Peter Stephen and ... Ludwig - 2011

8/4/2019 Peter Stephen and ... Ludwig - 2011

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Peter, Stephen and Ludwig

Paolo Tripodi

I

According to Timothy Williamson (2007), whatever role has beenleft for analyticity or conceptual truth after Quine (1951) and

Kripke (1972/80), does not justify the linguistic-turn conceptionof philosophy, namely, the view of philosophy as an a priori enterprise,

with a central core of statements that are analytic or conceptual, henceinsubstantial1.

In this note, I focus on Williamsons challenge to the following view:

(LT)ep Some theses of philosophy are somewhat insubstantial qua epistemo-logically analytic.

Williamson takes CR below to be a prima facie characterization of episte-mological analyticity (2007, 73):

(CR) Failure to assent to an analytic or conceptual sentence is constitutive of(at least partial) failure to understand at least one word occurring in it.

Moreover, perhaps the word insubstantial occurring in LTep can be

intuitively understood, prima facie, as meaning not being capable of

being treated as stating a fact. Ultimately, however, the point is that ana-

lytic sentences are epistemologically unproblematic because whatevercognitive work is necessary for understanding them is somehow alreadysufficient for accepting them2. Thus, the precise sense of insubstantial

is indirectly provided by the notion of epistemological analyticity itself.Philosophers such as the later Wittgenstein and Strawson endorsedsomething like LTep and CR (though they used a different terminology)

3.

Williamson chooses, however, not to explicate CR by articulating an

1 Williamson doesnt suggest that the method of philosophy is a posteriori.Rather, his work contains a novel picture of the armchair method of philoso-phy. However, he does reject the view of the a priori that emerged in the so-

called semantic tradition (see Coffa 1991).2 Williamson (2006, 2).3 The later Wittgensteins rejection of the idea of advancing theses in philoso-

phy amounts to the rejection of the idea of advancing substantial theses inphilosophy (see 1953, 128).


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explicitly constitutive connection between understanding an analytic sen-

tence and assenting to it, but rather to focus on a modal connection by

providing the following definition of epistemological analyticity (2007,

73-4):(UA) Necessarily, whoever (fully) understands an analytic sentence, assents to

it .

Williamsons ground for that choice is that CR UA. I take it for

granted that that is true, so that a successful challenge to UA would allow

sceptical conclusions about CR.

Williamson argues that UA is false. Indeed, in his view, the notion of

epistemological analyticity is empty: no sentence at all is epistemologi-cally analytic. Therefore, LTep is false: no sentences at all, not even cer-

tain theses of philosophy, are insubstantial qua epistemologically

analytic4.

Williamson challenges UA by constructing two imaginary cases of

people who understand certain analytic sentences without assenting to

them. He considers the most basic case possible of an analytic sentence,

that is, the simple logical truth

(1) Every vixen is a vixen.

Then he conceives of two characters who are counterexamples to UA1

below (hence, to UA).

(UA1) Necessarily, whoever (fully) understands (1), assents to it.

Williamson calls such characters, respectively, Peter and Stephen

(2007, 86-88). Peter, a competent native speaker of English, has a certain

logical insight, according to which the sentence (1) presupposes that there

is at least one vixen. More formally, Peter holds that every F is G is

true iff there is a value of the variable x such that x is F is true and

there is no value of x such that x is F is true but x is G is not true;

and every F is G is false iff every F is G is not true.

Peter has also the weird belief that there are no foxes, hence no vixens,

and never have been: the apparent evidence to the contrary is caused by

widespread fox-hallucinations organized by MI6. Based on both his

2 Paolo Tripodi

4 Moreover, if the concept insubstantial is based on the notion of epistemo-logical analyticity, no sentences at all are insubstantial in that sense.


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3Peter, Stephen ... and Ludwig

logico-philosophical theory and his conspiracy theory, Peter rejects sen-

tence (1), though he has a full understanding of the words occurring in it.Stephen is a competent native speaker of English with some worries

about vagueness. If asked to provide a semantic assessment of (1),Stephens immediate reaction is what about borderline cases? On reflec-tion, he believes that borderline cases for vague terms create truth-valuegaps. Thus, he outlines a semantic theory that generalises classical two-

valued semantics by treating the gap as a third value (indefinite, neithertrue nor false) and by using Kleenes three-valued strong tables. On

Stephens view, for every F is a G to be true is for the conditional x isan F x is a G to be true for every value of the variable x; for everyF is a G to be false is for x is an F x is a G to be false for some

value of x.Furthermore, Stephen believes that some clearly female evolutionary

ancestors of foxes are borderline cases for fox and consequently for

vixen. Since (1) is equivalent to for every x, x is a vixen x is avixen, he regards (1) as indefinite. Thus, he does not assent to (1) (he is

agnostic about that), but he has a full understanding of it.Williamsons point is clear enough: Peters and Stephens refusing to

accept (1) is not the result of deviant, partial or different understanding,

but rather the consequence of a genuine philosophical doubt. Moreover,since there clearly could have been, and perhaps are, people such as Peterand Stephen, we have counterexamples to UA1 (2007, 91).

