A Neglected Aspect of Hume’s Nominalism

Abstract

In this paper, I point to two problems engendered by two assumptions that Hume makes. The first is his nominalism: the view that all ideas are fully determinate with respect to all the aspects that are represented in them. The second, perhaps hitherto unnoticed, is that names denote ideas. I propose some solutions, aiming to find one that is Humean.

1. Introduction

According to Hume’s nominalism, all ideas are fully determinate with respect to all the aspects that are represented in them. “[T]he mind cannot form any notion of quantity or quality without a precise notion of the degrees of each” (T 1.1.7.3; SBN 18). Thus, an idea of an individual triangle needn’t represent it as having any taste or as sounding one way or another, but since it must represent it as having three sides and three angles, these must be represented as having precise magnitudes. Similarly, an idea of a dog represents it as having a “precise proportion” of shape, size, and colour. More generally, an idea of an individual is determinate with respect to a “particular degree of quantity and quality” of every feature that it represents the individual as having. The determinacy assumption is not restricted to aspects that are essential to the individual represented. Plausibly, an idea must represent an individual as having its essential properties (having three sides in the case of a triangle, for instance), but it may represent an individual as having a nonessential property. For instance, a triangle may be represented as being red, although being coloured is not essential to triangles. And it will then be represented as being of a particular shade of red.

For ease of exposition, I will say that Humean ideas are relevantly determinate, and label this the determinacy assumption. (This is the negative component of Hume’s nominalism. The positive component is an account of the way the mind manages to think general thoughts in the absence of ‘abstract ideas’—ideas that are not relevantly determinate.)

Hume’s rival, call him Locke for ease of exposition, thinks that there are, in addition, ‘abstract ideas’—ideas that include precisely the features that are necessary and sufficient for falling under the relevant term. ¹ These ideas are got “by separating from [individual ideas] the circumstances of Time, and Place, and any other Ideas, that may determine them to this or that particular Existence” (Locke [1690] 1975, III.iii.6). In particular, abstract ideas typically do not represent “particular degree of quantity and quality” of essential properties. ² So, for instance, the abstract idea of a triangle will be noncommittal with respect to its being right-angled or red.

My use of the term ‘nominalism’ is different from the customary one. The term is usually used to denote an ontological thesis, denying the existence of universals. But I want to focus on the semantic issue, on which nominalists—thus construed—may disagree. So it will facilitate the exposition to follow MacNabb (1951), and use the term ‘nominalism’ more narrowly, so that a “conceptualist,” who denies the existence of universals yet thinks that there are abstract ideas, will not count as a nominalist.

Hume discusses at great length the way general terms operate. He adduces three arguments against the existence of indeterminate ideas (T 1.1.7.3-6; SBN 18–20), and presents his (nominalist) account of the way general terms function absent abstract ideas. But he says nothing about the functioning of proper names. And this is a significant lacuna. In this paper, I consider some suggestions for filling it, and defend one of them.

The structure of the paper is as follows. I present one way of filling the lacuna and discern two problems that it engenders (sections 2 and 3). I then propose an alternative that is invulnerable to the problems and is in keeping with Hume’s other commitments (section 4).

2. The first alternative and the first problem it faces

According to the first suggestion, each proper name stands for one individual idea. (Call this the proper-name-individual-idea assumption, PNII for short). I will now present the first problem it engenders.

Hume distinguishes, in what has come to be known as his fork, between relations that depend only on ideas and those that “may be chang’d without any change in the ideas” (T 1.3.1.1; SBN 69) and gives examples of both kinds. The first kind is illustrated with a geometrical example. “’Tis from the idea of a triangle, that we discover the relation of equality, which its three angles bear to two right ones; and this relation is invariable, as long as our idea remains the same.” ³ By contrast, “the relations of contiguity and distance between two objects may be chang’d merely by an alteration of their place, without any change on the objects themselves or on their ideas.” Thus, the distance between Tom and Harry may change (if, for instance, they walk away from each other) without a change in their ideas (or in them). Similarly, causation does not depend only on the ideas of the cause and the effect: “the power, by which one object produces another, is never discoverable merely from their idea” (T 1.3.1.1; SBN 69).

