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In defense of metaphysical analyticity

Abstract:

According to the so-called metaphysical conception of analyticity, analytic truths are true in

virtue of meaning (or content) alone and independently of (extralinguistic) facts. Quine and

Boghossian have tried to present a conclusive argument against the metaphysical conception

of analyticity. In effect, they tried to show that the metaphysical conception inevitably leads

into a highly implausible view about the truthmakers of analytic truths. We would like to

show that their argument fails, since it relies on an ambiguity of the notion of ‘independence

of (extralinguistic) facts’. If one distinguishes between variation independence and existence

independence, the unwelcome view about the truthmakers of analytic truths no longer

follows. Thus, there is at best a challenge, but no conclusive argument. The door to the

metaphysical conception of analyticity is still open.

1 Introduction

It has been claimed that there are two different conceptions of analyticity, one metaphysical

and one epistemological. The metaphysical conception is built upon the idea that analytic

truths are true in virtue of meaning (or content) alone and independently of (extralinguistic)

facts. In contrast, the epistemological conception characterizes analyticity as truth that can be

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known (or, at least, justifiably believed) on the basis of understanding alone and

independently of empirical investigation.

How these two conceptions relate to each other is a matter of considerable

controversy.1 But since Quine’s “Carnap and Logical Truth”, a seemingly powerful argument

against the metaphysical conception has been around. Recently, it has been reinforced quite

vigorously by Paul Boghossian (1997). And it seems fair to say that it has already acquired

the status of philosophical orthodoxy. The core of the argument is simply this: According to

the metaphysical conception, analytic truth is supposed to be truth which is independent of

(extralinguistic) facts. But how could it be that anything is true independently of what the

facts are? The only way to make sense of this idea seems to be to assume that it is the

meaning (or content) of the truth itself that makes it true. This, however, is not acceptable.

The fact that a truthbearer means what it does typically, if not always, is a contingent fact. So

this cannot be the right kind of truthmaker for analytic truths which are considered to be

necessary (at least standard examples like “bachelors are unmarried”). In other words: The

truth value of an analytic truth does not seem to depend on the contingent fact of its own

meaning (or content).

If the Quine-Boghossian argument were successful, it would put a definite end to the

metaphysical conception of analyticity. However, as we would like to show in the following,

the argument fails. There may, of course, be all sorts of other problems with the metaphysical

conception, but at least they have nothing to do with this specific argument. In this modest

sense, we would like to defend the metaphysical conception of analyticity. We think that the

door to ‘truth in virtue of meaning’ is still open. Whether anything useful can be found behind

it remains to be seen. But insofar as the current orthodoxy concerning analytic truth rests upon

the Quine-Boghossian argument, it is time for an update.

1 See, for example, the debate between Paul Boghossian and Eric Margolis and Stephen Laurence (Boghossian 2003, Margolis/Laurence 2001).

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2 The Quine-Boghossian argument against the metaphysical conception of

analyticity

The first step of Quine’s critique of the analytic-synthetic distinction was an attack on the idea

of logical truth as truth by convention (see Quine 1936/1976). The second step was presented

in Quine’s famous papers “Two dogmas of empiricism” and “Carnap and logical truth”.

Among many lines of thought, there is also an argument to be found in Quine’s writings

which consists of a fundamental critique of the whole idea of ‘truth in virtue of meaning

alone’. In “Carnap and logical truth”, for example, Quine writes:

“Another point [...] was that true sentences generally depend for their truth on the

traits of their language in addition to the traits of their subject matter; and that logical

truths then fit neatly in as the limiting case where the dependence on traits of the

subject matter is nil. Consider, however, the logical truth ‘Everything is self-

identical’, or ‘(x) (x = x)’. We can say that it depends for its truth on traits of the

language (specifically on the usage of ‘=’), and not on traits of its subject matter; but

we can also say, alternatively, that it depends on an obvious trait, viz., self-identity, of

its subject matter, viz., everything.” (Quine 1954/1976 p. 113, emphasis in original)

The general thrust of this critique is clear enough: There cannot be any truth whose ‘factual

component’ is really zero; necessarily, both the ‘meaning component’ and the ‘factual

component’ have to be non-zero. Therefore, the idea of ‘truth in virtue of meaning alone’ is

doomed to failure.

