Reply to Timothy Williamson

1 A Tale of Two Theses

Williamson is correct in pointing out that a weaker and a stronger thesis is canvassed in E&M. The stronger thesis is that claims, such as ‘Socrates is necessarily but not essentially a member of singleton Socrates’, are true. The weaker thesis is that, even if such claims are not true, there is an issue as to their truth. I had intended the weaker thesis as a fallback position. Even if someone did not accept the stronger thesis they should be willing to accept the weaker thesis.

But the weaker thesis itself comes in a weak and strong variety (let us henceforth call them the weak and intermediate theses). According to the weak thesis, one may intelligibly make such claims whilst, according to the intermediate thesis, one may (in the current state of metaphysical inquiry) reasonably make such claims. As Williamson indicates, the vindication of the weak thesis is a ‘modest goal’ and ‘hardly in doubt’ (3). But it was never my intention merely to vindicate the weak thesis but also the intermediate thesis.

Consider again the examples concerning gold and goodness mentioned by Williamson (3). Gold is in fact the element with atomic number 79 and goodness is, let us suppose, what maximizes utility. In either case, one can intelligibly deny that gold is the element with atomic number 79 and intelligibly deny that goodness maximizes utility. However, there is a significant difference between the two cases. For given the current state of scientific inquiry, one cannot reasonably deny that gold is the element with atomic number 79 whilst, given the current state of ethical inquiry, one can reasonably deny that goodness is what maximizes utility. I had wanted to make out that the case of essence was more akin, in this respect, to the case of goodness than to the case of gold.

I must admit, though, that the distinction between the weak and intermediate theses is not always clearly marked in E&M. I talk of the ‘intelligibility of a position which makes such claims’, of the issue [in the corresponding semantic case] concerning ‘intelligibility rather than truth’, and of philosophers ‘agreeing’ on the modal facts but not on the essentialist facts; and such talk, taken on its own, might well appear to suggest the weak thesis. However, this talk, wherever it appears, is always followed up by remarks that make it clear that the stronger thesis is in question. I say such things as that the issue is one which ‘we are inclined to regard as a matter of substance’ (E&M: 5), that the claims in question ‘raise real issues’, or that they reflect a genuine difference of opinion’ (E&M: 11).¹

Indeed, in an earlier paper, ‘The Study of Ontology’ (Fine 1991), I introduced and developed what I called ‘a dialectical conception of modality, one that is determined by what is left open at a given stage of enquiry’ (263); and the paper on essence, published three years later, can be seen as implicitly invoking such a conception. Thus, although it is understandable that Williamson might appeal to the analytic/synthetic distinction (which in footnote 1 he grants ‘to Fine simply for the sake of argument’) or to the distinction between concepts and properties in attempting to make sense of the weak thesis, these other distinctions are not really relevant to what I had in mind.

The distinction between the weak and intermediate theses might not seem to amount to much, but I believe that the intermediate, in contrast to the weak thesis, is, and has been, extremely consequential for the study of metaphysics. Before ‘Essence and Modality’, many contemporary metaphysicians would have been happy to employ the concept of necessity and would have regarded talk of essence as simply a form of de re modal discourse (the Kripke of ‘Naming and Necessity’ is an example). Thus, they would not have recognized the need to admit into the conceptual repertoire of metaphysics a concept of essence in addition to the concept of modality. Vindication of the intermediate thesis should, and has, changed all this. We now recognize essence as a concept in its own right and, with its introduction, the field of metaphysics has opened up to include questions concerning the nature of things which previously could not even be raised, let alone answered. It was for this reason that I claimed, on the basis of the intermediate thesis, that ‘the subject [the metaphysics of identity] should not be taken to be constituted, either in principle or practice, by its claims of necessity’ (E&M: 11), though, to be fair, I should simply have said ‘in practice’.

The truth of the intermediate thesis rests, of course, on the current state of metaphysical inquiry. It was, I believe, correct, at the time, but it is entirely possible that someone might come along and convincingly show that, despite appearances, the various claims we have considered are all false; and, in this case, even the intermediate thesis can no longer be allowed to stand. Presumably, Williamson takes himself to be such a person; and so let us now turn to the arguments against the essentialist propositions considered in E&M.

