weiss, 2012 - naming and simplicity (draft)

8/12/2019 Weiss, 2012 - Naming and Simplicity (Draft)

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Naming and simplicity

Max Weiss

March 16, 2012

1 Introduction

As is well-known, Wittgenstein holds in the Tractatus that a propositional signis a fact. More specifically, such a sign is the fact that its elements stand in acertain relation to each other. Among the propositional signs are ordinary sentences,whose elements are words we bring into determinate relations by writing or speech.However, in a special kind of case, the elements of the propositional sign will allstand for objects; in this case the proposition is said to be completely analyzed.The names of the Tractatusare the elements of completely analyzed propositions.A name, therefore, stands for an object.1

It is also well-known of the same book that Wittgenstein there holds that objectsare simple.2 We find here much less explanation. But it may be inferred that anobject consists of no further objects, and requires of no further objects that theybe arranged in this or that way.

From these two doctrines follows a third: that only what is simple can be named.Such a view seems to be difficult to accept. For it appears to be an ordinaryphenomenon of human language, not to mention a major convenience, that somethings are named that have parts: nations and artifacts, molecules and organisms.Wittgenstein holds of such things that either we cannot name them, or they do not

consist of parts. I will refer to this view as the problem of the complex.Wittgenstein claims in the preface of his book to have found the solution to

the problems of philosophy. It would be disappointing if this were not intended toimply that theTractatuscontains the solution to any further problems it introduces:hence, in particular, a solution to the problem I just mentioned. Here Wittgensteinis widely held to have borrowed heavily from the theory of definite descriptions thatwas propounded by Bertrand Russell in 1905. Accordingly, although the words ofsentences appear to correspond to complex objects, these words are not really names

but covertly complex descriptions that break apart on analysis. The centrepiece ofsuch readings is a widespread treatment of 3.24. In what follows I will try to showthat this treatment of 3.24 is mistaken. The heart of my argument is a detailedconsideration of a pair of passages in the 1914-1916 Notebooksin which Wittgensteinstruggles with the problem of the complex for himself, almost two years after hewrote in a letter to Russell, your theory of descriptions seems to me to be quitecertainly correct.3

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A central aim of my reading of 3.24 is to show how this passage articulates theconception of analysis in theTractatus. I hold that the so-called Context Principleis essential to the development of this conception.4 My aim is to show that 3.24and related passages culminate Wittgensteins struggle to reach a point of view fromwhich ordinary language, while obscuring the forms of thought that we express by

its means, is nonetheless perfectly in order as it is.

2 Background

Before beginning the constructive interpretation let me summarize the reading of3.24 that I mentioned in introduction, and present some objections to it. Thebackground to this reading is the shift from 1903 to 1905 in Russells interpretationof so-called denoting phrases such as the queen of England, the king of France

or the difference between AandB. According to the Russell of 1903, what sucha phrase contributes to a proposition, or what it indicates, should be distinguishedfrom what the phrase eventually stands for, or denotes. The phrase indicates adenoting complex, which is a structured entity built up out of the meanings of themeaningful constituent words of the phrase. Thus, for example, the indication ofthe queen of England contains the queening relation, and the country of England,combined together under some kind of a form that befits the logical behaviour ofdenoting complex as a term. On the other hand, if there is exactly one person who

bears the queening relation to England, then this person is said to be the denotationof the indicated complex, and therefore also the denotation of the phrase itself. Now,a proposition like that expressed by the queen of England is lonely will consistof the indication of the phrase the queen of England together with the propertyof being lonely. If in fact the complex has a denotation, then there is an associatedproposition whose constituents are that person and the property of being lonely;the truth of this correlated proposition explains the truth of the proposition thatcontained the original denoting complex. In 1905, Russell rejects this view, onthe grounds that there is no proposition to the effect that the denoting complexhas a property itself, since in trying to construct one we always fall through tothe underlying denotation.5 Since Russell identified true propositions with facts,it followed that denoting complexes would not have properties at all, a disastrousconsequence. So, as is well known, Russell renounces this view in On Denoting,deciding instead that a complex noun phrase has no meaning in isolation butcontributes systematically to the meaning of the sentences in which it occurs.