Recently, essentially the same critique has been expressed and endorsed by Paul

Boghossian. He writes:

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“[…] I want to register my wholehearted agreement with Quine, that the metaphysical

notion is of dubious explanatory value, and possibly also of dubious coherence. I

believe that Quine’s discrediting of this idea constitutes one of his most enduring

contributions to philosophy. Fortunately for the analytic theory of the a priori, it can

be shown that it need have nothing to do with the discredited idea.” (Boghossian

1997, p. 335)

This hints at Boghossian’s main project, the aim of explaining the a priori in terms of

analyticity or, more precisely, in terms of an epistemological notion of the analytic. But the

critique of the metaphysical conception is independent of that project. It is nicely expressed in

the following passage:

“What could it possibly mean to say that the truth of a statement is fixed

exclusively by its meaning and not by the facts? Isn't it in general true — indeed,

isn't it in general a truism — that for any statement S,

S is true iff for some p, S means that p and p?

How could the mere fact that S means that p make it the case that S is true?

Doesn't it also have to be the case that p? As Harman has usefully put it (he is

discussing the sentence 'Copper is copper'):

what is to prevent us from saying that the truth expressed by "Copper is copper"

depends in part on a general feature of the way the world is, namely that everything is

self-identical. [Footnote with reference to Harman 1967/1999, p. 122.]

The proponent of the metaphysical notion does have a comeback, one that has

perhaps not been sufficiently addressed. If he is wise, he won't want to deny the

meaning-truth truism. What he will want to say instead is that, in some appropriate

sense, our meaning p by S makes it the case that p.” (Boghossian 1997, pp. 335-6,

emphasis in original)2

2 In another passage, Harman expresses the same doubt more explicitly: “There is an obvious problem in understanding how the truth of a statement can be independent of the way the world is and depend entirely on

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So far, this amounts to an argument to the effect that the metaphysical conception quite

naturally leads to the idea that the meaning of an analytic truth (e.g. a statement S’s meaning

that p) is what makes it true (what makes it the case that p).3 This idea however, Boghossian

continues, is highly dubious:

“But this line is itself fraught with difficulty. For how can we make sense of the idea

that something is made true by our meaning something by a sentence?

Consider a sentence of the form 'Either p or not p'. It is easy, of course, to

understand how the fact that we mean what we do by the ingredient terms fixes what

is expressed by the sentence as a whole; and it is easy to understand, in consequence,

how the fact that we mean what we do by the sentence determines whether the

sentence expresses something true or false. But as Quine points out, that is just the

normal dependence of truth on meaning. What is far more mysterious is the claim that

the truth of what the sentence expresses depends on the fact that it is expressed by

that sentence, so that we can say that what is expressed wouldn't have been true at all

had it not been for the fact that it is expressed by that sentence. Are we really to

suppose that, prior to our stipulating a meaning for the sentence

Either snow is white or it isn't

it wasn't the case that either snow was white or it wasn't? Isn't it overwhelmingly

obvious that this claim was true before such an act of meaning, and that it would have

been true even if no one had thought about it, or chosen it to be expressed by one of

our sentences?” (Boghossian 1997, p. 336, emphasis in original)

the meaning of the statement. Why is it not a fact about the world that copper is a metal such that, if this were not a fact, the statement ‘Copper is a metal’ would not express a truth? And why doesn't the truth expressed by ‘Copper is copper’ depend in part on the general fact that everything is self-identical (Quine, [1954/1976])?” (Harman 1967/1999, p. 119) 3 Sometimes Boghossian speaks of a statement meaning that p, sometimes he speaks of a speaker meaning p by a statement. We assume that this difference does not matter for the present discussion.

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Yet, this line of argument sounds much clearer than it actually is. For, there are at least

four different characterizations of the metaphysical conception to be found in Boghossian’s

and Quine’s writings:

(1) Independence: no dependence of the truth (value) on extralinguistic facts.

(2) Analyzability: being analyzable into a factual component and a linguistic component,

the factual component being null.

(3) Fixing: the truth (value) is fixed exclusively by the meaning, not at all by the

(extralinguistic) facts.

(4) Making it the case (truthmaking): the mere fact that a sentence S means that p makes it

the case that S is true.

However, these four characterizations are reducible to really just two different ones.