2 Essential Rot

I follow Williamson in using ‘s’ for the successor operation on natural numbers and ‘p’ for the predecessor operation (where we may stipulate that p(0) = 0). Given the iterative conception of the natural numbers (under which they are generated from 0 by successive application of the successor operation), we naturally judge:

to be false, and

to be true (p. 5).²

Before we proceed, let me remark that there is a real question in my mind as to whether (6*) is true under the iterative conception of natural numbers. I would be happy to grant that it is essential to 8 that it immediately succeeds 7, i.e. that it is essential to 8 that it stands in the immediate successor relation to 7, but I would be less happy in granting that it is essential to 8 that it stands in the identity relation to s(7).³ If this is so, then the judgements on which Williamson’s arguments rely do not even get off the ground. However, I am happy to admit, if only for the sake of argument, that we do naturally discriminate between (5*) and (6*) in the way he suggests.

Williamson is of the view that our natural judgements in this case are mistaken. For he takes ‘p(9)’ and ‘s(7)’ to be directly referential, by which he means that they contribute ‘only their referent to the compositional semantic evaluation of the larger expression in which they occur’; and, consequently, the substitution of ‘p(9)’ for ‘s(7)’ in (6*) should preserve its truth (7).

Although Williamson takes our natural judgements in this case to be ‘provably false’ (4), it seems to me that the considerations he advances do not go very far in establishing that this is so. One consideration he offers is that ‘there is no semantic obstacle to treating functional expressions [such as ‘p(9)’ and ‘s(7)’] as primitive’, rather than as disguised definite descriptions or the like. This may be so, but it does not mean that they directly refer to what we take to be their usual referent.

Another consideration is that we may provide a semantics for such expressions in which their semantic value is their usual referent. However, Williamson only provides a semantics of this sort for a language in which the means of construction are extensional; and yet we are all familiar with the fact that a semantics which is adequate for an extensional language (as when we take sentences to signify truth-values) may not be adequate when the language is taken to include non-extensional forms of expression.

A third consideration is that ‘unlike definite descriptions, functional expressions are scopeless’ (7). Now it should not be thought that a functional expression will be scopeless simply because, in contrast to the case of a definite description, it is not a quantifier expression or the product of variable binding. For where t is a term occurring in a sentential context of the form Ψ(φ(t)), we may take it to be subject to scope ambiguity as long as a distinction in content can be drawn between Ψ(λxφ(x).t), on the one hand, and λxΨ(φ(x)).t, on the other hand. Indeed, in the present case, the pro-essentialist will wish to draw a distinction in content between it being essential to 8 that p(9) is such that 8 is identical to it (£₈(λx(8 = x).p(9)), and p(9) being such that is essential to 8 that 8 is identical to it (λx£₈8 = x).p(9)); and it is no objection to such a view to be told that such a distinction in scope is not apparent in other contexts.

There are also powerful considerations on the other side. For the direct referentiality of functional expressions such as ‘p(9)’ and ‘s(7)’ is at odds with the very natural view according to which a directly referential term directly contributes its referent not merely to the determination of the content of an expression to which the term belongs but to the content itself. It is at odds, in particular, with a leading view in the philosophy of language, the Russellian view, according to which the content of a sentence is directly composed of the referents of its component parts.⁴

It may help to explain in some detail how this is so. Given a basic syntactic operation F, we may form a complex meaningful expression E = F(E₁, E₂, …, E_n) from appropriate constituent expressions E₁, E₂, …, E_n. The semantic content e of E will then be a corresponding function γ(e₁, e₂, …, e_n) of the respective semantic contents e₁, e₂, …, e_n of the constituent expressions E₁, E₂, …, E_n:

So much is common ground among different semantic theories.

Now the Russellian, and the objectualist more generally, will take propositions and other semantic contents to have a certain objectual or singular component, as given by the set of individuals that actually figure in the content. Given a semantic content e, let us use o(e) for the objectual component of e. Then a natural assumption concerning the objectual component is:

Indeed, it might be thought that if we are to be able to bind into the contexts occupied by the expressions E₁, E₂, …, E_n, it is essential that they still have objectual import.⁵

Let us use o(E) for the objectual component o(e) of the semantic content e of the expression E. We might call o(E) the objectual content of E. Then putting (*) and (**) together, we obtain:

In other words, the objectual content of a complex expression is the sum of the objectual contents of its constituent expressions.