How are we to understand Hume’s fork, which Price (1940b, 12) describes as “one of his most important services to philosophy”? From what Hume says about causation when he explains the (fork) distinction, it is clear he means that knowledge of the obtaining of relations that do not depend only on the ideas involved requires experience. “’[T]is evident cause and effect are relations, of which we receive information from experience, and not from any abstract reasoning or reflection” (T 1.3.1.1; SBN 69; my italics). Correlatively, relations of ideas yield a priori knowledge.

The same understanding of the way Hume construes the fork emerges when we consider the way he invokes it, most notably in the argument pertaining to the causal inference (T 1.3.6). Here, Hume argues that nature’s uniformity, a principle that figures essentially in any causal inference, can neither be “demonstrated” nor justified empirically (such a justification would be circular, invoking, like any empirical justification, the principle of uniformity). We cannot understand what a comparison of ideas is from Hume’s discussion of “demonstration” because he does not provide an independent explanation of “demonstration.” He says (unhelpfully) “the assurance of a demonstration proceeds [is deduced] always from a comparison of ideas” (T 1.3.4.3; SBN 84). But his discussion of the second justificatory possibility is illuminating. The discovery of the obtaining of a relation that does not “depend only on the ideas,” Hume says, “must in some respects be founded on the impressions of our memory and senses” (T 1.3.6.6; SBN 89)—i.e., requires experience. And because the argument against causal inference requires the two ways of establishing the principle of uniformity to be exhaustive (otherwise Hume won’t have shown that nature’s uniformity cannot be justified) and exclusive (the arguments against the two ways of justifying the principle are different), we can conclude that a “demonstrable” proposition is one that is knowable a priori. Since such a proposition “proceeds” from a comparison of ideas, such comparisons must themselves engender knowledge that is independent of experience.

Hume clearly thinks the two notions, ‘knowable a priori’ and ‘depending only on ideas,’ are coextensive. And his examples support this supposition. But are they really coextensive? I will now argue, by considering other examples, that they are not; that (given PNII) Hume’s characterisation (in terms of dependence only on ideas) fails to capture the distinction he has in mind.

According to PNII, the two names ‘Fido’ and ‘Spot’ stand for individual ideas, which, it is plausible to assume, are visual (or at least include a visual component). Because of the determinacy assumption, the two ideas include their colours, brownish and black, say. So the relation ‘X having a colour that is closer to brown than Y’s colour’ depends only on their ideas; by considering the ideas, we can tell that Fido’s colour is closer to brown than Spot’s. But the proposition ‘Fido has a colour that is closer to brown than Spot’s’ is not knowable a priori. This is in contrast with Hume’s geometric example involving the proposition that the sum of a triangle’s angles is 180 degrees. Indeed, ‘Fido’s colour is closer to brown than Spot’s’ is akin to ‘Fido is distant from Spot,’ which, Hume thinks, does not depend only on the ideas. To establish its truth, we need to consult experience. (Of course, we also need to understand the proposition, for which we need to possess the constituent ideas. But the ideas by themselves do not suffice.)

The same is true of the relation ‘X having the same angles as Y’ when X and Y are triangles. That two particular triangles are similar (have the same angles) is not knowable a priori. But the Humean ideas of triangles include the precise sizes of their angles, so this relation depends only on the two ideas. And, again, to determine the truth-value of the proposition, we need, in addition to understanding it, to consult experience.

Perhaps Hume intends his fork to pick out the semantic distinction between analytic and synthetic propositions, the truth of the first kind depending only on their meanings. True, he lacks the terminology, but it may nonetheless fit his intention. Indeed, this is how Price (1940b, 13), Bennett (1971, 238), Ayer (2000, 43–44) and Millican (2017) construe the fork. ⁴ “[A]ffirmations concerning relations of ideas are treated as being purely conceptual” (Ayer 2000, 43; my italics). On this (contentious) interpretation, Hume thinks analyticity and a priority coincide: there is no synthetic a priori knowledge. So this understanding of the fork also makes sense of the way Hume uses it in his argument concerning the causal inference.