For (2) can be taken as a mere re-description of (1), since ‘analyzability’ here is nothing but

analyzability into two different dependencies and it does not receive any further or different

explication in this context. Equally, (3) is nothing more than a reformulation of (1). Fixing of

a truth value just means independence of other factors. So finally, only two truly different

characterizations remain: independence and making-it-the-case (i.e. truthmaking).4

The Quine-Boghossian argument can now be seen to take the following shape. The

first step is from independence to making-it-the-case. It starts from the fundamental and initial

characterization (1) of analyticity: an analytic truth does not depend on (extralinguistic) facts.

Then, this idea is somehow taken to amount to, or to imply, (4) such that there appears to be

4 We will assume here that making-it-the-case is the same as truthmaking. If x makes it the case that s is true, then x is a truthmaker for s, and vice versa. Since no particular explication or conception of truthmaking is relied upon, this assumption should be harmless. We will also not care about the singular or plural, about how many entities are the truthmaker or truthmakers. Nothing seems to depend on that. Furthermore, we take it that any interesting conception of facts does not identify facts with true propositions. So we are not to assume, for example, that there has to be one unique fact like the fact that all bachelors are unmarried (or the fact that all things are self-identical) which serves as the truthmaker for the sentence ‘All bachelors are unmarried’ (or ‘All things are self-identical’).

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only one way to understand independence, namely, in terms of making-it-the-case. Finally,

the second part of the argument is supposed to refute the idea of making-it-the-case with

regard to analyticity. This part simply consists of the claim that a contingent (meaning) fact

cannot be the truthmaker of a necessary truth. For, this would make the truth of the

proposition expressed by the sentence a contingent truth, and it would make its truth

contingent upon a fact which is just of the wrong sort, namely a meaning fact. A true

proposition like the one expressed by the sentence “Snow is white or it isn’t”, even if it were

contingent after all, would certainly not depend for its truth on the fact that this sentence has

the meaning it actually has – but rather on some fact about snow, whiteness and the like.

Thus, it really seems quite implausible that meaning facts are the right truthmakers for

analytic truths.

The second step of the Quine-Boghossian argument is relatively straightforward, the

crucial part, however, is the first one. If independence inevitably leads to (4), then the

argument already is a real success. In any case, we will not take issue with the second step

here.5

3 Where the Quine-Boghossian argument fails: existence independence versus

variation independence

There is a fundamental problem with this argument, however. It rests on a confusion of two

different kinds of independence: existence independence and variation independence. A truth

value of a truthbearer is existence-independent of certain facts if it does not depend on the

existence of these facts – it is whatever it is, no matter whether these facts exist or not. It is

5 Yet, it is not so clear to us whether the second step is entirely unproblematic. It is not so obvious that a contingent fact can never be the truthmaker of a necessary truth. The difficulty of being of the wrong kind of facts, of course, remains.

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variation-independent of certain facts if it does not change with any possible variation of

these facts. These two kinds of independence are not conceptually equivalent, since a truth

value can be variation-independent of certain facts without being existence-independent of

them. How so? – Well, if some suitable truthmaker or other for the truth in question always

exists no matter how the relevant facts are varied. The truth “There are elephants”, for

example, is variation-independent of any particular facts about elephants, yet it is not

independent of there being some fact or other about elephants, i.e. the existence of at least one

elephant. If the possible variations of the relevant facts are such that the existence

requirements for the truth value are always fulfilled, then the truth value is variation-

independent. For the truth value to be what it is, suitable facts have to exist. So the truth value

is not existence-independent.

Analytic truth, so goes the defense of the metaphysical conception of analyticity, is the

case of something’s being true variation-independently of extralinguistic facts. Analytic truth

is not necessarily based on the idea of existence independence. Only if it were based on

existence independence, (4) would arguably follow from (1): If every truth requires a

truthmaker, and this also holds for analytic truths, but their truth value is independent of the

existence of extralinguistic facts, then the only remaining truthmaker would be linguistic ones

(the ‘meaning facts’, as you might call them).

It is correctly observed that if truth in general requires the existence of suitable facts,

so does analytic truth. At least, if we do not want to jettison the realistic core idea that truth

(in general) requires truthmakers, we have to accept the existence dependence of truth on

extralinguistic facts even in the case of analytic truths. As realists about truth, we cannot make

sense of the idea of something’s being true without there being any extralinguistic facts at all.6

6 This, however, is a bit of an overstatement. Of course, there is the phenomenon of self-referential truths, such as ‘This is a meaningful sentence’ and the like. In these cases, the truthbearer’s meaning really seems to be the truthmaker. Somehow they have to be distinguished from analytic truths – which, in general at least, are not self-referential in this sense.