Such an assumption would be justified under a Russellian conception of semantic content under which the proposition expressed by a sentence is ‘built up’ from the semantic contents of its parts. But it would also be justified under alternative, non-structural, conceptions of semantic content (as, for example, in Goodman 2019) and even under an extensional conception of semantic content as long as it was enriched with an objectual component. Thus, the structural aspect of Russellianism, which some have found objectionable, need not here be in question.

Let us now assume that there is basic syntactic operation of predicate application, taking an n-ary predicate F and n individual terms t₁, t₂, …, t_n into a complex sentence, which we may write, in usual fashion, as F(t₁, t₂, …, t_n), and that, in addition, there is a basic syntactic operation of functional application, taking an n-ary function term f and n individual terms t₁, t₂, …, t_n into a complex individual term, which we may write, in usual fashion, as f(t₁, t₂, …, t_n). We may then suppose that the complex term ‘s(7)’ is the result of applying the syntactic operation of functional application to the function symbol ‘s’ and the individual term ‘7’, that ‘p(9)’ is the result of applying functional application to the function symbol ‘p’ and the individual term ‘9’, that ‘8 = s(7)’ is the result of applying the syntactic operation of predicate application to the predicate ‘=’ and the individual terms ‘8’ and ‘s(7)’, and that ‘8 = p(9)’ is the result of applying predicate application to the predicate ‘=’ and the individual terms ‘8’ and ‘p(9)’. We may also plausibly grant that ‘s’, ‘p’, and ‘=’ have no objectual content, i.e. that o(‘s’) = o(‘p’) = o(‘=’) = ∅; and, given that the terms ‘7’, ‘8’, and ‘9’ are directly referential, what this will mean, in the present context, is that their respective semantic contents are the numbers 7, 8, and 9 themselves and hence that these numbers (or rather their singletons) are also their respective objectual contents.

It follows from (***) and the supplementary assumptions that the objectual content of the sentence ‘8 = s(7)’ is {8, 7} whilst the objectual content of the sentence ‘8 = p(9)’ is {8, 9}.

Thus the propositions expressed by these two sentences (their semantic contents) will not be the same and, since the difference in content may well be relevant to the truth of the essentialist claims under (5*) and (6*), we have good reason to think that their truth-values may also not be the same.

I am not claiming that these counter-considerations settle the matter. We have here a much vexed issue in the philosophy of language. But they do show that the considerations which Williamson advances are far from being decisive.

In any case, a related difficulty also arises under the possible worlds semantics for modal languages, where talk of objectual content is not even appropriate, given that ‘8 = 8’ and ‘9 = 9’ will express the very same (necessary) proposition.⁶ It is a feature of the functional expressions Williamson chooses that they are strongly rigid; ‘s(7)’ and ‘p(9)’ will designate the same individual, 8, in each possible world. But surely this is an incidental feature of such expressions. Where F is a predicate expression, can we not use the functional expression ‘#(F)’ to denote the number of F’s? Indeed, Hume’s principle, to the effect that #(F) = #(G) iff there is a one-one correspondence between the F’s and G’s, is commonly stated using such functional expressions rather than the corresponding definite descriptions. Or if one wants a “first-order” example, take the use of variables like ‘v’ and ‘a’ in physics to indicate velocity or acceleration. These may surely be taken to be abbreviations for functional expressions, such as ‘v(x, t)’ or ‘a(x, t)’, to indicate the velocity or acceleration of a body x at time t. But under the most natural reading of such expressions, they will not in general be rigid designators—the number of F’s or the velocity or acceleration of a body will in general depend upon the circumstances—and so these expressions cannot be taken to be directly referential.

It is not just that these are the most natural readings, but the most natural semantic principles governing the transition from a typed extensional language to its intensional counterpart determine that this should be so. For just as a first-order unary predicate F should now have as its intensional semantic value a function F taking each world w into an appropriate form of extension, viz. a function taking each individual (or each individual of the world) into a truth-value, so each function symbol f should have as its intensional semantic value a function f taking each world into an appropriate form of extension, viz. a function taking each individual (or each individual of the world) into an individual; and just as the semantic value of the predication F(t) will now be the function taking each world w into F(w)(t(w)), for t the intensional semantic value of t, so the intensional semantic value of the functional expression f(t) will be the function taking each world w into f(w)(t(w)), with the truth-value of F(t) or of the referent of f(t) depending, in general, upon the world. Thus, in the transition to the intensional language, there is no more reason in the case of function symbols than in the case of predicate symbols to suppose that their application will result in the rigidification of semantic value.

