The Atlas of Reality
Page 13
3.6 Can Grounding Relations be Grounded?
Are grounding facts themselves grounded? There seem to be four options:
Grounding facts are fundamental: simply and absolutely ungrounded.
Grounding facts are zero-grounded, grounded but not grounded by anything.
The straightforward account (using Litland's label): whenever the fact that p grounds the fact that q, the fact that p also grounds the fact that the fact that p grounds the fact that q.
All grounding facts are grounded in facts about essences (both quidditive and haecceitistic), and at least some of these essential facts are absolutely ungrounded.
There is an obvious problem with the first option. It entails that derivative (non-fundamental) entities are constituents of certain fundamental facts, namely, those facts concerning the grounding of those derivative entities in fundamental ones. It seems natural to assume that fundamental facts should be pure, to use Sider's (2011) term. That is, fundamental facts should involve only fundamental entities and fundamental properties.
Fine (2012b) and Litland (forthcoming) defend option 2, zero-grounding, as a solution to this problem. They rely on an analogy between theorems of pure logic and zero-grounded facts. We don't have to accept each theorem of logic as absolutely ungrounded. Instead, we accept that each theorem is true on the basis of a valid proof. However, the proof of a theorem of pure logic (unlike theorems of a theory like arithmetic or geometry) doesn't depend on beginning with any premises. A theorem of logic can be proved from the empty set of premises. In the same way, a zero-grounded fact has a metaphysical explanation, but the explanation does not involve appealing to any other, more fundamental facts. The fact that one fact is grounded in another can be demonstrated simply by showing how the first can be metaphysically explained in terms of the other.
There are a couple of problems with option 3, the straightforward account. First, it does not seem plausible that in all cases in which the fact that p grounds the fact that q, it is also the case that the fact that p grounds the grounding fact itself. Suppose that the existence of a shadow is grounded in a certain pattern of illumination on the sidewalk. It doesn't seem right that a mere pattern of light and dark on the sidewalk would have the metaphysical resources to explain how it is that it is able to explain the existence of a shadow. We need to know something about the very essence of light and darkness under these conditions in order to be in a position to know what can be metaphysically explained by the pattern, and those essential facts are not contained by the fact of the actual pattern of illumination and darkness.
Second, as Litland (forthcoming) points out, we need to have an account, not only of the status of positive grounding facts, but also of the status of negative grounding facts. That is, we must account for the falsity of positive grounding claims, such as the fact that p does not ground q. We certainly can't claim that whenever p does not ground something, it is p that grounds the absence of a grounding relation. The non-grounding fact p could be almost any fact, such as the fact that 2 + 2 = 4. That fact doesn't ground the fact that snow is white, but the fact that 2 + 2 = 4, all by itself, doesn't explain the fact that 2 + 2 = 4 doesn't explain the fact that snow is white.
Option 4 seems the most viable alternative to the Fine-Litland zero-grounding account. On this view, if p grounds q, then the fact that p grounds q is grounded in certain facts about the essences of the components of the facts p and q. In some special cases, the straightforward account is true. Suppose that p grounds q, and suppose that r contains all the facts about the essences of the constituents of p and q that are needed to ground the grounding relation between p and q. In this sort of case, it is plausible to suppose that r also grounds the fact that r grounds the grounding relation between p and q, since r contains all of the information about essences needed to explain the relation between p and q. Consequently, it would seem also to contain all the information needed to explain the relation between itself and the grounding claim. Similarly, if r is the ground of the absence of a grounding relation between p and q, it is plausible to suppose that r also grounds the fact that r grounds the absence of this grounding relation, since r would contain all the necessary information about the relevant essences (see Rosen 2010, Dasgupta 2014).
Paul Audi (2012) objects to the claim that the straightforward account could be right about any grounding relation, since no fact can ground its own ability to ground further facts. But why think this? Perhaps the thought is that we would need to add some information about the essence of the grounding relation itself. However, we might reasonably doubt whether there is such an essence. Or, we might suppose that every essence contains implicitly the relevant information about the essence of the grounding relation, since it is the very essence of an essence (we might say) to ground certain grounding relations.
3.7 Connections between Grounding and Entailment
Does grounding entail metaphysical entailment? That is, if p grounds q, does p also metaphysically entail q? Does it follow that necessarily if p then q? Let's call this the thesis of Grounding-Entailment Entailment, or GEE.
3.8T Grounding-Entailment Entailment (GEE). Necessarily, if the fact that p grounds the fact that q, then p metaphysically entails q (i.e., necessarily if p is true, then q is true).
Kelly Trogdon (2013) argues in favor of GEE. If p grounds q, then there should be no unbridgeable gap between p and q, since otherwise p offers no metaphysical explanation of q. An explanatory connection between the two requires that the grounding relation itself be grounded in essential properties (in Fine's sense) of p, q, or the entities they involve. But whatever connection is grounded in such essential truths must itself be a necessary truth. The last step seems to be a non sequitur, or perhaps a begging of the question. Essential truths are necessary, but how do we know that all truths grounded by essential truths are themselves necessary, without assuming the Grounding-Entailment Entailment thesis?
