealist, who was influenced by the work of G.W.F. Hegel. Bradley argued that only one thing existed: the Absolute. He had a number of arguments for this conclusion but the most influential one involved what has become known as Bradley's Regress.
Bradley connects two problems. First, there is the problem of grounding or explaining relational truths. Second, there is the problem of grounding or explaining the distinctness of distinct things. Bradley seems to suggest that these are one and the same problem. For two things to be distinct, they must be related somehow to each other. But, Bradley argues, there are hidden paradoxes lurking in the idea that one thing could be related to another thing.
Prima facie, however, these are separate problems. Couldn't there be relational truths that don't involve two or more distinct entities? Couldn't there be such a thing as self-relatedness? Couldn't there be two distinct but unrelated things? On the other hand, there are a couple of things to be said in favor of Bradley's combination of these two problems. First, in general, there couldn't be relatedness without some plurality in the world. It wouldn't make sense to have relations if it were impossible for a relation to hold between two things. If there were no plurality or multiplicity in the world, there would be no way to differentiate between relations and monadic qualities. Second, there couldn't be distinctness without relatedness. After all, being non-identical is itself a relation. It would be a contradiction to say that two things exist and yet are absolutely unrelated to each other.
In any case, even if Bradley is wrong to combine the two issues, his proof that there cannot be any relational truths is interesting in its own right.
Here's a reconstruction of Bradley's main argument (Bradley 1897/1930: 21–29):
If two distinct things exist, then their distinctness must be explained by (by being grounded in) their standing in some distinguishing relation to one another (at the very least, the relation of distinctness).
More generally: if n distinct things (where n ≥ 2) exist, then their distinctness must be grounded in their standing in some distinguishing relation or relations to each other (either by pairs or collectively).
If the distinctness of n things is grounded in their standing in some distinguishing n-ary relation, then (i) that relation must exist, (ii) the relation must be distinct from each of the n things, and (iii) the distinctness of the n things must be partly grounded in the distinctness of that distinguishing n-ary relation from each of the n things.
The partial grounding relation between distinctness facts is transitive and asymmetric—so no cycles of grounding.
If two distinct things exist, then there is an infinite regress of explanations of their distinctness (from 1–4).
Such an infinite regress cannot exist.
Therefore, there cannot exist two or more distinct things, and no two things are related.
Bradley's argument for clause (i) of premise 3 relies on the fact that a relation cannot be something like a quality that is predicated of one or both of the relata. Therefore, the distinguishing relation must exist in its own right. It cannot be something merely predicated of the relata.
Moreover, this relation must be distinct from its relata (clause (ii) of premise 3), for it is impossible for something to be both related to something else and to be the relation by which it is related to that other thing. A relation (if it exists at all) must always be distinct from its relata.
Moreover, if the two things could not ground their own distinctness but require a distinguishing relation to do so, that distinguishing relation had better be distinct from each of the two things. Thus, the distinctness of the relation from its relata is presupposed by the relation's doing its job of distinguishing them. Consequently, the distinctness of the relata depends upon the distinctness of the relation from the relata (clause (iii) of premise 3).
Here's how the regress works. Suppose that a and b are distinct. Then there must be a distinguishing relation R1 that relates a and b and that grounds their distinctness. To do this job, R1 must exist and be distinct from both a and b. Thus, the distinctness of a and b is partly grounded in the distinctness of R1 and a, and in the distinctness of R1 and b. Now, since R1 and a are distinct, their distinctness must be grounded in their standing in some distinguishing relation R2. But R2 must be distinct from both R1 and a, and so the distinctness of R1 and a is dependent on the distinctness of R2 and a. In the same way we can generate further links in the dependency regress: the distinctness of R2 and a grounded in the distinctness of some R3 and a, and so on.
The key step in the argument is premise 3, especially clause (i), which introduces a new distinguishing relation that holds between the first distinguishing relation and its relata. Some philosophers, following Plato's lead, have introduced the instantiation, participation or exemplification relation. (We called such philosophers ‘Realists’ in Chapter 7.1) This is the relation that is supposed to hold between a relation and two or more things whenever those things stand together in that relation. Exemplification might do the work of distinguishing a relation from its relata. But for the argument to work, we have to suppose both that such a relation exists, and that its holding between R, a, and b is what explains the fact that R, a, and b are mutually distinct. To take a concrete example, suppose that hill A is due north of hill B. The two hills stand in the one-north-of-the-other relation, or the north-of relation, for short. Suppose that the north-of relation is itself a thing, no less than hills A and B are. If so, it does seem that the three
things, the north-of relation, A, and B, all stand together in some relation: the ternary (3-place) relation of the first thing's being a relation that the second thing stands in to the third thing.
