Responses to Humean Humility, Russellian Monism, and Ramseyan Humility

A crucial premise in the argument for Humean Humility is the contention that if there are certain concepts that cannot be understood except in terms of each other, then they cannot be understood at all.

31.4.1 Holistic understanding

According to a traditional argument for the existence of self-evident beliefs, when we inquire what justifies a belief, what justifies the justifier, and so on, there are only four possibilities: the series goes on forever, it runs around in a circle, it stops with items that are unjustified, or it stops with items that are self-evident (or epistemically basic). If the first three options are considered untenable, it follows that no beliefs are justified unless some beliefs are self-evident.

A response on the part of some coherence theorists is that the “run around in a circle” alterna­tive has been two narrowly and simplistically conceived. It has taken justification to be linear (A is justified by B, which is in turn justified by C, which is in turn justified by D,..., which is in turn justified by A). But instead it should be regarded as holistic.A is justified by B and C and vari­ous other items in one's system of beliefs; B is justified by A and D and various other items; more generally, each item is justified not by any single other item but by some combination of them. A web of mutual support of this sort is supposed not to incur the objection to simple circularity.

We might adopt a similar model to defend the idea of holistic understanding—a coherence theory of concepts, as it is sometimes called.We understand concept F in terms of concepts G and H among others, G in terms of F and K, and so on; we understand each by knowing its relation to the rest.To make this work in the case of concern to Hume, we might have to add a few more concepts to body and solidity.

The holistic strategy may sound promising, but in the end I think it is no better off than the more simple-minded strategy. We may see this by restating its claims in terms of the rela­tion of partial grounding. To say that P is partly grounded in Q is to say that for some item R, P is wholly grounded in Q and R. Restating the coherence theory above in these terms, we have it that our understanding of F is partly grounded in our understanding of G and that our understanding of G is partly grounded in our understanding of F. But nearly all contemporary theorists of grounding take as one of its axiomatic properties that it is strongly asymmetrical, in the sense that not only can two things not be wholly grounded in each other, but neither can two things even be partially grounded in each other (see Rosen 2010, 115—116). Understanding solidity and body each just partly in terms of the other would in that case be out of the question.

31.4.2 Reid’s definition of straightness

Thomas Reid, though a pioneer of non-Euclidean geometry in his work on visual space, tried over a period of years to vindicate Euclid by showing that the parallel postulate of Euclidean geometry is provable from the other postulates. He thought we could do this if we used a bet­ter definition than Euclid's of straightness. Here is one of his own definitions crafted for the purpose:

D1. Right line is that which cannot meet another Right line in more points than one, otherwise they perfectly coincide, and are one and the same.¹³

This definition turned out to be inadequate for the job, but that is not my topic. As Reid acknowledged, his definition is not of the standard form for definitions. In the standard form, we would say “L1 is straight iff____________.” In this form, we say “L1 and L2 are both straight iff__________.”

Can we use a similar strategy to define solidity? If we did, we would say

D2. B1 and B2 are both solid iff neither one can penetrate the other.

Hume's complaint was that solidity in one body could be understood only in terms of solid­ity in another, making for a circular definition.

It is a consequence of Reid's definition that if two lines intersect in more than one point, they cannot both be straight; at least one of them must be curved. But Reid's definition will not tell us which line is curved, and to that extent it may be regarded as not giving us a full under­standing of straightness. Similarly, it is a consequence of D2 that if two items interpenetrate, at least one of them must not be solid.¹⁴ But D2 will not tell us which of two interpenetrating things fails to be solid, and to that extent it does not give us a full understanding of solidity.

31.4.3 Causal structuralism

In an influential article, Sidney Shoemaker has advanced the view that properties are individu­ated by the causal powers they bestow on their bearers (1980). The Shoemaker view, dubbed causal structuralism by John Hawthorne (2001), can be developed in a way that challenges Humean Humility, Russellian Monism, and Ramseyan Humility all three.

Here is one of Shoemaker's formulations of his view:

What makes a property the property it is, what determines its identity, is its potential for contributing to the causal powers of the things that have it. This means, among other things, that if under all possible circumstances properties X and Y make the same contribution to the causal powers of the things that have them, X and Y are the same property.

(Shoemaker, 212)

He goes on to claim the following consequences for the view: the causal potentialities of a property are essential to it; properties having the same causal potentialities are identical; causal laws hold necessarily when they hold at all.

Shoemaker’s view is antithetical to two of the premises in Lewis's argument for Ramseyan Humility. The combinatorial premise says that if a world is possible in which chilling water hardens it and heating water vaporizes it, so is a world in which heating and chilling have the opposite effects.This is not so if causal laws are necessary.