In addition, there are some possible counter-examples to GEE. Jonathan Dancy (2004) argues that q can be grounded in p, even if p does not entail q, since there could be other conditions that enable the grounding to take place. For example, my obligation to do A might be wholly grounded in the fact that I've promised to do A, even though there are other conditions (such as my being able to do A) that must be present in order for this grounding to take place. Dancy's objection is especially apt, since it might be that the necessity for these conditions is itself grounded in the essences of p and q. There might also be grounding disablers. Grounding might sometimes be a defeasible relation, one that holds in normal conditions but that can be defeated by abnormalities.
The possibility of grounding enablers and disablers could also be relevant to questions about truthmakers for universal truths. Perhaps the fact that everything is F is grounded in the conjunction of facts of the form x is F, for each actually existent x, with the relevant total totality fact (the fact that the existent things are all the existent things) as an enabler of this grounding relation, and not part of the ground.
If GEE is false grounding can still count as a kind of explanation. It is not obvious that an explanans must always entail its corresponding explanandum. It is enough if the explanans is sufficient in the actual circumstances (given the presence and absence of enablers and disablers) for the explanandum.
3.8 How is Grounding Different from Causal Explanation?
Jonathan Schaffer (2016) has argued that, structurally and formally, causation and grounding are very similar. Both support non-accidental generalizations, both delimit a specific kind of necessity (causal or natural in the one case, metaphysical in the other), and both can back explanations. However, Schaffer also notes some differences. First, a cause is distinct or separate from its effects in a strong sense. In fact, we can use grounding to define the relevant sort of separateness:
Def D3.10 Separate Existences. x and y are separate existences if and only if x is not identical y, x does not ground y, y does not ground x, and nothing
grounds both x and y.
When one fact grounds another, the two facts are definitely not separate existences in this sense. This brings out one very important difference between the two.
Second, assuming GEE, grounding entails metaphysical supervenience, while causation does not. Finally, Schaffer (2014) argues that there can be indeterministic causation, but not indeterministic grounding. In fact, causation can be probabilistic in nature, as when some cause makes a certain effect more likely than it would otherwise be. Nothing like that seems to happen in the case of grounding.
3.9 Conclusion: Grounding and Ontological Economy
When applying Ockham's Razor, do we look at all entities posited by the theory or just the fundamental ones (i.e., those that are either ungrounded or zero-grounded)? Here was our initial statement of Ockham's Razor:
PMeth 1 Ockham's Razor. Other things being equal, adopt the simplest theory.
What does it mean for a theory to be simpler? One widely accepted criterion is that the simpler theory posits fewer entities (quantative economy) and fewer types of entities (qualitative economy). In seeking such simplicity, do we minimize only fundamental things and types of things, or all things and types?
It might seem that a theory's having a large number of both derived (non-fundamental) entities and derived types or properties is a virtue rather than a vice. Schaffer argues that the correct version of Ockham's Razor demands that we maximize the ontological “bang for the buck,” that is, that we achieve an optimal balance of minimizing fundamental entities while maximizing derivative entities (especially useful ones) (see Schaffer 2014: 9).
There's some reason for thinking, however, that we should minimize the number and variety of derived entities, as well. The so-called special sciences, like chemistry, geology, and metereology, deal almost exclusively with derived entities, like mountains and hurricanes. Nonetheless, such social scientists still make use of Ockham's Razor, minimizing the postulation of theoretical entities, even though those entities are not fundamental ones. Schaffer argues that special scientists apply the Razor only when the new entities threaten to require new fundamental forces, as in cases of telekinesis (Schaffer 2014: 18).
However, ontological economy (the reduction of the number of things and types) isn't the only domain of application of Ockham's Razor. We don't just try to minimize the number of theoretical entities; we also prefer relatively simple explanations of derived facts, even when the more complicated explanations add no new fundamental entities. This demand for simpler explanations could (in some cases) bring with it a demand for fewer derived entities. Moreover, if grounding always involves an appeal to the natures or essences of the fundata, then it seems that a rich set of fundata requires a comparably rich set of fundamental facts about derived-entity essences. This should also count as a cost of the theory.
What does seem clear is that the minimizing of fundamental entities should always take priority over the minimizing of derived entities.
What if there is no fundamental level? What if there are no ungrounded or zero-grounded facts? On this supposition, all facts, and therefore all entities, would be derived. Schaffer argues that we should deny that such a scenario is really possible (Schaffer 2014: 18). Nothing could exist unless there is a fundamental explanation of its being in metaphysical terms. If, however, we do take seriously the possibility of a world without a metaphysically fundamental level, we could still use the relation of grounding to define a kind of relative fundamentality (as Schaffer 2014 demonstrates). Then we could simply give priority to the minimizing of more fundamental facts over less fundamental ones.