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But, properly understood, this is not really a problem for the metaphysical conception

of analyticity. Quite on the contrary, it rather strengthens the case for this conception, since it

enables a quite plausible subsumption of analytic truth under truth in general. Analytic truth is

no exception as far as truthmaking in the existential sense is concerned. It requires the

existence of suitable extralinguistic facts, too. But because analytic truth is variation-

independent, it does not require the existence of any specific extralinguistic facts. Just about

any possible variation of extralinguistic truthmakers will do. So in this properly restricted

sense, the ‘factual component’ really does reduce to null, as Quine has put it.

At this point one might wonder how extralinguistic facts could make analytic truths

true, given that analytic truths are said to be true independently of them. But once again, if we

clearly focus on the kind of independence which is supposed to hold here, namely variation

independence, no special problem for the truthmaking of analytic truth arises. There is a

general problem of how to account for the truth of general truths in terms of truthmakers, and

there are various ways one could try to deal with it. If the paradigmatic form of an analytic

truth is something like ‘All Fs are Gs’, we are facing the problem of truthmakers for general

truths. According to one conception of truthmakers, proposed by David Armstrong (1997),

such a general truth requires two things. First, certain singular facts have to exist. If, for

example, a and b are all the Fs, then the following singular facts have to exist: the fact that a is

F, the fact that a is G, the fact that b is F, and the fact that b is G. Second, there has to be the

fact that a and b are all the Fs there are – a closure fact. These facts serve as a truthmaker for

‘All Fs are Gs’. Exactly the same can be said if the sentence is an analytic truth. The

truthmakers for analytic truths do not behave any different from those for synthetic truths. In

particular, in some other world certain other facts serve as a truthmaker for the same truth

(facts about c and d and their being all the Fs in that world, for example). The fact that a truth

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is analytic merely implies that there is no variation in the facts such that a truthmaker would

be missing. But the truthmaking is exactly the same for analytic and synthetic truths.7

The meaning of an analytic truth, then, is such that no matter what the extralinguistic

facts are, a suitable truthmaker is always provided. Thus, the fundamental shortcoming of the

Quine-Boghossian argument is its implicit and exclusive identification of the idea of

independence of (extralinguistic) facts with the idea of existence independence. In order to

explicate a metaphysical conception of analyticity, however, it is much more plausible to rely

on variation independence. At least this is so for anybody who takes seriously the idea of

truthmaking.8 Far from refuting the metaphysical conception, the argument points to a viable

understanding of it.

Yet, one may still have the impression at this point that we have not really defended

what Quine and Boghossian have been attacking all along, namely that analytic truths are

“true in virtue of meaning alone”. For, the “alone” in this famous phrase seems to suggest that

nothing less but existence independence will do as a proper defense of metaphysical

analyticity.9 But note that this does not seem to be a very convincing account of what Quine

and Boghossian actually have been attacking. Rather, Quine speaks of “logical truths [...] as

the limiting case where the dependence on traits of the subject matter is nil” (op. cit., p. 113,

our emphasis) and Boghossian asks what it could mean “to say that the truth of a statement is

fixed exclusively by its meaning and not by the facts” (op. cit, p. 335, our emphasis). These

formulations suggest that we are right to focus our defense on the question if analytic truths

7 One might therefore conclude that any fact serves as a truthmaker for any analytic truth. For, any fact is such that its existence entails the truth of the analytic truth. – This may be so, but only if the entailment conception of truthmaking is presupposed. And the entailment conception cannot be correct for reasons independently of the issue of analyticity, as has been observed, for example, by Greg Restall (1996). The problem is, in a nutshell, that entailment (the existence of the entity entails the truth) is not strong enough, as can be seen from considering necessary connections and necessary truths. Perhaps, an additional relevance condition is a solution to this problem, as Restall suggests, or reference to the topic or subject matter of the truth has to be taken into account, as Barry Smith (1999) proposes. But the problem is a general problem for truthmaker theory, not a special problem for analytic truths. 8 It is not our burden to defend the idea of truthmaking here. Rather, Quine and Boghossian implicitly rely on it in their argument. 9 Thanks to an anonymous referee for pressing this point.