So much for alleged the background to passage 3.24 of the Tractatus, whereWittgenstein writes:

A proposition about a complex stands in an internal relation to a propo-sition about its constituents.

The complex can only be given by its description, which will be right orwrong. A proposition that mentions a complex will not be nonsensical,if the complex does not exist, but simply false.

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When a propositional element signifies a complex, this can be seen froman indeterminateness in the propositions in which it occurs. In suchcases weknowthat the proposition leaves something undetermined. (Infact the generality-sign contains a prototype.)6

According to the reading I contest, Wittgenstein here follows the Russell of 1905 ina rebuff of the Russell of 1903. Thus Black and Ricketts:

[Wittgenstein] is following Russells theory of description, according towhich any statement about the King of France is counted as false if theking of France does not exist.7

Wittgenstein embraces Russells theory of descriptions to analyze awayappearances of explicitly or implicitly complex names.8

Similarly, on Harts reading, if a proposition apparently mentions a complex, then itcontains a definite description, which must be analyzed away following the approachof Russell in 1905.9

The three authors extend their 1905-Russellian account toward an interpretationof the indeterminacy that Wittgenstein attributes to propositions that mentiona complex. In the Tractatus, the paragraph 3.24c that mentions this indeterminacyfollows the statement of 3.24b that propositions about nonexistent complexes arefalse. So, these commentators trace the indeterminacy of propositions that mentiona complex to their behaviour under negation. Since a proposition that mentions acomplex must do so by description, its negation has the form F( x)(Gx). But forthe negated proposition there is not just one but rather two ways in which it canhold. It may be true because the ( x)(Gx) is improper, and it may be true becausethe denotation does not satisfyF. The truth of the negation is therefore essentiallydisjunctive, and for this reason the negated proposition is indeterminate. Sincea proposition cannot be determinate unless its negation is determinate as well, itfollows that there would be an indeterminacy in any proposition that mentions acomplex.

Let me conclude the section by recording some prima facieobjections to thisreading. None of the objections is decisive, but together they demonstrate the needfor another approach.

(1) The reading reduces the relevant notion of indeterminacy to a feature of arbi-trary conjunctions. So it founders on the absence of any mention of indeter-minacy in the setting of a general discussion of truth-functions. Rather, thenotion of indeterminacy appears in the context of discussions of generality.10

(2) Wittgenstein says that the analyzing proposition will be about the constituentsof what the analyzed proposition is about. However, before a Russellian anal-ysis, a statement involving the queen of England would be about the queen,and afterwards it would be about queening and England. I do not know ofany fears recorded by Wittgenstein that the nation of England might be eatenby its regent.11

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(3) The reading attributes to Wittgenstein a fairly technical point about a logicalproperty of the Russellian analysis. For this reason, the interpretation doesnot lend proper voicing to the remark we know that this proposition doesnot leave everything determined. The we of the passage should not beunderstood as we who analyze with Russell but rather as we who understand

the unanalyzed.(4) The reading does not square itself to the hard problem of 3.24, namely the

parenthesized comment that concludes it: the sign for generality [Allgemein-heitsbezeichnung] already contains a prototype.12

My impression is that the Black-Hart-Ricketts reading gathers most of its plausi-bility from the fact that in the Tractatus, the mention in 3.24c of indeterminacyimmediately follows 3.24bs mention of falsehood of propositions about complexes.

Wittgensteins notebooks contain ancestors of these two paragraphs at 15.5.15 and21.6.15 respectively. In other words, the ancestors are separated by more than amonth, and, as well see, the context of the ancestor of 3.24c indicates an entirelydifferent understanding of indeterminacy in which generality plays the central role.My impression is that the suggestion of an explanatory link between 3.24b and 3.24cis purely an accident of Wittgensteins cut-and-paste method of composition.13

3 A 1915 puzzle

TheNotebookscontain two sustained discussions of the issue, separated by a coupleof weeks. The first one starts to creep in around 25.4.15, and then breaks off at1.6.15; the second resumes at 14.6.15 and continues until W ran out of space at22.6.15. The discussions circle around what appears to Wittgenstein as a kind ofparadox: he seems to be constantly reawakening himself to each of the forces thathold it in place, trying as he changes register to detect any shift in their balance.