Now, Williamson argues as follows against LTep. As the possible casesof Peter and Stephen show, not even the most elementary case possible of

an analytic truth, that is, the simple logical truth (1), is epistemologi-cally analytic; hence, no sentence at all is epistemologically analytic5. Inparticular, no theses of philosophy are either epistemologically analytic or

insubstantial (in the sense provided above). Consequently, LTep is false.

II

Who are Peter and Stephen supposed to be in Williamsons thought-experiments? They are two philosophers who fully understand (1). Since

they explain (1) in non-standard ways, they dont assent to it. Peter pro-vides a non-standard explanation of every, for he regards it as existen-

5 Moreover, Williamson (2007, 92-6) shows item by item how to generalizehis sceptical conclusions about epistemological analyticity to other kindsof analytic sentences.


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4 Paolo Tripodi

tially committed. Stephen considers (1) as equivalent to for every x, x is

a vixen x is a vixen (as usual), but then he provides a non-standardexplanation of 6.

Now, what are such non-standard explanations? They are unorthodoxphilosophical theories. But what does philosophical theory mean, in itsturn, in the context of Williamsons imaginary cases? Consider somealternatives:

(i) Substantial explanatory theory (either metaphysical or quasi-scientificor sui generis).

(ii) Suggestion for linguistic or conceptual revision (e.g. revisionarymetaphysics in Strawsons sense7).

(iii) Conceptual analysis (on this see below).

It seems clear to me that (i) is the best candidate for what Williamson

has actually in mind in building the imaginary cases of Peter andStephen. Perhaps an indication that that is actually the case comes fromWilliamsons suggestion that

alternatively, one can imagine that Peter thinks that foxes were onlyrecently hunted to extinction, but that his presentist conception of time

implies that [(1)] is true only if there is now at least one vixen. Yetanother alternative is that Peter is a metaphysician who denies [(1)] on thegrounds that putative macroscopic objects such as foxes do not exist, forif they did they would have vague boundaries, which are metaphysicallyimpossible (2007, 87).

The question, however, is not what alternative Williamson does have inmind(an exegetical point). The question is, rather, what alternative he can

endorse in order for the imaginary cases to be counterexamples to UA1 (a

philosophically interesting point) and, above all, what option (if any) he

must rule out in order for the imaginary cases to be counterexamples toUA1 (the philosophically crucial point).

Part of the answer is that both (i) and (ii) make Peter and Stephencounterexamples to UA1. In fact, it is prima facie perfectly plausible that

a philosopher is thoroughly competent in his native language and per-fectly understands a certain analytic sentence (e.g. (1)), but he proposes

6 Of course, they also explain vixen in non-standard ways, but in what fol-lows I shant focus on that.

7 See Strawson (1959, 9).


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alternative metaphysical views (either substantial or revisionary8) on that

kind of sentences. For example, it would be absurd to claim that a scholar

such as Vann McGee, who has published purported counterexamples to

modus ponens for the indicative conditional in English9, does not per-fectly understand the English words if and then or the connective .

If we ask him to describe the standard concept of indicative conditional, he

can do it better than anyone else on earth. He simply has theoretical rea-

sons for rejecting the standard reading. By the same token, it would be no

less absurd to say that a person such as Michael Dummett, who doesnt

accept the classical view of negation, doesnt fully understand the English

word not or the classical reading of the connective . He is perfectly

able to make it clear the conceptual differences between the classical con-cept and the intuitionistic one. However, he has theoretical reasons to

favour the latter concept.

