The Atlas of Reality
Page 10
There is also a useful distinction between one fact's wholly grounding versus only partially grounding another. For example, one might think that the meaning of a word on a particular occasion is partly grounded in the intentions of the speaker, but not wholly grounded in those intentions, since the meaning also depends on current linguistic practices and conventions. Let's suppose that one fact can be wholly grounded (jointly) by a set of facts, and not just by one other fact taken alone. For example, the fact that the set {0,1} has two members is wholly grounded in the fact that is has 0 as a member together with the fact that it has 1 as a member (and perhaps also by the fact that 0 and 1 are different). It is then easy to define partial grounding in terms of whole grounding:
Def D3.2 Partial Grounding. The fact that p is a partial ground for the fact that q if and only if there is a set Γ of facts containing the fact that p such that Γ (wholly) grounds the fact that q.
Fine (2012a) also defines a relation of weak grounding, a relation that is useful in defining the logic of grounding:
Def D3.3 Weak Grounding. That p is a weak ground for the fact that q if and only if either the fact that p grounds the fact that q or p = q.
3.1.5 Grounding is different from conceptual priority, reduction, and supervenience
Let's grant that we have pretty good reason to believe that there is metaphysical grounding. We still need to investigate whether this is an independent, indispensable notion, not definable in terms of other familiar relations.
3.1T.1T Indefinable Grounding. The grounding relation is unique and indefinable.
3.1T.1A Definable Grounding. The grounding relation is definable in terms of other relations.
We might think, for instance, that grounding either is or is definable in terms of conceptual analysis, reduction, or supervenience.
Consider conceptual analysis or conceptual priority first.
3.1T.1T.1 Conceptual Analysis and Indefinable Grounding. Grounding is not definable in terms of conceptual analysis.
What is conceptual analysis? What is it to analyze one thought or proposition into another? These are difficult questions to answer, because the notion of analysis has been used in somewhat different ways by different philosophers since at least the time of Leibniz in the seventeenth century. We nonetheless take a stab at it. First, a conceptual analysis of one proposition in terms of another preserves the semantic content or cognitive significance of the analyzed proposition (the analysandum). At the same time, the structure of the two propositions should be similar, with the exception that simple elements in the analysandum have been expanded into more complex expressions in the analysans (the product of the analysis). So, for example, one might analyze the proposition that Brown is a ophthalmologist into the slightly more complex proposition that Brown is a medical doctor specializing in the treatment of the eyes, with the underlying thought that the cognitive significance of being an opthamologist just is (for those who have that concept) exactly the same as that of being an eye doctor.
The first thing to note is that there seems to be a mismatch between the domains of grounding and conceptual analysis. Grounding, at its core, seems to relate facts or entities “in the world” (as we might say), while conceptual analysis is clearly not such a relation. Rather, conceptual analysis relates propositional contents, thought of as objects of thought and understanding. On some views, there is no real difference between facts and true propositions, but on many other views they are fundamentally different.
More importantly, there are some instances of grounding that have nothing to do with conceptual analysis. For example, suppose that it is part of the very essence of water to consist of H2O molecules (as Saul Kripke 1980 argues). Then the fact that the pitcher is full of water is wholly grounded in the fact that it is full of H2O molecules, despite the fact that the concept of being water cannot be analyzed as consisting of H2O molecules. Conceptual analysis is supposed to be a priori, something that we can verify from the philosophical armchair. We should be able to recognize the truth of the analysis simply on the basis of possessing the relevant concepts, while facts about grounding can be empirical discoveries (although Hofweber 2009 demurs).
The upshot is that grounding does not seem definable by conceptual analysis.
What about reduction? Historically, there have been two conceptions of reduction in analytic philosophy. The first was theoretical reduction (in the sense of Ernst Nagel 1961): the reduction of one scientific theory (like chemistry or geology) to another (like physics). The second was ontological reduction: reducing one object or class of objects to another, by showing that objects of the first kind are really nothing but objects of the second kind.
3.1T.1T.2 Theoretical Reduction and Indefinable Grounding. Grounding cannot be defined in terms of theoretical reduction.
3.1T.1T.3 Ontological Reduction and Indefinable Grounding. Grounding cannot be defined in terms of ontological reduction.
Grounding and theoretical reduction seem quite disparate. Grounding relates facts to other facts (or to sets of facts). Theoretical reduction relates theories to other theories, where these theories are understood to be products of human activity, in the form of sentences of a language or some other sort of representational model. Grounding has nothing to do with human theories of this kind. Still, one might think that where a theoretical reduction is possible, the reduction shows that one set of facts (the facts represented by the reduced theory) are grounded in another set of facts (the facts represented by the reducing theory).
Unfortunately for this supposition, most philosophers of science are agreed that theoretical reductions as conceived of by Ernst Nagel and other contemporaries of his are impossible. Nagel (1961: 352) hoped that we could discover a set of “bridge” principles that would enable us to deduce the sentences of the reduced theory by means of sentences in the reducing theory. But in fact the relation between two successful scientific theories (like molecular biology and quantum physics) cannot be captured by such a simple deductive process. Still, one might hope that some or all facts of molecular biology might be grounded (at least partially) in microphysical facts.