The central refrain is the investigators acknowledgment of what he calls a feel-

ing that he can give a name to seemingly ordinary objects. He mentions for examplethe feeling that he can name his watch (15.6.15), a knife or a letter (19.5.15), a copyof a book (23.5.15), even the landscape around him or the motes in the air (30.5.15).This kind of feeling, he remarks, is completely natural, so there must be some truthin it. He also considers related cases to dismiss them as logical contrivances, forexample: that he can name an object together with its motion, as with the-moon-orbiting-the-earth orbits the sun, or again, perhaps, as with quotation of tunes orsentences (19.5.15). But, although such marginal cases can perhaps be explained

away as tricks of language, Wittgenstein finds himself bound by the authority of afeeling that certain kinds of everyday thing can be named. The question thereforearises how this acknowledgment could ever seem to constrain us.

The counterpoint to the central refrain is Wittgensteins insistence that every-day objects are complex. Thus, he asserts that what is complex must include hisaforementioned watch (7.5.15, 15.6.15, 22.6.15), a copy of a book (23.5.15), also forexample a pencil-stroke and a steamship (25.4.15). For Wittgenstein it would seem

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that such objects inherit their complexity from the complexity of what is spatiallyextended (7.5.15, 13.5.15, 24.5.15, 14.6.15, 17.6.15, 18.6.15, 19.6.15) or of what ismassive (22.5.15, 20.6.15).14 Thus, at the heart of Wittgensteins problem is aconjunction:

(i) that an ordinary thing can be named, but

(ii) that ordinary things are complex.

To my ear, the rhetorical structure of the NBpassages suggests that the conjunctsstem from grounds that are firm but disparate, so that they could meet to strike uswith their transparent consequence: that sometimes, what can be named is complex.The two NB passages that interrogate the notion of the complex are bookendedsquarely by explicit formulations of this datum (25.4.15 and 30.5.15; 14.6.15 and22.6.15; cf. also the precursor to 3.24 at 13.5.15). Its because the datum presentsa problem that Wittgenstein resolves it into its component vectors (i) and (ii) andrestates them repeatedly, like someone in disbelief that he has hands.

The conjunction of (i) and (ii) presents a problem for Wittgenstein for thefollowing reason: he takes up his investigation of the complex from the point ofview

(iii) that what can be named is simple.

Taking for granted that nothing simple is complex, between the principles (i-iii)there is an immediate contradiction. The pressure he acknowledges explicitly:When I say x has reference do I have the feeling: it is impossible that x shouldstand for, say, this knife or this letter? Not at all. On the contrary (19.5.15; cf.also 6.5.15 and 15.5.15). It is probably fair to say that the principle (iii) is notself-evident; nor is it a truism like (i) or a metaphysical banality like (ii). How washe driven against them? I want first to try to understand the genesis of Wittgen-steins attachment to (iii); Ill then turn to the question whether in NBwe find aresolution of the problem of the conjunction of (iii) with (i) and (ii).

4 Genesis of (iii)

It is natural to suppose that the doctrine of the simplicity of the nameable descendsin a straightforward way from Wittgensteins Russellian heritage. Most obviously,inPrincipia, Russell uses the device of contextual definition to reduce Freges broad,mathematically acculturated notion of a function to his idiosyncratic notion of a

propositional function. In this way, he excises the category of syntactically complexterms from his foundations for mathematics. However, the developments of ODtranspose the site of ontological commitment from the conditions of sense to theconditions of truth; before OD we could not perhaps acknowledge the sense of thedifference between Brookline and Brooklyn is large without admitting somethingindicated by the difference between Brookline and Brooklyn at least into the do-main of being; afterward we must still accept the existence of some such entity as

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the difference between Brookline and Brooklyn if we maintain, as seems reasonable,that they differ greatly. Moreover, according to Russell, we must then think thatthe propositional function (xis large) is true of that entity; taking the entity to bea, then this amounts to acceptance of truth of a proposition a. But I have justgiven an explanation that proceeds by assigning a name to the difference between

Brookline and Brooklyn. Such an entity would be a prime case of a complex; andto the explanation given there does not seem to be any clear alternative. So, infact OD very nearly requires the naming of complexes. Furthermore, later devel-opments in Russells philosophy maintain some role for the notion of a complex,most saliently in the explanation of truth that subserves the multiple relation the-ory of judgment.15,16 It seems to me implausible that the Russell of the multiplerelation theory would deny that a complex could have properties, that it could beconstituent of truths, and also that it could be named. So, the doctrine of thesimplicity of what can be named seems rather inimical to Russells own thinking.