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can be true independently of the (extralinguistic) facts in some philosophically interesting

sense. For, once we put aside the phrase “truth in virtue of meaning alone” and its undeniable

rhetorical force, this seems to be the real philosophical issue here.

4 Conclusion

Let us mention two remaining problems. First, analytic truth should be distinguished from

metaphysically necessary truth. Second, it should be distinguished from logical truth.

Metaphysically necessary truths also seem to be true variation-independently (even

though not existence-independently). No matter what the extralinguistic facts are, the sentence

‘Hesperus is Phosphorus’ is always true, as Kripke has argued forcefully (cf. Kripke 1980).

But intuitively, we do not want to count this sentence as analytic. So there is need to elaborate

a feasible distinction between necessity and analyticity. And this is so even if we do not

switch to an epistemological conception of analyticity.

However, one major idea regarding analyticity can be put to work here. Analytic truths

can be conceived of as a special subclass of necessary truths, namely those that are generated

by certain structural features of their meaning. One variety of this idea is what might be

called ‘meaning inclusion’. Intuitively characterized, in a case of meaning inclusion the

meaning of one expression is included in the meaning of another expression. For example, the

meaning of one predicate (‘is a bachelor’) may be included in the meaning of another

predicate (‘is male’), at least, if ‘meaning’ here is taken in an extensional sense.10 In addition,

however, this sort of semantic inclusion should be non-accidental in a certain way. So there

has to be a reason – and the right kind of reason – for the existence of the semantic inclusion

in question. This would be so if the relevant expressions have acquired their meaning in such 10 Of course, according to some intensional interpretations of ‘meaning’, the inclusion relation would hold just the other way round.

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a way that semantic inclusion was intended or designed. Accidental meaning inclusion, on the

other hand, is not sufficient for analytic truth. One thing or substance may have acquired two

different names ‘a’ and ‘b’ by two entirely independent acts of baptism. In this case, semantic

inclusion would be set up by pure chance, neither intended nor designed. Consequently, a

sentence like ‘a = b’ might be true necessarily and variation-independently, but it should not

be counted as analytic. The situation is different, however, in cases of non-accidental

semantic inclusion like ‘Bachelors are unmarried’.11

One way in which the right kind of semantic inclusion can come about is explicit

definition. Probably there are other ways, too, but explicit definition is an obvious first

candidate. Quine already conceded – somewhat inconsistently with his overall position, as it

seems12 – that explicit definition or stipulation can bring about semantic inclusion or

synonymy:

“Here the definiendum becomes synonymous with the definiens simply because it has

been created expressly for the purpose of being synonymous with the definiens. Here

we have a really transparent case of synonymy created by definition; would that all

species of synonymy were as intelligible.” (Quine 1951/1980, p. 26)

This passage nicely illustrates the idea that, in the case of explicit definition, semantic

inclusion occurs exactly because it has been ‘created expressly’ for this very purpose.

Certainly, this is possible, and it should be regarded as a paradigm of non-accidental meaning

inclusion.

Another way in which semantic inclusion can be brought about might be by means of

reference fixing mechanisms. If the reference of two expressions is determined by

11 The two expressions ‘furze’ and ‘gorse’ might be another example of accidental synonymy and, therefore, the sentence ‘All furze is gorse’ will not turn out as analytic. This seems right to us, since, intuitively, this sentence does not count as analytic. (In addition, one might question whether the two expressions really are synonymous, as they can figure in informative identities.) 12 As has been already observed by Grice and Strawson (cf. Grice/Strawson 1956).

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mechanisms which are such that their application necessarily leads to semantic inclusion, then

it seems appropriate to speak of the kind of non-accidentality we are looking for.13

A third possibility might be semantic complexity, reminiscent of the classical view

advocated by Locke and Kant. If a system of expressions allows for suitable complex

expressions, i.e. expressions built up from other expressions, then a certain complex

expression can be semantically included in another one (again, in the extensional sense)

simply because it contains it as a constituent in the appropriate way. For example, the

complex expression ‘is an F and a G’ is semantically included in the expression ‘is an F’

because the former quite literally contains the latter in the appropriate way. Therefore, a

sentence like ‘Everything which is an F and a G is an F’ becomes an analytic truth because it

is true variation-independently in virtue of non-accidental semantic inclusion.14

There might be even more ways in which non-accidental semantic inclusion can be

brought about. But the three we have just mentioned are quite plausible and they seem to be

good enough to distinguish analytic truths from variation-independent truths in general.15

Another variety of the idea that analytic truths are generated by certain structural

features of their meaning is implicit definition. With implicit definition, a certain meaning is

generated in a non-accidental way such that the existence of a truthmaker is guaranteed.