Notes
1. In this example and in the following one, the grounded feature is a holistic one, while the grounding facts pertain to the locations and relations of the microscopic parts. As we shall see in Chapters 18 and 22, it is not in fact so obvious that grounding should always run in this “bottom-up” direction.
2. In a seminar on grounding at the University of Texas at Austin, fall of 2015.
Part II
Dispositions
4
Conditionals
In Part II (consisting of Chapters 4–6), we are concerned with the dispositions and powers of things. From the time of the ancient Greeks, especially from the time of Aristotle onward, philosophers have recognized that the properties or features of things seem to come in two kinds: the way things are in fact (actuality), and the way things could be but aren't (potentiality). Some things are actually hot or actually red, while some things aren't hot but are potentially hot or aren't red but are potentially red.
However, this distinction between actuality and potentiality does not really correspond to a dichotomy between actual properties and potential properties, since even potentialities are properties that things have actually or in fact. I may only be only potentially a speaker of Basque, but I have the potentiality in fact. The potentiality itself is actual, even if the property that is had potentially (the speaking of Basque) is only potential. There is, though, a dichotomy between two kinds of properties: those properties that attribute some kind of mere potentiality to things, and those that don't. At least, at first glance, a property like being red describes how things are in fact, without saying anything about how things might be potentially. Other properties, like being teachable or being fragile, do involve the attribution of potentialities to things. Metaphysicians use the term ‘categorical’ for those verbs, adjectives, and predicates that designate properties that are only about the actual world and ‘dispositional’ for those terms that are also about what could potentially be the case. We will say that categorical properties are designated by categorical terms, while dispositional properties are designated by dispositional terms.
Dispositional properties typically involve potential facts by way of some condition. For example, a fragile object is one that is potentially broken, in the sense that it would break if struck with sufficient force. Consequently, one popular approach to the metaphysics of dispositional properties (adopted, for example, by Gilbert Ryle in his influential book, The Concept of Mind (1949)) takes them to involve ascribing a conditional property, a property corresponding to a conditional statement (one involving ‘if’ or a synonym of ‘if’). Ryle's conditional account of dispositions raises a further question: what is it in the world that makes a conditional statement true? Answers to this question fall into four categories: (i) conditional statements are fundamental truths, of which no further account can be given (Hypotheticalism), (ii) conditional statements are made true by the world's laws of nature (Nomism), (iii) conditional statements are made true by the actual distribution of categorical properties (Neo-Humeism), and (iv) conditional statements are made true by the powers of things (Powerism).
We will begin by looking at some recent work on the semantics and logic of conditionals (Section 4.1), followed by a consideration of Hypotheticalism (Section 4.2 through Section 4.4), Nomism (Section 5.1), Neo-Humeism (Secion 5.2), and Powerism (Chapter 6).
4.1 Counterfactual Conditionals: Semantics, Logic, and Metaphysics
A counterfactual conditional is a conditional expressed (in English) in the subjunctive, as opposed to the indicative mood. The difference in moods corresponds to a difference in truth-conditions. Consider the following pair of propositions, used illustratively by David K. Lewis in his seminal work, Counterfactuals (Lewis 1973b:. 3):
(1) If Oswald did not kill Kennedy, then someone else did.
(2) If Oswald had not killed Kennedy, then someone else would have.
(1) is in the indicative mood, while (2) is subjunctive. Let's suppose that we all believed that the Warren Commission was right, and Oswald acted alone. In that case, we would certainly count (1) as true (since our confidence that Kennedy was killed by someone is independent of our belief that Oswald was in fact the killer), and we would count (2) as false (since, believing Oswald to have been acting alone, we suppose that had he not carried his plans, Kennedy would not have been assassina
ted at all). The obvious falsity of (2) also tells us that we cannot interpret the conditional in (2) as the material conditional of standard propositional logic.
In standard logic, the statement ‘if p, then q’ is true just in case p is false or q is true. This rule corresponds to reading the ‘if/then’ statement as a material conditional, in the sense that the truth-value of the conditional depends only on the facts about the actual truth or falsity of its parts (its logical ‘matter’). Since the antecedent of both (1) and (2) is false (Oswald did in fact kill Kennedy), the corresponding material conditional must be true. Since (2) is false, a counterfactual or subjunctive conditional cannot be a material conditional.1
Counterfactual conditionals must also be distinguished from what C.I. Lewis called the “strict conditional” (Lewis 1932). A strict conditional ‘if p, then q’ is true if and only if it is impossible for p to be true and q to be false. (3) would be an example of a strict conditional:
(3) If this box were red and square, then it would be red.
If the box is red and square, it is impossible for it not to be red. However, there are examples of true counterfactuals that would be false if they were read as strict conditionals. Consider (4):
(4) If McCain had won the vote in Michigan and Florida, he would have been elected President in 2008.
(4) seems true, given the closeness of the electoral vote in 2008. However, it would not be true, if read as a strict conditional. It is surely possible for McCain to win those two states without winning the Presidency. This could have happened were he to have won Michigan and Florida but lost states which he did in fact win. Hence, the counterfactual conditional is not a strict conditional.