Perhaps, however, this conclusion should be qualified by considerations of Rus-sellian acquaintance. Russell decides in 1905 that to give a complete analysis ofa proposition is to reveal its composition from items with each of which were ac-quainted already. He also maintains that the use of a name contributes its beareras constituent of the proposition expressed. From these two theses it follows thatwe must be acquainted with the bearer of a name whose use we understand; thisconclusion is if anything only reinforced in the shift to the multiple relation theory.But now the simplicity of the nameable would follow from the further premise that

only what is simple can be an object of acquaintance. In Wittgenstein, however, thissuggestion is quickly scotched: even though we have no acquaintance with simpleobjects we do know complex objects by acquaintance, we know by acquaintancethat they are complex (24.5.15).

It would run beyond the scope of this paper17 to develop a full account of theorigin of the doctrine in early Wittgenstein that only what is simple can be named.However, I take it to be at least coeval with the theory of propositions as pictures.Certainly, the doctrine is not an obvious consequence of that theory. For example,

when we arrange blocks on a table to represent a configuration of cars, it seemsunreasonable to object that the blocks do not have carburetors.

Wittgenstein seems to hold from very early on that a representation of complex-ity is a representation that things are a certain way. Hence, the representation ofcomplexity involves agreement or disagreement with the way that things are. Nowthe picture theory, as applied to atomic representations, interprets this agreementor disagreement as a commonality of form between the representation and the stateof affairs represented. But then, a representation of complexity must share the form

of the state of affairs it represents. In practice, representations appear to fall shortof this rather dramatically. They do not perfectly mirror the complexity of thesituation; they are somehow incompletely articulated. However, their sense lives offof the possibility that their complexity be spelled out in full. They are propositionsonly by courtesy of the promise of their complete articulation.

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5 The turning point

The first surviving sustained discussion of complexes breaks off after 31.5.15 for twoweeks foray into the nature of the a prioriand the tautology. Abruptly Wittgen-stein resumes with an announcement:

We have become clear. . . that names may and do stand for the mostvarious forms, and that it is only the syntactical application that sig-nalises [charakterisiert] the form that is to be presented. Now what isthe syntactical application of names of simple objects? (14.6.15)

The face of theNotebooksthus evinces a feeling of progress on Wittgensteins partbut why? There is no obvious connection of the 1-14 June discussion to the issue ofcomplexes: in those two weeks of entries, the words Komplex, Gegenstand, and

Name occur a total of zero times. On the other hand, the last two weeks or soof May find him circling obsessively around the contradiction of theses (i-iii). Butthen the entry of 30.5.15 famously begins: words are like the film on deep water.Wittgenstein continues:

It is clear that it comes to the same thing to ask what a sentence is, andto ask what a fact isor a complex.

And why should we not say: There are complexes; one can use namesto name them, or propositions to portray them?

The name of a complex functions in the proposition like the name of anobject that I only know by description.The proposition that depictsit functions as a description.

But if there are simple objects, is it correct to call both the signs forthem and those other signs names?

Or is name so to speak a logical concept?

[. . . ] (30.5.15)

This passage contains the seed for the resolution of the problem in its concludingsentence. Here Wittgenstein decides that name is a logical notion, a characteriza-tion of expressions that depends on their syntactical employment. For convenience,I shall refer to this result as the discovery.18 It is evident from the texts thatWittgenstein does not take his discovery to afford any immediate resolution of hisproblem: here we can see only that Wittgenstein alights on a program for under-standing what a name is. At just this point he breaks off his discussion in apparent

confidence that the framework is set for the problem to unwind itself.Wittgenstein resumes the discussion two weeks later by continuing to press his

doubts against the thesis that complexes cannot be named. Indeed, the mid-Junerecapitulation shows that Wittgenstein takes the moral of his discovery to be thatwe need to attend to syntactical application in order to distinguish various names asstanding for various formsnot just for simples but for other forms as well, i.e., alsofor complexes. Even the last sentence of the notebook reads: the name compresses

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its whole complex reference into one. So even in the throes of the discovery, hewrites that the components are to the complex as a plan of a town is to a mapof a country. He seems initially to find that the discovery if anything bolsters thecase that complexes can be named. For it appears that names of complexes satisfyeverything the discovery leads him to require of names of simples (14.6.15).