However, if this is so, and the holding of the exemplification relation is thought to be prior in terms of explanation to the holding of the north-of relation, then we seem to fall into an infinite regress. The holding of the exemplification relation by the north-of relation, A, and B would itself have to be explained by a prior holding of the four-place exemplification relation between the exemplification relation, the north-of relation, A, and B. And so on to infinity.
We have already encountered Bradley's Regress in Section 7.2.1.3, in our discussion of universals. As we saw, Ostrich Nominalists object to the introduction of relations as things. They suppose that A's being north of B is not to be understood in terms of A's and B's standing with the north-of relation in the exemplification relation.
Realists (7.1T), who do believe in the existence of universal like NORTH-OF, will attempt to block the regress at the second step by denying the existence of the exemplification relation. Such Realists employ the slogan, Relations relate! In other words, a relation doesn't need some further entity to connect it to its relata. In the context of Bradley's Regress, such Realists would have to claim that a relational universal can be the ground for its own distinctness from its relata. In effect, such relations do relate themselves to their relata, contrary to step 3. The NORTH-OF universal could ground its own distinctness from its relata, pehaps by simply being a universal, rather than a particular. Consequently, there is no need to introduce an EXEMPLIFICATION universal, and thus no reason to posit another instance of exemplification linking it to the other three entities (the NORTH-OF universal and the two hills).
Bradley has supplementary arguments for premise 3. He explicitly considers an alternative, namely, that the relation is merely a property or “adjective” of the relata. We could take this in the spirit of Ostrich Nominalism. We could ask. Why not posit primitive, irreducibly relational facts, with no third entity involved?
In response, Bradley proposes a three-part dilemma (or trilemma). Either (i) this property is predicated of one relatum but not the other or (ii) it is predicated of each (distributively) or (iii) it is predicated of both taken together (collectively). (Presumably, we can ignore the other logical possibilities: that it is predicated of neither or that it is predicated of the relata plus some additional things.) Bradley argues that none of (i)–(iii) are workable:
The relation is not the adjective of one term, for, if so, it does not relate. Nor for the same reason is it that adjective of each term taken apart, for then again there is no relation between them. Nor is the relation their common property, for then what keeps them apart? They are now not two terms at all, because not separate. (Bradley 1897/1930: 27n1)
There are two parts to Bradley's argument here, H1 and H2:
H1. If the relation is predicated of just one of the relata, then this fact cannot ground the relatedness of the two. If it cannot ground their relatedness, then neither can it ground their distinctness (since distinctness is a relation).
H2 (H2a and H2b). If the relation is predicated of both of the relata, either distributively (H2a) or collectively (H2b), then it marks no difference between the two, and so it cannot ground the distinctness of the two relata.
Let's consider each claim in turn.
Reply to H1. Why can't the ground of distinctness consist in the fact that some property is predicated of one of the two things and not of the other? For example, suppose that a is black and b is not. To avoid a regress, let's suppose that these facts are primitive and fundamental and so not to be analyzed in terms of a relation to some universal.
We might worry here about what the truthmaker for b's not being black could be. Could it simply be b? Couldn't b be essentially and intrinsically non-black? Perhaps Bradley considered it to be impossible for such a fact to be fundamental. Perhaps it must be grounded in some further fact: either that b has a property that is incompatible with being black or in the fact that b lies outside the Totality Fact for BLACKNESS (thought of now as a shareable universal). Either of these would depend on some further relation: a relation of incompatibility between the two incompatible properties or a relation of lying-outside between B and the extension of the property it doesn't have. Even if being non-black were fundamental, one might think that it could ground b's distinctness from a only if being black and being non-black stand in some kind of relation of logical incompatibility. Bradley could argue that, once again, the problem has only been shifted back a step: how are we to explain those relational facts? Another infinite regress threatens.
Reply to H2a. Bradley claims that distinctness cannot be grounded in a common property, a property possessed by each of the two relata. This seems reasonable. How could the fact that two things are alike in a certain way possibly ground their distinctness (their non-identity)? Or, to put the point another way, two monadic facts cannot add up to a relational fact. If Bob is in New York and Jones is in New York, this constitutes a relation between Bob and Jones only on the assumption that Bob and Jones are distinct, which is just what we are trying to ground.