But equally clearly, Hume’s characterisation of the fork (assuming PNII) does not pick out the analytic/synthetic distinction. The truth-value of ‘Fido’s colour is closer to brown than Spot’s’ is not determined by the meaning of the sentence (as perhaps Hume thinks are the truth-values of arithmetical sentences). Yet, as I argued above, on PNII, we can tell just by considering the two ideas that Fido’s colour is closer to brown than Spot’s. So the truth-value of this (nonanalytic) proposition depends only on the two ideas. ⁵

It might be thought that the difficulty is restricted to Hume’s fork as it is presented in the Treatise, and its counterpart in the Enquiry is invulnerable to it. There are, after all, significant differences between the two accounts. The Treatise (T 1.3.1.1; SBN 69) includes a typology of relations, dividing the seven relations Hume takes to be basic into those that depend only on ideas (resemblance, contrariety, degrees in quality, proportions in quantity or number) and those that do not (relations of time and place, proportion in quantity or number, degrees in any quality and causation). In the Enquiry, by contrast, Hume simply draws a distinction between “relations of ideas” and “matters of fact.” The first kind of proposition is “discoverable by the mere operation of thought, without dependence on what is any where existent in the universe.” The second is “not ascertained in the same manner” (E 4.1–2; SBN 25). There is no commitment here to the Treatise’s claim that all propositions involving some relation (similarity, for instance) fall on the same side of the fork.

But, in fact, the Enquiry account is also vulnerable to the difficulty (given PNII) because it shares with the Treatise two assumptions that jointly engender it: that relations of ideas are discovered by “comparing” ideas, and that ideas are relevantly determinate. That the two assumptions suffice to engender the difficulty is easy to see. If the ideas of Fido and of Spot are relevantly determinate, they include (for instance) their precise shade of colour. So a “comparison” (consideration) of the two ideas reveals that Fido’s colour is closer to brown than Spot’s. Yet this proposition is not knowable a priori.

It is straightforward to ascertain that Hume makes both assumptions in both texts. Clearly, he makes the first assumption in the Treatise. In the Enquiry, it does not appear in Hume’s presentation of the fork; it appears only later, in his discussion of geometric reasoning:

If the mind, with greater facility, retains the ideas of geometry clear and determinate, it must carry on a much longer and more intricate chain of reasoning, and compare ideas much wider of each other, in order to reach the abstruser truths of that science. (E 7.2; SBN 60–61; my italics)

The determinacy assumption is discussed in the Treatise early on (in the section on abstract ideas) and in great detail. Its presentation in the Enquiry is very brief and includes no supporting argument. It appears towards the end, in Hume’s argument against the claim that primary qualities exist in the objects themselves:

Let any man try to conceive a triangle in general, which is neither Isosceles nor Scalenum, nor has any particular length or proportion of sides; and he will soon perceive the absurdity of all the scholastic notions with regard to abstraction and general ideas. (E 12.15; SBN 154–55)

Because the problems I discerned arise for both of Hume’s accounts of relations, I can here bypass the dispute between those (Gotterbarn 1974, 274; Beck 1978, 83–84; Frasca-Spada 1998, 126–27; Owen 1999, chap. 5; Beebee 2006, sec. 2.2–4) who think the Treatise’s account of relations represents Hume’s considered view and those (Kemp Smith 1941, 355; Millican 2017) who favour the Enquiry.

The same difficulty arises in the case of monadic predication, which Hume does not discuss. The idea of Fido is fully determinate with respect to the “precise notion” of its colour. So Fido’s colour depends just on his (individual) idea. But knowledge of the proposition ‘Fido is brown’ is neither a priori nor analytic, its dependence being only on the idea notwithstanding.

I conclude that given PNII, Hume’s characterisation of the fork fails to capture the notion he has in mind (a priority or analyticity), the one that he invokes in the (important) argument against the causal inference.

Why have I focused on names? Doesn’t the problem arise for any expression that refers to an individual? If there’s a problem with ‘Fido’s colour is closer to brown than Spot’s,’ it will be noted, it also arises for ‘My dog’s colour is closer to brown than your dog’s’! ⁶ The answer is that the problem does, indeed, arise for any expression that refers to an individual, but it is hard—perhaps impossible—to consider the general question within Hume’s (imagistic) theory of ideas. We know what the idea of Fido could be, but what is the idea of ‘my dog’ or ‘the tallest man in New York’? This is a special instance of the more general difficulty Hume’s theory of ideas has in accounting for complex sentences (including propositional connectives, quantifiers, etc.). So it is more profitable to consider it as it arises in the case of proper names.

3. The second problem engendered by PNII

I will now argue that the PNII very implausibly limits the sort of thoughts we can have, thus impugning Hume’s science of man. I begin by briefly reviewing Hume’s (implicit) theory of thought, which is an offshoot of his account of general ideas (T 1.1.7).