Ontological reduction is much closer to grounding. In fact, one might reasonably suppose, as Gideon Rosen (2010) does, that ontological reduction is a special case of grounding: if entity x is reducible to the entities in set S, then intrinsic facts about x are wholly grounded in those involving the members of S. Still, as Rosen recognizes, there might be cases in which some fact is grounded in some other facts in the absence of ontological reduction. One might think, for example, that some facts about a thing are grounded in other facts about that same thing. For instance, one might think that in each case in which one has a justified belief, the fact that the belief is justified is grounded in facts about other beliefs, or in other facts about one's memory or sense organs. This wouldn't require an ontological reduction of justification to other things.
Finally, consider the relation of supervenience, which we introduced in Chapter 2.
3.1T.1T.4 Supervenience and Indefinable Grounding. Grounding is not definable in terms of metaphysical supervenience.
We defined weak supervenience in Chapter 2 (D2.6). That definition gave us a relation between two sets of properties. We could modify it slightly to get a relation between two classes of possible facts:
Def D3.4.1 Weak Supervenience (Facts). A set of possible facts A weakly supervenes on a set of possible facts B iff it is impossible for two worlds to agree on which B facts exist but to disagree about which A facts exist.
We could talk similarly about supervenience for propositions. To bring this even closer to grounding, consider the special case in which a single proposition weakly supervenes on a set of propositions:
Def D3.4.2 Weak Supervenience (Truth-Value of a Single Proposition). The truth-value of a proposition p weakly supervenes on a set of possible facts B if and only if it is impossible for two worlds to agree on which B facts exist but to disagree about the truth-value of
p.
There is also a notion of strong supervenience in the literature, but the distinction between strong and weak supervenience is irrelevant for our current purposes. Supervenience expresses a kind of covariation or correlation between possible facts.
There are at least three reasons why grounding cannot be defined in terms of supervenience. First of all, grounding is an asymmetric relation, while supervenience is not (see Stoljar 2015). It is possible for two sets of facts to supervene on each other. For example, the set of facts about which numbers are less than or equal to other numbers supervenes on the set of facts about which numbers are greater than or equal to other numbers, and vice versa. It won't help to try to define grounding in terms of one-way supervenience. That is, we can't say that set A of facts grounds set B if only if B supervenes on A and not vice versa. Consider three sets A, B, and C, such that any one of the sets supervenes on the union of the other two, but not vice versa. This would be a case of circular partial grounding, using the proposed definition of one-way supervenience: A would partially ground B, and B would partially ground A.
Second, and more fundamentally, the granularity of the two relations are different. Grounding is more fine-grained than supervenience, able to distinguish between facts and sets of facts that supervenience must count as equivalent. Supervenience is an intensional relation. If propositions p and q are necessarily in agreement in truth-value (true or false in exactly the same worlds), supervenience must treat the corresponding possible facts as interchangeable. In contrast, grounding is hyperintensional, able to draw distinctions between metaphysically equivalent facts. So, for example, we saw that the existence of {2} is grounded in the existence of the number 2 (and not vice versa), even though 2 and its singleton exist in exactly the same worlds.
Third, grounding implies an explanatory relation between the fundans and the fundatum, while supervenience requires no such explanatory relation between the supervening facts and their base. It is the presence of this explanatory relation that makes grounding relevant to issues of ontology. Explained facts can be treated as less fundamental, and so less subject to considerations of economy, like Ockham's Razor (PMeth 1).
3.2 Relation between Grounding and Truthmaking
If grounding is a kind of explaining how (Litland 2013), then to say that p grounds q is to say that for p to be the case is a way for q to be the case. This could be explicated in terms of truthmakers: all of the truthmakers for p are also truthmaker for q, but not vice versa. This is a much more stringent condition than the condition of p's entailing or necessitating q. Proposition p could necessitate q without any of p's truthmakers being truthmakers for q, for example, if truthmakers for p contain facts that are superfluous for q's truth.
3.2.1 Interdefinability?
Given this connection between truthmaking and grounding, we might hope that we could simply define grounding in terms of truthmaking. But this supposition faces an immediate problem. Truthmaking was defined in terms of grounding: x is a truthmaker for p only if p's truth is (wholly) grounded in the existence of x (see Rodriguez-Pereyra 2006: 960). To define truthmaking in terms of grounding and grounding in terms of truthmaking is viciously circular. Still, it would be interesting if the two notions were inter-definable, that is, if we could either define truthmaking in terms of grounding or grounding in terms of truthmaking. This would leave us with the difficult problem of deciding which notion is metaphysically prior to the other.
As we suggested above, it seems that one fact grounds another just in case any truthmaker for the proposition corresponding to the first fact is also a truthmaker for the proposition corresponding to the second.
3.2T Truthmaker to Grounding Link. The fact that p (wholly) grounds the fact that q if and only if: (i) p & q, (ii) the truth of p necessitates the truth of q, and (iii) necessarily, if p & q, then every truthmaker for p is a truthmaker for q.