Implicit definition has usually been appealed to in attempts to establish the apriori.16 But one

can also utilize it as part of a defense of metaphysical analyticity. Then, the focus is more on

13 This idea has recently been put forward by Gillian Russell. Cf. Russell (2004). 14 The idea of analyticity in virtue of (non-accidental) semantic complexity seems to be exactly what Jack Lyons (2005) has tried to spell out in his recent defense of analyticity. Of course, if this were the only source of analyticity, analytic truth would become a rather limited phenomenon, as Lyons somewhat seems to admit. Note that we do not presuppose here that the various constituent representations and their meaning relations have to be epistemically accessible, not even for competent users. Whether metaphysically analytic truths are also epistemically accessible in a special way really is a separate issue. To the extent to which non-accidental meaning inclusions are epistemically accessible in such a way, metaphysical analyticity coincides with epistemological analyticity. And it is at least plausible that some non-accidental meaning inclusions admit of a special form of epistemic access. This may help to explain why it is so difficult to sort out the two conceptions. 15 We have not dealt with indexical sentences like ‘I am here now’ so far. They have the kind of twofold meaning that Kaplan and others have described. It seems as if analyticity rather applies to the character or ‘diagonal intension’ than to the content or ‘horizontal intension’ of such sentences. Yet, we are entering the field of two-dimensional semantics here, a topic much too complex to be dealt with in this paper. 16 Cf. Wright, Hale (2000), Boghossian (2003). For a critical discussion of this epistemological project, see Horwich (1998), ch. 6.

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the meaning which is brought about by implicit definition, rather than on our epistemic access

to it. There may be certain conditions which have to be fulfilled in order for an implicit

definition to successfully generate a suitable meaning, as can be learnt from unfortunate cases

like Prior’s logical operator ‘tonk’. But if these conditions hold in a given case (and there is

no reason to be overly skeptical here), then a meaning is established in the required

intentional, non-accidental way which guarantees the truth of the defining sentence. And the

kind of guarantee here arguably is a form of variation-independence of extralinguistic facts.

Thus, implicit definition may provide another variety of analytic truth.

There is further work to be done here, of course, but no principled reason for

skepticism. We suggest that recent developments in the theory of meaning and content can be

exploited in quite fruitful ways for this purpose.17

As to the second demarcation problem, the distinction of analytic truth from logical

truth, we would simply like to suggest that logical truths are a subclass of analytic truths.

Firstly, because logical truths are also true variation-independently. Secondly, because they

owe their variation independence only to the meaning of the logical expressions. They are, as

it is often put, true independently of the interpretation of non-logical expressions. So logical

truths can, after all, be subsumed quite nicely under the rubric of analytic truths.

Admittedly, we do not know at present whether these ideas will sufficiently solve the

two demarcation problems we have discussed, and maybe other problems are lurking in the

background, too. Our main goal, however, was only to scrutinize whether the Quine-

Boghossian argument can put the metaphysical interpretation of truth in virtue of meaning

alone to rest in a single stroke. After closer inspection, we have found no compelling reason

why it should. Yet, if the metaphysical conception of analyticity will really prove to be

17 For example, we have in mind teleological theories of meaning and content of the sort that Ruth Millikan and Fred Dretske have worked out. Cf. Millikan (1984, 2004), Dretske (1995).

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philosophically interesting or fruitful in the end – and how it precisely relates to the

epistemological conception – remains to be seen.18

References:

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18 One of us (F.H.) wants to thank the Fritz Thyssen Stiftung for generous support of his research project on the metaphysics of facts during which this paper was written. The other one (J.H.) wants to thank his parents for a quite similar reason. Many thanks for comments and helpful criticisms to Alex Byrne, Thomas Grundmann, Stanislaus Husi, Christian Löw, Peter Schulte, and Timothy Williamson.

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