Hume is well aware that general terms are required for any predicative (as opposed to existential) thought, both conception and belief. The simplest thought, ascribing a predicate to an individual, ‘Fido is brown,’ e.g., requires the general term ‘brown.’ Modern predicate logic reflects this in formalising the thought ‘Fido is brown’ as ‘Bf,’ making it clear that a predicate (B), which is a general term, is ascribed to an individual (f).

Locke can easily account for the thought that Fido is brown. He will identify it with an ordered pair of ideas: the individual idea of Fido and the abstract idea ‘brown.’ ⁷ But Hume can have no recourse to abstract ideas. To allow for predicative thoughts, he proposes a different account of general terms, eschewing abstract ideas. ⁸ A general term, Hume suggests, stands for a single representative individual idea (exemplar) associated in the mind via the general term with a revival set of relevantly similar individual ideas. ⁹ For instance, the general term ‘brown’ stands for some individual brown idea (‘Fido,’ e.g.), associated by the mind via the word ‘brown’ with other ideas of things that are brown. This mechanism ensures that the word ‘brown’ applies to most, if not all, brown things and only to them. The fit is imperfect because of human limitations. Our finitude prevents us from having all the individual ideas of things falling under a general term.

This does not, as yet, constitute an account of complete thoughts. It tells us to what things the word ‘brown’ applies, but it doesn’t tell us how we think, for instance, the thought ‘Fido is brown.’ Garrett replies on Hume’s behalf:

Because he holds that all belief consists in an idea’s having liveliness, it seems that conceptual judgments [judgments that classify, ascribe a predicate to an object] consist in the occurrence of a lively idea within the revival set of the appropriate occurring abstract idea elicited by a general term. (2015, 75)

Thus, to believe that Fido is brown is for a vivid idea of Fido to belong to the revival set of ‘brown.’ Merely to conceive of Fido being brown is for a faint idea of Fido to belong to the revival set of ‘brown.’

So much for Hume’s account of predicative thought. And now to the problem. On PNII, the word ‘Fido’ stands for a relevantly determinate idea of Fido, which depicts him as being of some colour, say brown. (More precisely, the idea depicts him as being of a particular shade of brown. But for ease of exposition, we can ignore this nicety.) Can we conceive of Fido as being of another colour? To conceive of Fido as black (say) is for the revival set of ‘black’ to include the idea of Fido. But the idea of Fido, we are assuming, is brown. So it does not belong to the revival set of ‘black’! This means that I can only think of him as having the colour I think he has. To be sure, I can form an idea which is like Fido’s except for being black. But it will not be an idea of Fido, which, we are assuming, is brown. ¹⁰ This implication of PNII flies in the face of the (psychological) reality. We can conceive of various alternative ways individuals might be!

Note that the conclusion is not that I can only think of Fido as having the colour he actually has. For all I have shown, I may be mistaken about his colour. Hume does adduce an argument against this possibility, but he subsequently (sensibly) recants. The argument relies on the Copy Principle. “Our ideas are copy’d from our impressions, and represent them in all their parts. When you wou’d any way vary the idea of a particular object, you can only encrease or diminish its force and vivacity. If you make any other change on it, it represents a different object or impression” (T 1.3.7.5; SBN 96). Each idea represents (is an idea of) an impression, and this requires, Hume is claiming, that the idea resemble the impression it represents precisely (except in respect of vivacity). Hume’s more considered view is that an idea needn’t represent its object perfectly. “I have seen Paris; but shall I affirm I can form such an idea of that city, as will perfectly represent all its streets and houses in their real and just proportions?” (T 1.1.1.4; SBN 3). Garrett (2006, 308) notes a reason for thinking that representation for Hume allows for imperfect resemblance. He takes falsehood to consist in a failure of ideas to “conform” to or “agree” with what they represent (T 3.1.1.9; SBN 458). So there couldn’t be false beliefs about existing things unless it were possible to represent those things by means of ideas that did not entirely resemble them.

So Hume can allow for mistaken beliefs about objects’ properties. Still, the fact that he cannot countenance us conceiving of objects as being different from the way we believe them to be mars his science of man.