We also want to allow for the case in which a set of facts (and not just an individual fact) grounds a further fact. For example, we want the facts that p and that q to jointly ground the fact that (p & q).
3.2T.1 Generalized Truthmaker to Grounding Link. The facts corresponding to set Γ of propositions (wholly) grounds the fact that q if and only if (i) q and every member of Γ is true, (ii) the joint truth of the members of Γ metaphysically necessitates the truth of q, and (iii) necessarily, if both q and every member of Γ are true, then, for every p in Γ, every truthmaker for p isis a part of a truthmaker for q.
It seems that if we were to take truthmaking as a primitive or indefinable notion, we could in this way define grounding in terms of it. Suppose, for example, that a ball's being colored is grounded in its being scarlet. If there is some truthmaker for the ball's being scarlet, it seems that this would also necessarily be a truthmaker for its being colored. Suppose, for another example, that the moral attributes of an action are wholly grounded in certain of its non-moral attributes. On that assumption, it seems plausible to suppose that the truthmakers for the predications of those non-moral attributes to the action will jointly constitute a truthmaker for the predication of the moral attribute. As a final example, suppose that the fact that (p or q) is always wholly grounded in any fact corresponding to one of its disjuncts. So, if p is true, then the fact that (p or q) is wholly grounded in the fact that p. Clearly, any truthmaker for p will also be a truthmaker for the disjunction, satisfying the Truthmaker to Grounding Link.
So Truthmaker to Grounding Link seems to capture at least some cases of grounding in terms of truthmakers. However, we shall see (in Section 3.4) that other cases of grounding (extra-conceptual grounding) cannot be so captured.
3.2.2 Can grounding theory replace truthmaker theory?
Kit Fine (2012a) has argued that we should simply replace truthmaker theory with the theory of grounding. Fine finds two problems with truthmaking. First, truthmaker theory is too restrictive in terms of what can be grounded: it only provides a metaphysical explanation of the truth of propositions. It doesn't provide an explanation for the existence of things or for any properties other than truth. Second, Classical TruthmakerTheory (2.1T) is too restrictive in terms of what can act as a ground: all truthmaking is done only by attributing existence to some truthmaker.
As we discussed in Chapter 2, there are Non-Classical Truthmaker Theories (2.1A.1T), like Spectral Truthmaker Theory (2.1A.1T.1), that avoid Fine's second complaint. On Spectral Truthmaker Theory, truthmaking is done not by just the existence of the truthmaker but also by the truthmaker's being a certain way intrinsically. Thus, Non-Classical Truthmaker Theory and Fine's grounding theory come very close to one another.
Nonetheless, Fine's first complaint still applies. Truthmaker Theory provides explanations for the truth of certain propositions but not for the existence of things, nor for propositions' having properties other than truth, nor for things' (other than propositions) having any properties. Insofar as we find metaphysical explanations in such wider cases plausible, we are going to need a theory of grounding that goes beyond Truthmaker Theory. In addition, Fine points out that Truthmaker Theory is not well suited to providing certain kinds of chains of grounding chain. For example, social facts are plausibly grounded in psychological facts, psychological facts in neural facts, and neural facts in physical facts. It isn't the fact that certain psychological propositions are true that grounds the truth of social propositions. Rather, it is the psychological facts themselves that ground both the truth of the psychological propositions as well as the social facts, which in turn ground the truth of the social propositions. Truthmaker theory isn't enough to capture these relations. In order for truthmaker to form a chain, in each link the maker and the thing made would have to belong to the same category, but this never happens in truthmaker theory.
However, it is one thing to supplement Truthmaker Theory with a wider theory of metaphysical grounding; it is quite another thing to dispense with Truthmaker Theory altogether. Truthmaker Theory provides, as we saw in Chapter 2, a link bet
ween propositions and the world. Suppose, for example, that WhiteSnow is the truthmaker for the proposition that some snow is white. Is (1) some snow white because WhiteSnow exists, or (2) does WhiteSnow exist because some snow is white?
Truthmaker Theory seems committed to answer (1). So, on the one hand, it does seem that grounding is conceptually prior to truthmaking: we have used the notion of grounding in our definition of truthmakers. But, on the other hand, truthmaking seems to require some link between propositions and the world; so, if we try to simply translate truthmaker talk into grounding talk, the resulting translation will be in some tension with the thesis that grounding is always a form of explanation. Explanation is a relation between true propositions, or between the facts they correspond to, while truthmaking is a relation between propositions and entities in the world at large.
Consider, for example, a simple and relatively uncontroversial case of truthmaking: electrons are truthmakers for the proposition that electrons exist. The proposition is true because the electrons exist. If we try to translate this into the language of grounding (as a relation between facts), we might translate it into this claim: the fact that electrons exist explains the fact that electrons exist. But that is an obvious falsehood. Facts don't explain themselves!
Of course, we could say that the fact that electrons exist grounds the fact that it is true that electrons exist, and that fact grounds the fact that it is true that it is true that electrons exist, and so on. Perhaps that shows that grounding theory can link truth to the world in the right way after all, so long as we take grounding to be primarily a relation between facts (and not between propositions). This suggests that we take factive grounding to be more fundamental than non-factive grounding.