Williamson is concerned to avoid mounting an argument against essentialist discourse that might be used against modal discourse. But once non-rigid functional expressions are allowed, it is hard to see how the required distance between the two forms of scepticism can be maintained. For can we not use a Quine to hoist Williamson by his own petard? Letting P be the predicate ‘is a planet’, we naturally judge:

to be false, and

to be true. A mistake, under Williamson’s supposition that the terms ‘#(P)’ and ‘8’ are directly coreferential! And the same mistake, surely, as we make in the essentialist case! But then why be so bothered by it in the one case yet not in the other?

3 Does the Rot Spread?

I have suggested that the judgements we naturally make in the case of (5*) and (6*) are not mistaken; or, at least, not mistaken for the reason Williamson gives. However, for present purposes, let me grant that Williamson is right and that we are mistaken for the very reason that he gives. Williamson then goes on to argue that the mistake we make in this case casts doubt on the kind of essentialist claims made in E&M, since what leads us to make the mistake in the one case also leads us, though less obviously, to make the same mistake in the other cases as well.

So, granted that we do indeed make a mistake in the case of (5*) and (6*), what might lead us to make it? He suggests that it is:

This is indeed possible. After all, we make mistakes all the time and for all kinds of reasons, good and bad. But by Williamson’s own lights, there is a simpler and more natural explanation of why we make the mistake. In discussing the distinction between functional expressions and definite descriptions, he writes:

But given that we naturally paraphrase functional expressions as definite descriptions, why should it not be the substitution of the one for the other that leads us to make the mistake? We simply read ‘it is essential to 8 that it is p(9)’ as saying that it is essential to 8 that it is the predecessor of 9, thereby overlooking the fact that ‘p(9)’, in contrast to ‘the predecessor of 9’, is directly referential? If this is so, then what leads us to make the mistake in this case will not apply to the kinds of case considered in E&M in which such functional expressions are not in play. I might add that if the mistake we make is the same as in the Quinean modal case considered above then it can hardly be put down to the operation of a relevance filter.

But again, let me be concessive and grant Williamson’s hypothesis that what leads us to make the mistake is that ‘the complement [‘8 = p(9)’] has the constituent ‘9’, deemed irrelevant to answering the question ‘What is 8?”.

Those of us who work in the theory of essence will recognize in Williamson’s notion of irrelevance a linguistic cognate to the metaphysical notion of ontological dependence, the notion of one thing depending for its identity upon another. _‘Essence and ontological dependence are related by the following principle (using what I hope, in the present context, is a reasonably clear notion of being directly about):

In other words, if x is irrelevant to y in the sense that y does not ontologically depend upon x, then it is not essential to y that A. This principle, I would claim, is correct. However, there is a related linguistic principle which may not be correct:

In other words, if a term contained in A directly refers to something irrelevant to y then it is not essential to y that A.

The linguistic principle will follow from the ontological principle given the following semantic principle:

But if Williamson is right about the referential role of functional expressions then Referential Link and, presumably, also Linguistic Link will be incorrect. For when A contains a functional expression, the proposition it expresses may not be directly about the objects to which its constituent sub-terms directly refer.

What I would therefore like to suggest is that, given that we take Williamson’s hypothesis seriously, then what might most plausibly lead us to reject (5*) is the unthinking acceptance of Referential Link. We mistakenly believe (though correctly if the objectualist is right!) that the complement of (5*) is directly about the number 9 and, on the basis of this incorrect belief, we then infer, on the basis of Ontological Link, to the incorrect conclusion that (5*) must be false.

But this means that the same underlying error cannot be at work in the examples from E&M, as Williamson wishes to maintain, since the ontological principle is in fact correct and it is only this good principle, and not the bad linguistic form of the principle, that is involved in the judgements we make about these examples. Williamson, of course, may not like this notion of ontological dependence, but that is a separate matter. Once it is taken on board, we will no longer have any reason to think that the underlying errors that he detects in his own cases will spread to the cases considered in E&M.