4. Giving up PNII

I concluded (section 2) that nominalism in conjunction with PNII prevents Hume’s distinction between relations that depend only on ideas and those that also depend on something else from capturing the two important distinctions he might have in mind (a priority and analyticity). And I argued (section 3) that the same conjunction also prevents Hume from countenancing the belief that an object has a different characteristic than the one we think he actually has. Clearly, Hume is committed to nominalism. So if we are looking for a Humean solution to these two problems, we need to consider alternatives to PNII.

There are, of course, several accounts of names that are not vulnerable to the difficulties. The one involving the most radical departure from Hume’s is to be found in theories of names that follow Mill (1884) in supposing names to involve no description of their reference. For instance, Kripke (1980, 91) suggests that the reference of a name is an object determined by a dubbing ceremony (“baptism”) at which the object is indicated by a demonstration, and the name is subsequently spread by acts of communication. Successful reference to the object dubbed in the baptism requires an appropriate causal chain from the baptism to the use of the name, but no information about features of its bearer. Clearly, none of Hume’s difficulties arises here. No knowledge can be gleaned about the referent of a name by examining the name, so there will be no unwelcome dependence of relations only on ideas, and it will be possible to conceive the bearer of any name as having any of its inessential properties and to conceive of it as not having it. ¹¹

Such accounts are not Humean. Clearly, Hume thinks names denote ideas (of some sort). Here are a few (out of many) occasions in which this commitment is apparent. He says his idea of Paris does not “perfectly represent all its streets and houses in their real and just proportions” (T 1.1.1.4; SBN 3), adverts to the ideas we form of individual objects (T 1.3.6.1; SBN 86–87), to his idea of God (T 1.3.7.2; SBN 94), and to that of Rome (T 1.3.9.4; SBN 108). Finally, in his explanation of our enjoyment of fiction, Hume says:

We have been so much accustom’d to the names of Mars, Jupiter, Venus, that in the same manner as education infixes any opinion, the constant repetition of these ideas makes them enter into the mind with facility, and prevail upon the fancy, without influencing the judgment. (T 1.3.10.6; SBN 121–22; italics mine)

Now, by itself, the supposition that names stand for “ideas” is not substantive, because the term ‘idea’ has no pretheoretical meaning. Indeed, Locke defines “ideas” as “that which [Man’s] Mind is employ’d about whilst thinking” ([1690] 1975, III.i.1). And nothing substantive follows from a definition. But Hume (and perhaps Locke too) thinks ideas are images. This means an idea includes some information pertaining to the individual it stands for. I conclude, therefore, that giving up the supposition that names stand for ideas is not a Humean alternative to PNII, and that we should look for a better suggestion. ¹²

According to the description theory of names (Russell 1956), the meaning of each name is some definite description, ‘the F.’ For instance, the name ‘Aristotle’ means ‘the teacher of Alexander the Great.’ To use a Humean terminology, this is an indeterminate idea that leaves out most features of Aristotle—his height, the colour of his eyes, etc.—features that a (visual) Humean idea of him must include. So this too is not a Humean account of proper names, although it is closer to Hume’s than Mill’s, contending, as it does, that names include some information about their bearers. ¹³

There is in Garrett (2015, 55–56) a hint as to a Humean account of the semantics of names that retains the assumption that all ideas are relevantly determinate. Garrett notes that individuals have different spatial and temporal parts (can be “viewed” from different “perspectives”). To reflect this fact, Garrett suggests, Hume should mimic—in the case of names—his account of general terms, in which a single term is associated with several individual ideas. A name will elicit an exemplar idea and a readiness to revive other ideas that are of the same individual, but from different “perspectives.” For example, “the revival class of a monument will include ideas of it as seen from the front and another of it as seen from the back; the idea of a person will include, amongst others, the idea of her as a child and another of her as an adult.”

The suggestion is reminiscent of phenomenalism (Russell 1926, chap. 3; Price 1940a, 93), according to which each object is identified with a set of impressions (“sensibilia”), at most one of which may be currently in a person’s mind. The set includes “the multitudinous variety of perspectival and other distortions” (Price 1940a, 99). Thus, an impression of an elliptical coin will be included in the set constituting a round coin. Similarly, an impression of a bent stick will be included in the set constituting the straight stick, as will a luminous impression, corresponding to the way the stick appears in the moonlight.