That the discovery nonetheless reconfigures his perspective can be seen by com-paring the earlier remark: we have acquaintance with complexes. We know byacquaintance that they are complex (24.5.15). For although at 30.5.15, he seemsto advance a weaker claim that determining the form of the signified object requiresappeal to syntactical application of a name, Wittgenstein resumes the topic withthe seemingly strengthened formulation: it is only the syntactical application thatsignalises the form.19 However, the strengthening here is only apparent: in bothcases, what Wittgenstein is saying is that to discover the form of the object signi-fied, we cannot consider only the sign by itself, but must consider the applicationtoo.20 In neither case does there arise any question of, as it were, summoning upthe object signified for personal inspection; rather, this is just what Wittgensteinintends to exclude. Thus, in return for an escape route from his antinomy, Wittgen-stein trades away any independent, properly epistemic purchase on the notion ofcomplexity. The concept of a name becomes a logical concept, and the question ofthe form of the object signified by a name reduces to that of syntactical application.It is no surprise to find him on the heels of his discovery to be wondering: but whatabout the denotation [Bedeutung] of names out of the context of the proposition?

(14.6.15).

6 Unpacking the discovery

Let me summarize where we are. We found Wittgenstein to be struggling with anantinomy: that ordinary objects can be named, and ordinary objects are complex,but nothing complex can be named. Then he discovers a principle for resolution:

that the syntactical application of a name determines entirely the form of theobject signified.

To understand the principle, we need to understand the relevant notions of syn-tactical application and of form. Now, I think it is clear that Wittgenstein takesthe form of what is signified at least to decide the question of whether what issignified is simple or complex. Moreover, it seems even that further formal varietydetermines the details of internal composition of what is signified. Thus, for ex-

ample: When I say this watch is shiny, and what I mean [meine

] by this watchalters its composition in the smallest particular, then this means not merely thatthe sense of the sentence alters in its content, but also what I am saying about thiswatch straightaway alters in its sense. The whole form of the proposition alters(16.6.15). By what I mean by this watch Wittgenstein means his watch: thuswhat he is saying is that as its internal changes occurperhaps, even, for example,as the hands sweepso the sense of what he says changes too, for the form of the

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watch characterizes what he says. Simplicity, then, is a kind of limiting case. Justas the form determines any structure there is, so it determines no structure.21

The other term of the discovery is the notion of syntactical application; here I canmake out two passages to indicate sources of its character. At 17.6.15, Wittgensteinrepeats that the complexity of the object signified by a name characterizes the sense

of a proposition expressed by means of that name. But, a proposition is not fullyarticulated until it reflects its sense in such a way that the parts of the sense standapart form each other in the expression. Hence, in a proposition whose sense ischaracterized by reference to a complex object, the constituents of that objectmust find themselves expressed apart from each other as discernible segments ofthe proposition itself. Thus, the demand for simple things is the demand fordefiniteness of sense (18.6.15).

Wittgenstein now raises an objection: he thinks he cannot rule out a priorithat the complexity of ordinary objects be infinite. Then, it would seem, not onlydoes ordinary language elide by biological exigency what in real sharpness we woulddistinguish: rather, nothing adequate to an object could be said by us in principle.But then the definiteness of sense could not be underpinned by appeal to full artic-ulations mere possibility. So he writes: does not this possible infinite complexityof the sense impair its definiteness?