Of course, Wittgensteinians think that metaphysicians are under the

illusion of providing substantial explanations, whereas in fact they pro-

vide only conceptual explanations in the misleading disguise of factual

explanations. On such a view, Peters and Stephens non-standard explana-

tions of (1) entail that they misunderstand (1)10. Such a claim depends on

two assumptions: the idea that such explanations are not ultimately theo-

retical (substantial) but rather conceptual (insubstantial); and the idea that

different conceptual explanations of a certain word entail different under-

standings of that word. As I shall show below, I agree, with some qualifi-

cations that concern the meaning of conceptual, on the latter point. In

the present context, however, I prefer to remain agnostic on the former

assumption, for I regard it as question-begging against the friends of sub-

stantial metaphysics (including Williamson). Thus, I concede that meta-

physical theories provide somewhat substantial explanations. Then I also

concede that if Peter and Stephen are metaphysicians, then they are coun-terexamples to UA1.

III

However, what about the case (iii)? It depends on how one conceives of

conceptual analysis. Consider three sub-cases:


8 Perhaps revisionary metaphysicians cannot be properly described as refus-

ing to acceptan ordinary analytic sentence such as (1). They propose theadoption of a new conceptual scheme even though, in a certain sense, theyacceptthe ordinary, old one (e.g. for practical purposes).

9 Williamson (2007, 92).10 See e.g. Schroeder (2009) and Glock (2010).


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6 Paolo Tripodi

(iiia)Reductive analysis (e.g. a physicalistic theory of the mental).

(iiib) Systematic non-reductive theory (e.g. Williamsons (2000) theory of

knowledge)11.

(iiic) A priori connective analysis (the expression is Strawsonian rather than

Wittgensteinian, but consider, for example, both Wittgensteins per-

spicuous presentation of grammatical facts and Strawsons descriptive

metaphysics)12.

It seems to be not only logically possible but even highly probable

that a philosopher fully understands an analytic sentence (e.g. (1)) but

puts forward alternative conceptual views, either reductive or systematic,

about that sentence. Therefore, both (iiia) and (iiib) make Peter andStephen counterexamples to UA1. Or so I grant. For example, it would

be perverse to think that a person such as J.J.C. Smart, who doesnt

accept the ordinary, mentalistic conceptualization of the mind, doesnt

fully understand the English mental predicates. He is perfectly able to

describe the mental concepts that people ordinarily associate with such

predicates. Nonetheless, he attempts to show that those very ordinary con-

cepts can be reduced to a vocabulary in which every term is defined in

physicalistic terms.So far, so good: real cases seem to support Williamsons conclusions;

imaginary cases allow him to generalize such conclusions to any analytic

sentence whatsoever. My ultimate claim is, however, that in

Williamsons imaginary cases unorthodox philosophical theory must be

implicitly taken not to mean (as in (iiic)) a priori connective analysis.

Otherwise, Williamsons claim that Peter and Stephen fully understand (1)

becomes false and consequently Peter and Stephen cease to be counterex-

amples to UA1. In other words, Williamson must implicitly rule out thepossibility for Peter and Stephen to be like a third character, call him

Ludwig, who provides a connective analysis of (1). For Ludwig is not a

counterexample to UA1.

Let me make Williamsons assumption more explicit. What is connec-

tive analysis? I propose the following definition:

11 See Williamson (2010, 5). I wonder whether cases (iiia) and (iiib) should beincluded in case (i). This doubt, however, is irrelevant for my main argument.

12 See Wittgenstein (1953, 122) and Strawson (1959, 9). The differences ofscope, generality, and even method between the later Wittgenstein andStrawson are irrelevant for my present purposes.


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(CA) Connective analysis is the a priori description of the conceptual connec-tions (and exclusions) in the web of one or more words13.

My definition is minimal and incomplete. It is minimal because it

aims to capture a feature that is common to the conceptual investigationsof people such as the later Wittgenstein, Strawson, Ryle, Anscombe,

Hart, Winch, Kenny, Malcolm, and so on. It is incomplete because it

doesnt mention the essential theme of clarity (which was, after all, the

main goal for such philosophers)14.

For my present purposes, it is worth noting that connective analysis

has a merely descriptive character. Both Wittgenstein and Strawson

famously put stress on this aspect15.

Now, CA has one corollary:

(CA1) The connective description of the conceptual behaviour of a certainword identifies a certain concept associated to that word.

Consider a word w. Suppose that two philosophers P1 and P2 intend to

provide a connective analysis of the concept expressed by w (notice that

their purpose is to provide the analysis of one and the same concept). But

suppose that they come up with two different connective analyses ofw.

Now, CA1 supplies an argument for the conclusion that P1 understands wdifferently from P2:

(I1) The connective analysis ofw provided by P1 identifies the concept c1associated with w, while the connective analysis provided by P2 identi-fies the concept c2 associated with w, and c1c2 (this follows fromCA1, given the stipulated scenario).