Plausibly, phenomenalism is an improvement on the version of idealism imputed by many to Hume, according to which objects are identified with individual impressions. “The very image, which is present to the senses,” Hume says, “is with us the real body” (T 1.4.2.36; SBN 205; my italics). Price (1940a, 100) plausibly suggests that it would make more sense for Hume to identify objects with sets of impressions, because this better fits the view of the “plain man [who] … says ‘That’s the cat’ when he sees it through uneven glass, or reflected in a cylindrical mirror.”

Russell’s phenomenalism is designed to enable us to construct an objective space of perceptions on the basis of subjective appearances. He starts with subjective perspectives, each of which is the momentary set of perceptions of some mind—actual or merely possible—with its own private space. A momentary commonsense thing is then identified with a set of perceptions (“appearances”), each “viewed” from a different perspective. Finally, a single three-dimensional “objective” space is constructed, within which different perspectives and “things” are located. Each sense datum is associated with two places in objective space. One is the place at which it is, and, correlatively, the object of which it is a constituent. The other is the place from which it is perceived.

Garrett proposes to include in the revival set diachronic perspectives in addition to Russell’s synchronic ones. The proposal can help us construct an objective space of phenomenal objects across time (if all spatiotemporal perspectives are included). But it doesn’t help us with Hume’s two problems because all of Garrett’s perspectives—whether past, present or future—are actual. For instance, “the revival class of a monument will include ideas of it as seen from the front and another of it as seen from the back; the idea of a person will include, amongst others, the idea of her as a child and another of her as an adult” (Garrett 2015, 55–56; my italics). And we think the monument could look different when seen from the front from the way it actually does, and a person could have been different as a child from the way she actually was. So at least some of the unwelcome dependencies of relations only on ideas will not be eliminated. If Fido is brown throughout his life, there will only be brown ideas of him in the revival class of the name ‘Fido.’ Hence, the proposal will render ‘Fido is brown’ dependent only on the idea (and hence, knowable a priori). And it will still be impossible to conceive of (brown) Fido as being black instead.

But in Garrett’s suggestion to how Hume’s problems can be solved, there is a clue that names, too, should be construed as standing for classes of ideas. Instead of the spatial and temporal “perspectives,” which Garrett picks, we should focus on the modal one, which pertains to ways an individual might be. Here is an elaboration of the suggestion.

The idea in the mind when we use a name is relevantly determinate, but it is associated with a revival class of relevantly determinate ideas, all depicting various ways the named object could be. Thus, if (brown) Fido could be black, the revival class of the name ‘Fido’ will include an idea of a black individual. It will also include ideas of individuals differing from Fido with respect to other inessential characteristics of Fido. If Fido could only have been a dog, the revival class will only include ideas of dogs. If there are no essential properties (and Fido could have been Paris, for instance), the revival class of Fido will include every individual idea subject to our cognitive limitations.

It might be objected that there is a disanalogy between the mechanism I propose (on Hume’s behalf) to account for the way proper names function and the one Hume (explicitly) offers in the case of general terms. We generally do not have experience (impressions) of objects as they could have been, only as they are, so the ideas in the revival class must be constructed by the imagination. For instance, I have only experienced Fido as brown, and I construct an idea of him as black by putting together the appropriate simple ideas. In the case of general terms, by contrast, Hume seems to think the individual ideas in the revival set are those of individuals that we have encountered. “When we have found a resemblance among several objects, that often occur to us, we apply the same name to all of them… . After we have acquired a custom of this kind, the hearing of that name revives the idea of one of these objects” (T 1.1.7.7; SBN 20; my italics).

The reply is threefold. First, there is a passage that suggests revival sets are not restricted to ideas with corresponding impressions. The mind “may run over several [ideas], in order to make itself comprehend its own meaning, and the compass of that collection, which it intends to express by the general term” (T 1.1.7.10; SBN 22). Now, the (general) term ‘house’ applies, Hume knows, to houses I have not encountered, so their ideas must be contained in the revival set for the term, because the revival set is supposed to “express … the general term.”

Second, Hume takes the mechanism for avoiding false generalisations from an exemplar of a general term to be reliable, albeit fallible.