Wittgenstein takes the syntactical application of a name to include the logicalrelationships to other propositions that are borne by propositions containing thename. Thus, for example: perhaps we assert of a patch in our visual field that it is

to the right of a line, and we assume that every patch in our visual field is infinitelycomplex. Then if we say that a point in that patch is to the right of the line, thisproposition follows from the previous one, and if there are infinitely many points inthe patch then infinitely many propositions of different content follow logicallyfrom that first one (18.6.15e). Wittgenstein summons here an idea he recordednine months earlier as

(a).(b).aRb= Def[aRb]

at 5.9.14. This is evidently a symbolic anticipation of the slogan a proposition

about a complex can be analyzed into statements about its constituents and astatement that describes the complex completely (2.0201). Thus, the discoveryleads Wittgenstein to redeploy this idea from a new angle. Previously, one in-spected the internal constitution and reported the results as an analysis, therebydiscovering an instance of the consequence relation. But now instead, the conse-quence relation discloses the analysis, and only thereby do we make out complexityin the objects. One might thus even say: what articulates the proposition is not itsinternal structure but its position in the system of logical relationships.

Wittgenstein now transposes his objection to the new framework. He takes thelogical conception of definiteness to require that the syntactical application of thesign be decided in advance, so that it must in particular be decided already foreach consequence of the given proposition that it is indeed a consequence. Forexample, there would be no sense to the investigators saying that his watch is inthe drawer unless it had been decided already that from this it followed that somewheel of the watch was in the drawer too. But of course, perhaps he had not the

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least knowledge that the wheel was in the watch; so how could he have meantby this watch the complex in which the wheel occurs (18.6.15i)? How could aproposition treat of infinitely many points without being infinitely complex? Inthe next section, I will argue that the allusion to prototypes of 3.24 summarizesWittgensteins response to this objection.

I promised to state a second mentioned source of syntactical character. Following22.6.15i, lets suppose thatA is a rod andB is a ball. We can straightforwardly findreasoning that treats A and B interchangeably: for example, from the hypothesisthat everything massive is spatially extended, we may conclude of each ofAandBthat it is extended if massive. However, Wittgenstein claims that it is only A that weintelligibly describe as leaning against a wall. Here, Wittgenstein remarks, theinternal nature ofA and B comes into view. By internal nature Wittgensteinmeans internal complexity. Thus, an apparent irregularity of logical type is like atelltale seam that unmasks the simplicity ofAandB as merely constructed.22 Todiscover the internal complexity of meaning we must attend not only to networksof implication but also to what has been called logical grammar.23

7 Generality and the prototype

Wittgenstein ties the determinacy of sense to the possibility of full articulation. But,since he cannot fix any a prioribound on the complexity of meaning, therefore he

cannot yet presuppose that full articulation would be possible even in principle.Though, following the discovery, he traces the complexity of meaning to the syntac-tical application of signs, this by itself promises no solution. The discovery simplyrotates the problem by ninety degrees, recasting the subtleties of truth-making assubtleties of inference.24 The underlying predicament is familiar. A speaker mayutter a proposition yet be unable to distinguish exhaustively the cases in which theproposition is true from those in which it is false. Indeed, if syntactical applicationof the sign were supposed to reside in the power of the speakers discernment, thenthe discovery would threaten to undermine the determinacy of sense.

I think there are two issues here to be untangled. First, there is a threat ofin-principle impossibility of full articulation, which would imply that the notion ofdeterminacy of sense, as construed by the picture theory, is outright incoherent.Second, there appears to remain a mystery how through syntactical applicationthe determinacy of sense could be secured. It is to address the first issue thatWittgenstein invokes the notion of generality:

When we see that our visual field is complex we also see that it consists

ofsimpler parts.We can talk of functions of this and that kind without having any par-ticular application in view.