(I2) P1 and P2 associate different concepts with the word w (this followsfrom I1).

(I3) P1 understands w differently from P2 (this follows from I2).

Notice that by different descriptions I mean descriptions capturing dif-

ferent concepts, whereas I am referring neither to differences in style, in

mode of presentation or in idiom16 , nor to differences in richness of detail.

13 See Strawson (1992, ch. 2) and Hacker (2001, 23).14 See Glock (2002).

15 See Wittgenstein (1953: 109) and Strawson (1959: 9). In this paper I amnot concerned with the question whether Wittgenstein's and Strawsonsexplicit meta-philosophical views perfectly cohere with their actual meth-ods.

.16 See Strawson (1959: 10-11).


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this result by building up two imaginary cases. But then it turns out that

his thought-experiments implicitly depend on the very assumption that

philosophy is not an insubstantial enterprise such as the Wittgensteinian

and Strawsonian a priori connective analysis. This, however, is whatshould have been proved, rather than assumed, in the meta-philosophical

argument against such linguistic philosophers. More precisely, on such

an assumption one can jump to the conclusion that it is false that some

theses of philosophy are insubstantial qua epistemologically analytic,

even without taking into account at all the issue of epistemological ana-

lyticity. In fact, the assumption that it is false that some theses of philos-

ophy are insubstantial immediately entails that such theses are not insub-

stantial qua epistemologically analytic (but, strictly speaking, neither quaanything else). On that implicit assumption, the imaginary cases of Peter

and Stephen, Williamsons sceptical conclusions about epistemological

analyticity and even his overall argument against LTep become superflu-

ous. Thus, Williamsons argument against LTep begs the question against

the later Wittgenstein, Strawson and their followers.

IV

I conclude by replying in outline to three possible objections.First objection: the step from I2 to I3 is controversial. Reply: if I2 is

taken to mean that P1 and P2 express, by using w, two different concepts

of I2, then I3 easily follows from I2. But such a reading of I2 is sug-

gested by the very notion of a priori connective analysis (and conse-

quently by I1). Of course, the connective analyst intends to describe the

conceptual behaviour of a shared concept. Nonetheless, she ultimately

describes the conceptual behaviour of what she takes to be the standard

concept. Her key access to that concept is her own individual semanticcompetence17. Thus, her connective analysis of w is the mirror of her

understanding of that word18.


17 I am assuming, here, that even if, as many believe, the references (or eventhe meanings) of ones expressions are determined by factors which areexternal to one, semantic competence (both communitarian and individual)is not determined by such factors. See Marconi (1997, ch. 4).

18 Connective analysis (in my sense) seems to be a somewhat trivial activity(though it can be more or less complete). The main goal ofhistorically realconnective analysts, however, was to achieve conceptual clarity. But seman-tic competence is notsufficient for achieving this further result, philosophi-cal ingenuity is required.


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Second objection: Peters and Stephens eccentric theories are logical

rather than philosophical. Reply: Peters and Stephens mistakes concern

logical concepts such as every and . This is not to say, however, that

the mistakes are logical in kind: one can make a non-logical mistakeabout logical concepts. To be sure, Peters and Stephens mistakes are not

deductive errors19. Their eccentricity concerns their theoretical reasons for

not accepting (1) (rather than their understanding of it). Here logic is

nothing but philosophical logic (= a philosophically motivated semantic

theory about certain logical concepts).

Third objection: Peter and Stephen are counterexamples to UA1 even if

they are conceived of as laymen rather than as philosophers. Reply: sup-

pose that they are two laymen who, in virtue of some elementaryinsights, dont accept (1). The main question is: should we say that they

fully understand (1)? Prima facie, there is no straightforward answer to

this question, for there is no litmus test for understanding20. In easy, nor-

mal cases, however, there are some partial, rough, context-relative ways

to compare a persons understanding of w with another persons under-

standing of w. But Williamsons imaginary cases, in which Peter and

Stephen are conceived of as laymen, are controversial rather than normal.