Reply to H2b. Bradley objects that a relation that is predicated of two things collectively cannot account for the separation of a and b. Bradley's argument seems to be most clearly targeted at Fundamental Relations of Distinctness (9.2A.1). Bradley echoes our objection based on Relata more Fundamental than Relations (the claim that the existence and distinctness of the relata of any relation cannot be grounded in or made true by the holding of the relation itself; see the discussion of 9.2A.1). Two things cannot have the common property of belonging together to a pair of distinct things without being somehow independently distinct from each other. The ground of the distinctness of a and b cannot be the fact that they both belong as parts to the pair set {a, b}, since the existence of the pair as a pair depends on their independent distinctness.
What if a and b are two parts of a structured whole, like two amphibians in a structural universal (see Section 10.3)? Suppose, for example, that a is the pitcher position and b the catcher position in a baseball team c. In this case, we might suppose that the existence of a and of b is each partly grounded in the existence of the whole c, namely, that c is ontologically prior to both a and b and that c's essence or nature provides the grounds for the distinctness of a and b. You can't have a baseball team without a pitcher and a catcher that are distinct from each other.
Bradley might respond that this just pushes the problem back a step. We will now need an account for the distinctness of a from c and for their relatedness (and also for that of b's distinctness from and relatedness to c). However, we can ask Bradley, in turn: why can't c itself be the ground for these truths? Since a and b are both parts of c, we don't need an account of the separateness of a from c—for the simple reason that they aren't separate at all.
Perhaps this conclusion would not be unacceptable to Bradley. It would push us toward the view that the totality of all things (as a structured whole) is the metaphysically fundamental reality, grounding the nature and distinctness of all of its constituents. This might be merely a version of a moderate or Priority Monism, of the kind that we will examine in more detail next (in connection with Jonathan Schaffer's work).
Before we leave Bradley, we need to consider a second regress argument that occurs in the same passage (Bradley 1897/1930: 26–7). We can call this regress the internal regress, in contrast to the external regress that we have just considered.
Suppose a and b are related to each other. There must be two moments or aspects of a—one of which is a qua related to b, and the second a qua existing on its own (apart from its relation to b). Bradley claims that there cannot be a genuine case of relatedness without both of these aspects. These two aspects of a can't be simply identical to each other, since they involve contrary characteristics of a (as related to b, as not related to b). Co
nsequently, for a to be related to b, there must be some unity (and hence some relatedness) between two distinct things: a-as-related-to-b, and a-as-not-related-to-b. This launches a second infinite regress.
In response, we could insist that these two aspects are not really distinct. They are distinct only in our thought or intention. Both aspects are really just a, after all. The aspects are both abstracted in thought from what is one and undivided in reality (to use Aristotle's term). Bradley's retort might be that this would entail that the act of abstraction generates a falsehood or fiction, which would still preclude the real existence of a relation.
Finally, let's consider the import of Bradley's Regress for Constituent Realism, UP-Realism combined with Constituent Ontology (9.1A). Bradley's Regress could be developed against combining Constituent Realism with any sort of self-individuating pairs of things, including bare particulars, haecceities, or even primitively distinct universals (see Section 9.3.2). On a pure version of Constituent Ontology, the one and only primitive relation is that of being-part-of. Primitive relational facts involve at least three things: a and b as distinct proper parts of a whole c. We could express this fact as: a and b jointly compose c.
There is no temptation to introduce a fourth entity. c is the truthmaker for this relational fact. It is by virtue of the existence of c that a and b jointly compose c. This may help with both regresses. The relationality of a and b to c (and to each other) is contained entirely in the being of c.
Does Constituent Realism work both when c is ontologically prior to a and b and when a and b are ontologically prior to c? (Let's assume that we can understand ontological priority in terms of grounding. If x is ontologically prior to y, then the existence and intrinsic character of y is wholly grounded in some facts that include the existence and intrinsic character of x.) In the first case, when the whole is prior to the parts, all three entities exist only as-related to the others. In the second case, when the parts are prior to the whole, a and b have independent existence but no internal relatedness to c, and c has internal relatedness to a and b but no existence independent of the relation, so in both cases the internal regress seems to be avoided.
The Atlas of Reality Page 40