For we dont have any examples before our minds when we use F x andall the other variable form-signs. (19.6.15a-c)

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All invisible point-masses, etc., must come under the generality notation.(21.6.15f)

In very broad contours, the idea is this. Nobody can run through the totality ofdistinct situations which are sufficient for a watch to be on the table.25 So instead,Wittgenstein proposes, the relevant features of such situations must be projected bymeans of a variable into a single surveyable formula. A formula subsumes such vari-ety by means of an abstraction embodied in the prototype. For example, by meansof a prototype we can represent that a region w overlaps with the interval (0, 1) onthe real line in the following way. Suppose that the relation Pos(x, y) holds betweenxand y iffy is a point in the regionx. Such propositions as Pos(w, .5), Pos(w,/4),etc., express disjoint classes of possible situations in which w overlaps with (0, 1).By applying the N-operator26 of the Tractatusto a prototypical representation ofall those propositions, one obtains a proposition

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would be even more preposterous to try to ground the forms of meaning in actuallinguistic precedents, for those are finite. In the Notebooks, Wittgenstein wantsto turn such skeptical challenges aside. Nothing we can say would exclude everypossible misunderstanding. But this is not the relevant standard. The speakerspowers to anticipate legalistically every such challenge will at some point give out.

Then we fall back on the determinacy of sense.It is clear that I knowwhat I meanby the vague proposition. But nowsomeone else doesnt understand and says: Yes, but if you mean thatthen you should have added such and such; and now someone else againwill not understand it and will demand that the proposition should begiven in more detail still. I shall then reply: Now thatcan be taken forgranted. (22.6.15d)

8 Conclusion

In the previous section I argued that the indeterminacy of ordinary propositionsstems from the pervasiveness of prototypical representation. This interpretationreceives support from a comparison of 3.24c with its ancestor passage.

That a name signifies a complex object is seen from an indeterminacy inthe proposition in which it occurs, which results from the generality of

such propositions. We know that by this proposition not everything isyet determined. The sign for generality containsa prototype. (21.6.15)

That a propositional element signifies a complex can be seen from anindeterminacy in the proposition in which it occurs. We know thatby this proposition not everything is yet determined. (The sign forgenerality containsa prototype.) (3.24)

Another change in the passage reveals the resolution of the antinomy that vexed

Wittgenstein in the May and June of 1915. The name of the Notebooksgives wayto the propositional element of the Tractatus. At this point it might be wonderedwhether this isnt just a verbal dodge. If it is impossible to correlate a name witha thing, doesnt this also exclude the correlation of propositional elements? Thisresponse underestimates the force of the discovery that the forms of meaning ofsigns are determined by syntactical application. One can surely correlate a soundwith a speck of dust, by emitting the sound in the presence of the speck. Butaccording to the discovery, such a correlation confers no meaning. The investigator

of theNotebooks

felt, in mid-May, that he could assign a name to a thing. Thediscovery strips this feeling of its logical authority.Granted that an ordinary propositional sign is not a concatenation of names,

on the grounds of the indeterminacy that everybody detects, it must be noted thatthe sign is still a concatenation, not of names, but of propositional elements. Andwhat are these? As Wittgenstein asked: does the logic ofPMapply to our propo-sitions just as they are? As he struggles with this problem in the Notebooks, he

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Notes1This paragraph summarizes 3.14, 3.2, and 3.201, 3.202.22.02.3Reprinted at p.57 of Cambridge letters, ed. Brian McGuinness (Blackwell, 2008). McGuiness

dates the letter to November-December of 1913.4Here, my interpretation builds on work of Michael Kremer in Contextualism and holism in

early Wittgenstein (Philosophical Topics 25(2), 1997). Although I do not argue the point directly,I take my conclusions to testify in several ways to the suggestion of Goldfarb (WittgensteinsUnderstanding of Frege, in E. Reck, ed., From Frege to Wittgenstein, Oxford UP, 2002) thatby starting from a Russellian framework and thinking through the problems of logic for himself,Wittgenstein reaches some affinities with Frege.

5On Denoting, 485ff., in Mind, New Series 14(56), 1905. Cf. On Fundamentals, esp. 380ffin the Collected Papers of Bertrand Russell, vol. 4.

6This is the translation of Pears and McGuinness (Routledge, 1963). Pears-McGuinness doesnot align well with Anscombes translation of the Notebooks 1914-1916 (Blackwell, 1961).

7Max Black, A Companion to Wittgensteins Tractatus, p.112 (Cambridge, 1964).8

Wittgenstein against Frege and Russell, p.237n20, in Reck. Cf. also Pictures, logic, and thelimits of sense, p.85n41, in The Cambridge Companion to Wittgenstein (Cambridge UP, 1996),where Ricketts signals deference to Harts paper on on the issue. Although I disagree with Rickettshere, it should be noted that his writings played a big role in shaping my conception of how tothink about early analytic philosophy.