There may, of course, be other ways in which we could have been led into error. But one form of error can, I think, be ruled out. In application to (5*) and the like, Williamson’s relevance filter operates at the purely linguistic level:

Thus, we are misled by how something is said when this has no bearing, as it should, upon what is said. But then let us control for this form of error by expressing ourselves in such a way that irrelevant linguistic detail cannot intrude on our judgement. Thus, in the case of singleton Socrates, I say: take the object x that is Socrates and take the object y that is singleton Socrates; then it is essential to y to have x as a member, though not essential to x to belong to y. It seems to me that our judgements in this case are just as firm as when we employ singular terms within the scope of the essentiality operator. (This is of course akin to how Kripke attempted, through the use of rigid designators, to assure us in ‘Naming and Necessity’ of the truth of certain de re modal claims.) It is therefore hard for me to see how the application of a heuristic that operates purely at the linguistic level could somehow be interfering with our judgement in such cases.

4 Methodological Musings

Let me conclude with some brief remarks on a comment that Williamson makes towards the end of his paper:

I do not think this comment is altogether fair to the metaphysics community. For one thing, there was not that much haste. It took almost 20 years after the publication of E&M for it to begin to be extensively cited.⁸ But more to the point, I doubt that the acceptance of a new paradigm was based upon nothing more than a few observations (whether questionable or not). There were, I suspect, a number of other factors at work which together were as important, if not more important, than the observations themselves. There was the establishment of a good notation, which enabled one to express essentialist claims in an especially perspicuous way, somewhat analogous to the way in which modal claims were already expressed. There was the growing awareness, perhaps somewhat aided by the choice of examples from E&M, that within the multitude of ways in which ‘what is X?’ questions might be understood, there was one of purely metaphysical import that was independent of semantic or cognitive considerations (real as opposed to nominal definition, identity as opposed to identification). There was the development of a logic laying out the principles by which we might reason with the concept of essence and a semantics for which the logic was sound and complete (Fine 1995b; 2000). Williamson talks of ‘the heavy theoretical cost of abandoning the intensionalist framework, with all its well-established abductive virtues, in favour of various half-baked hyperintensionalist alternatives with all their complications and difficulties’ (13). I do not know whether he wishes to include my semantics for the logic of essence among the half-baked alternatives, but it is a relatively straightforward modification of the possible worlds semantics for modal logic and so I like to think that it may, with some charity, be regarded as being at least three quarters baked. But more significant than these other factors, to my mind, is that the concept of essence can be put to good use in the formulation and consideration of philosophical doctrines, whether this takes the form of views previously not considered or of views previously considered but improperly formulated. As an example of such good use we need look no further than Williamson’s own paper. He writes, ‘Natural numbers are often, and very naturally, understood as metaphorically constructed in a similarly iterative way: a natural number is the result of starting from 0 and adding 1 as many times as needed.’ But we would like to be able to get beyond the metaphor and one way to do this is to understand the iterative conception of natural numbers as one in which it is taken to be of the essence of each natural number n+1 to be the successor of n (and of the essence of 0 to be a natural number which is not the successor of any natural number). This then explains why the natural numbers are well-founded under successor since any series of definitions must be well-founded; and similarly for the iterative conception of sets, under which it may be taken to be of the essence of each set to have certain particular objects as its members. Thus the ‘observations’ concerning numbers and sets are not just isolated intuitions but may well be regarded as integral to a proper understanding of what these objects are and of how they behave.

When I reflect on the process by which essentialist ideas have recently come to be more commonly accepted what strikes me is not the speed or lack of caution by which they were accepted but the similarity to the process by which the idea of de re modality previously came to be accepted (much of which was driven by the advent of ‘Naming and Necessity’). Again, there was a good notation, the development of quantified modal logic, a semantics for such logics, a clear delineation of a metaphysical concept in contrast to related semantic or cognitive concepts (such as analyticity and aprioricity), and the use of the concept in the formulation and consideration of philosophical doctrines (such as physicalism or the necessity of origin). I am not saying we have as yet as strong a case for embracing essentiality as for embracing de re necessity. But if I am asked where we should go from here, I would not say with Williamson that we should look to see how our essentialist judgements might be misguided. We should accept them tentatively but consider further how the essentialist ideas behind them might be put to good use. Philosophical objections to concepts are nearly always tendentious; and if a concept can be shown to be useful then no one is going to care about any tendentious philosophical objection that might be raised against it.

Competing Interests

The author has no competing interests to declare.