Shoemaker’s view is also antithetical to Russellian Monism. The Russellian Monist insists that things must have intrinsic properties and therefore posits properties not yet known to phys- ics.As pointed out in Langton and Lewis (1998), Shoemaker’s view greatly reduces the number of intrinsic properties. One might think initially that the property of being an ellipsoidal star is intrinsic. But if the laws of nature are necessary truths, and if they permit a star to be ellipsoidal only if it orbits another star, then no star could be ellipsoidal unless there were another star.This would violate one of Langton and Lewis’s conditions for being an intrinsic property, namely, that a solitary thing could have it. Shoemaker’s view arguably also implies the stronger result that there are no intrinsic properties. This follows if we use one of Langton’s further condi­tions for an intrinsic property: an intrinsic property is one that a thing could have even in the absence of laws (Langton, 119).Thus if sugar would no longer dissolve in water if certain laws were suspended, its water-solubility is not an intrinsic property. By this standard, no properties are intrinsic for Shoemaker, since none could be had in the absence of laws. Properties are what make the laws.

The respects in which Shoemaker is at odds with Ramseyan Humility and Russellian Monism are also respects in which he is at odds with Hume. Shoemaker would challenge Hume’s con­tention that causal laws are contingent, as well as Hume’s view that the redness of an impression is intrinsic to it. Shoemaker is also opposed to Hume in another way, which will be easier to see if we first consider his reply to an objection to causal structuralism by John Hawthorne.

Hawthorne’s objection is that causal structuralism identifies properties we should regard as distinct. To see this, let us first state causal structuralism by reference to Ramsey sentences. Let causal laws be written in the form AnB, meaning that having property A nomologically neces­sitates having property B. Now take the conjunction of all the laws and construct its Ramsey sentence: replace all property constants by variables and form the existential generalization that contains quantifiers for each of these variables. Finally, define each property as the property that satisfies the open sentence that results if you delete “its” quantifier (that is, the quantifier containing the variable that replaced the constant for that property). In effect, this is to define each property as the property that plays a certain causal or nomic role. It is a consequence of this style of definition that each property bears the causal relations it does to all other properties essentially: if A did not nomically necessitate B, A and B would not be the properties they are.

Suppose now that there is a world containing just four properties, A, B, C, and D, related by just three law,AnC, BnC, and (A&B)nD. Here A and B must be regarded as distinct properties, for as Hawthorne notes, “Their coinstantiation has different effects (the addition of D to the world) than is produced by either being instantiated alone” (224). But A and B have the same definition in terms of Ramsey sentences.A is defined as the property F such that 3G3H3K[FnH & GnH & (F&G)nK]. B is defined as the property G such that 3F3H3K[FnH & GnH & (F&G) nK]. By rewrite of bound variables, the second definiens is equivalent to “the property F such that 3G3H3K[GnH & FnH & (G&F)nK],” which is equivalent to the first definiens by com­mutation of conjuncts.The two definitions are so closely equivalent that they define the same property, in which case structuralism identifies properties that are intuitively distinct.

In a postscript to his article, Hawthorne notes that Shoemaker has said in reply that he had not envisioned defining properties in terms of Ramsey sentences in the manner described above. Instead, he proposes defining them as follows: Do not replace all property constants in the book of laws by variables, but only the constant A, the one you wish to define.Then say “A is the property V (a variable) such that VnC, BnC, and (V&B)nD.”This does not merely say that A is the property that necessitates C and, along with some C necessitator, necessitates D; that would be equally true of B. It says that A is the property that necessitates C and, along with B, necessitates D.That is not true of B, so the distinction between A and B has been upheld.

But notice at what cost. If we defined B in the same manner, we would say that B is the prop­erty V such that AnC,VnC, and (A&V)nD—defining B in terms ofA.We are defining A as the property that (among other things) couples with B to produce D, and we are defining B as the property that (among other things) couples with A to produce D. By mentioning the properties in the definientia by name rather than simply referring to them by quantified variables, we are committing a circularity—precisely the circularity thoroughly Ramsified functional definitions are supposed to avoid. It is also precisely analogous to the circularity Hume complains of in the attempt to define solidity in terms of bodies and bodies in terms of solidity.¹⁵

So we need to come to grips with the question whether defining each of two properties in terms of the other is a vice. It must be conceded that such definitions considered simply as identities might be totally true—for instance, A might indeed be the property that couples with B to produce D while B is the property that couples with A to produce D. But given the larger purposes the definitions are meant to subserve, the circularity does turn out to be vicious.

In Hume's case, the definitions are essential routes to our understanding of the concepts defined. If we understand what bodies are, it is because we understand what solidity is, and if we understand what solidity is, it is because we understand what bodies are. It follows that we do not understand either concept. If we did, we would understand each because we understand the other, which violates the asymmetry of “because.”

In Shoemaker's case, the definitions are supposed to tell us what “makes a property the prop­erty it is."They are meant not merely to give us necessary truths about properties, but to give the essence of these properties in a more than merely modal sense—essence in a sense that might be spelled out by saying the property is the property it is because it is related thus and so to other properties.There is that “because" again, which must needs be asymmetrical. So the circularity Shoemaker proposes, like the one Hume exposes, turns out to be vicious, and Hume's case for Humility stands against the challenge from Shoemaker.

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