9The whole sense of the Tractatus, p.279ff, in the Journal of Philosophy 68(9), 1971. Hartalso maintains the converse view, that a proposition contains a definite description only if itmentions a complex. In my opinion, the converse is not quite so wild an attribution as one mightbe led to suppose by comparison with, for example, 2.02331. But in any case, it is not essentialto Harts reconstruction of the argument for the existence of simples, nor to the line of criticism I

pursue here.10For another instance of the linking of generality with indeterminacy, see Philosophical Remarkspp.275-276 (ed. Rush Rhees, Blackwell, 1975). The distinction of generality from truth-operationis sharp in the Tractatus; cf. 5.521.

11In other words, Russells analysis is directed toward ordinary extrinsic descriptions, which donot specify their object by articulating its internal structure. It seems more likely that Wittgensteinhas in mind instead the problem of phrases like the difference between A and B, the deathof Caesar and so on. Russell in 1905 attempts to treat these intrinsic descriptions uniformlywith the extrinsic ones. But this attempt does not even pretend to eliminate statements aboutcomplexes; it rather presupposes them. I pursue this line in section 4.

12I want to show how the parenthetical comment is the decisive one, but for now let me just

observe that it is not parenthesized in the antecedent paragraph 3.210106 of the Prototractatus.Black (ibid.) mentions as a second-line account of indeterminacy the idea that generality isalways indeterminate, but he does not spell out why this should be, nor why we should feel it.

13In the Prototractatus the two paragraphs have antecedents at 3.20105 and 3.20106.14This metaphysical banality is not the sort of thing one naturally seeks out in Wittgenstein.

I confess to struggling for weeks to read my way around these passages, but they stand up forthemselves.

15Cf. Kremer (ibid.), p.95, makes this point in Contextualism and holism in the early Wittgen-stein.

16Although the text is not so clear on this point as is, for example, the Grundgesetze, it is

natural to interpret truth-functions in PMas predicates that attribute properties or relations topropositions, and to take Russell at his word when he says that p q says ofp and q that oneimplies the other. Moreover, in Theory of Knowledge(Allen and Unwin, 1984), Russell considersvarious examples of properties of complexes: for example, as expressed by A precedes in thecomplex (111) or A and B and similarity form a complex of the same for as (113).

17Or: of this version of this paper.18I would like also to avoid for the time being the very complicated issues involving the re-

lationship of Wittgensteins discovery to the so-called context principle that is attributed to

14


15/15

DRAF

T

Frege.19Cf. also 16.6.15: the syntactical employment of the names completely characterizes the form

of the complex objects which they denote.20See 18.6.15: not the propositional sign by itself, but it together with its syntactical applica-

tion.21I dont know of any passage here where Wittgenstein mentions formal variety among the

simples themselves, as we might understand Freges distinction between function and object. Butcf. 16.6.15: Relations and properties, etc. are objects too.

22Wittgenstein gives another example that falls amusingly flat in translation: The watch issittingon the table is senseless!

23This passage raises further questions I cannot deal with here. How does it align with thediscussion in Tof related themes? E.g., Green is green, the good is more or less identical thanthe beautiful and all that. Note, furthermore, that in the final analysis, if two expressions can eachsensibly occur in some context, then every context in which the one sensibly occurs is a contextin which the other does too. This feature cannot be broken by composition of expressions withthe featureeven if we include something like -abstraction to allow certain kinds of contextualdefinition. So, an analysis of the ordinary expressions may need to posit some kind of ambiguity.

I think there is constant tension here with the impulse of 3.3442.24To be precise, the rotation is 90 counterclockwise, according to Per Martin-Lof (Truth of a

proposition, evidence of a judgment, validity of a proof, Synthese73 (1987), p. 411).25As Russell puts it: practically, if we were to attempt it, Death would cut short our laudable

endeavour. . . (PoM, p.70).26Supposing Xis a class of propositions, then NX is equivalent to a conjunction of all negations

of elements ofX.

weiss, 2012 - naming and simplicity (draft)

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