Of course, theres nothing especially puzzling in the logical possibility ofsuch controversial scenarios: it just illustrates the fuzzy edges of the con-

cept understanding a word. Yet, the main question is still unanswered. One

might be tempted to dissolve it rather than to answer to it, for ultimately

we can say what we like, as long as we know that we are making a par-

tially arbitrary linguistic decision rather than a statement of fact21. But to

invoke conventions and arbitrary linguistic decisions in dealing with a

fuzzy concept such as understanding would be to take a firm meta-philo-

sophical stand, based on an a priori ruling out of the rival view, according

to which philosophical questions related to the problem of vagueness

should be taken at face value22. Thus, it is better to resist the temptation

to dissolve the main question. Consider, rather, the imaginary scenarios

by adding some details. Imagine that we provide Peter and Stephen with

the standard explanation of the words occurring in (1). In particular, we

10 Paolo Tripodi

19 See Schroeder (2009, 88-9).

20 See Marconi (1997, 56) and Williamson (2007, 97-8).21 See Wittgenstein (1989, 23) and (1953, 16). See also Kennys (1984) crit-

icism of Chomsky (1980, 51) and Hymans (1991) discussion of blind-sight.

22 See Williamson (2007, ch. 2).


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describe the conceptual connections of the concepts every and . There

are two possible outcomes. On the one hand, suppose that we find that

they are already very much aware of our explanations, but they keep on

defending their eccentric doubts by obstinately arguing and arguing. Insuch a case, we would probably be inclined to consider them as fully

understanding (1) (despite their not accepting it). On the other hand, sup-

pose that they appear to be very little aware of our conceptual explana-

tions, but they keep on defending their eccentric doubts by obstinately

declaring that their explanation is the standard one. In such a case, we

would probably regard them as at least partially misunderstanding (1). In

other words, the more Peters and Stephens views resemble philosophical

theories (as in Williamson original cases), the less we are inclined to con-sider their eccentricities in terms of semantic deviance; the less their

views resemble philosophical theories, the more we are inclined to con-

sider their explanations as descriptions of their semantic competence, and

to interpret their eccentricities in terms of semantic deviance. Thus the

imaginary cases of Peter and Stephen as laymen ultimately depend on the

imaginary cases of Peter and Stephen as theoretical thinkers23. Therefore,

if my main objection is right, both kinds of imaginary cases implicitly

rest on the question-begging assumption that philosophy is not a sort of

connective analysis (but rather a sort of substantial theory).

This is not to say, however, that the Wittgensteinian legacy is vindi-

cated. In fact, in my view Williamsons argument against LTep does prove

something, namely, the following conditional thesis T1.

(T1)Ifphilosophy is not merely descriptive (but it is rather a sort of substan-tial explanatory theory), then the notion of epistemological analyticity isempty.

Williamson establishes such a thesis by argument, for he shows that

for the most elementary case of an analytic sentence (and, in fact, for any

analytic sentence whatsoever), one can build up a counterexample, in

which an imaginary metaphysician perfectly understands that sentence

but, based on theoretical grounds, he doesnt accept it.

However, here I am not able to evaluate neither whether the prescrip-

tive part of Williamsons book provides a compelling argument for the

thesis that philosophy should be explanatory and substantial, nor whetherWittgensteins idea that philosophy in the end can only describe the actual


23 It seems to me that Williamson agrees on this point (see 2007, 99).


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use of language (1953, 124), while it must do away with all explana-

tion (1953, 109) (otherwise it becomes conceptually misleading), iswell-grounded or is nothing but a dogma. Perhaps everything relies on

two rival conceptions of necessity24

. But this is a different, perhaps evenmore fundamental, issue25.

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Vienna Station, Cambridge, Cambridge University Press.Chomsky, N. (1980), Rules and Representations, New York, Columbia

University Press, Oxford, Blackwell.

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Glock, H-J. (2002), Clarity is not Enough, in R. Haller and K. Puhl (eds.),Wittgenstein and the Future of Philosophy. Vienna, Hlder-Pichler-Tempsky, pp. 81-98.

(2010) From armchair to reality?,Ratio (new series) 33, 339-48.Hacker, P.M.S. (2001) On Strawsons rehabilitation of metaphysics, in

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12 Paolo Tripodi

24 On this see Marconi (2010).25 An early version of this note was presented to the workshop The nature of

philosophy. On Timothy Williamsons The Philosophy of Philosophy at

the University of Parma in November 2010: I wish to thank Andrea Bianchi,Richard Davies, Pasquale Frascolla, Marco Santambrogio and DanieleSgaravatti for their comments on that version. Thanks also to GiulianoTorrengo for his remarks on a later version of this note. My special gratitudegoes to Diego Marconi for many insightful discussions and comments.


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Schroeder, S. (2009), Analytic Truths and Grammatical Propositions. In H.-J. Glock and J. Hyman (eds.), Wittgenstein and Analytic Philosophy.Essays for P.M.S. Hacker, Oxford, Oxford University Press.

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Universit di Torino

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Peter Stephen and ... Ludwig - 2011