[A]fter the mind has produc’d an individual idea, upon which we reason, the attendant custom … readily suggests any other individual, if by chance we form any reasoning, that agrees not with it … If the mind suggests not always these ideas upon occasion, it proceeds from some imperfection in its faculties … But this is principally the case with those ideas which are abstruse and compounded. On other occasions the custom is more entire, and ’tis seldom we run into such errors. (T 1.1.7.8; SBN 21)

But a revival set composed only of ideas of objects encountered is too meagre to render the mechanism reliable. Under the experiential restriction of revival sets, the mind would often fail to “suggest” counterexamples to a false generalisation. For instance, suppose all the houses I have seen had an even number of windows. I will generalise on the basis of an exemplar that all houses do, and since my revival set includes only ideas of houses with an even number of windows, there will be in it no idea of a house with an odd number of windows to “crowd in upon [me]” (T 1.1.7.8; SBN 21), and correct my error. But clearly, I do avoid this error (and others of its ilk).

Finally, if there is a disanalogy, it doesn’t impugn the proposed account of proper names; it only renders it (somewhat) disanalogous to that pertaining to general terms. The difference is in the way the revival sets are constructed, not in the way they function.

Must I have a distinct idea of every different way Fido could have been? ¹⁴ The answer is reminiscent of the one Hume gives in the case of general terms. Because of our cognitive limitations, the revival set for Fido will not include all the ways he might be (and perhaps include ways he might not be). But it will include ideas representing many different ways Fido could have been but isn’t. And this explains, Hume would say, why we usually do not err in conceiving of different ways things could have been.

So far, I have explained what the name Fido means. What is it to believe he is (say) brown? On PNII, to believe that Fido is brown is to have an enlivened idea of Fido in the revival class of the term ‘brown.’ And this is also true on my Humean nominalist account of proper names. The only difference is that the enlivened idea is one out of several ideas in the revival set of ‘Fido’ (assuming, plausibly, that his colour is not an essential property). So the revival set of the name ‘Fido’ will also include an enlivened idea of a brown Fido (and enlivened ideas of Fido having other characteristics we take him to have).

I am not claiming that the nominalist account of proper names functions well. Perhaps, for instance, Hume is too sanguine about the possibility of constructing revival sets that will “usually” prevent error. After all, there are infinitely many ways Fido could be, and the capacity of the mind, he insists in another context, is limited, “and can never attain a full and adequate conception of infinity” (T 1.2.1.2; SBN 26). But this difficulty arises in the case of general terms as well: there are, for instance, infinitely many triangles. ¹⁵ And my aim is not to endorse Hume’s nominalism, but rather, to extend it to proper names in a way which Hume would find acceptable. And clearly, he would. His account of the functioning of general terms is derived by inference to the best explanation from the fact that we manage to think general thoughts despite not having abstract (indeterminate) ideas. We do not directly observe the revival sets or the mechanism responsible for preventing mistaken generalisations from exemplars. The analogous account of proper names best explains, Hume would say, the fact that we can (and often do) conceive of individuals as having properties different from those we think they have. And it also renders Hume’s fork more useful a distinction than does PNII.

This Humean account of names clearly solves the two difficulties PNII cannot. Hume can now allow for conceiving of what we think is not actual in the same way that he allows for general terms to apply to several, qualitatively different, things. (There is here a structural analogy between possibility and plurality.) Neither will Fido’s colour depend only on the idea because the revival class associated with the name includes individual ideas of dogs differing in their colour from the colour we take Fido to have. So the proposition ‘Fido is black’ will not be knowable a priori. By contrast, and as it should be, the fact that Fido has a tail does depend on the idea (assuming that having a tail is necessary for being a dog), since all the ideas in Fido’s revival class are of tailed objects.

The problem pertaining to relations is also solved, because there will now be appropriately fewer relations that depend only on ideas. Thus, the proposition that Fido’s colour is closer to brown than Spot’s will not depend only on the ideas, since both revival classes will include ideas of dogs of all colours both dogs can have. So I conclude that the lacuna I discerned in Hume’s nominalism is filled in a way of which Hume would approve.

I end with a speculation. Locke doesn’t discuss proper names in great detail. He only says that “the Mind [has] distinct Ideas of the Things, and retain[s] … the particular Name that belongs to every one” ([1690] 1975, III.iii.2). Crucially, he omits discussion of the nature of ideas of proper names. Perhaps he takes ideas of proper names, like ideas of general terms, to be abstract; to include precisely the features that are essential to the named individual. This supposition would enable him to contend in a simple fashion with the two difficulties I discerned in PNII, unavailable to Hume, who rejects abstract ideas, and must have recourse to a more complex account.