Ontology and Method in Wittgenstein's Tractatus.pdf

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Ontology and Method in Wittgenstein's TractatusAuthor(s): Charles B. Daniels and John DavisonSource: Noûs, Vol. 7, No. 3 (Sep., 1973), pp. 233-247Published by: Wiley

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Ontology and Method in Wittgenstein'sTractatus

CHARLES B. DANIELS AND JOHN DAVISON

UNIVERSITY OF VICTORIA

We shall in the following put forward an interpretation ofWittgenstein's Tractarian views concerning ontology and method.

On certain points, however, our interpretation becomes more an

exercise in educated guessing in that we can find no textual

authority for what we say; but we nonetheless believe that it is

reasonable to suppose that someone with Wittgenstein's views

might have come down on the side of these issues that we have.

Where we can find textual support for one of our points, or where

one of our points can be seen to explicate a somewhat dark passage

in the text, we indicate this by placing the number of the passagein parentheses after the point.1

I. Introduction

Wittgenstein's Tractatus Logico-Philosophicus is primarily an

essay in ontology in the classical tradition. It is also an unstinting

advocacy of a certain ontological method, namely, that of showing

the fundamental categories of being through a language that

mirrors the world. And, more remarkably, it is written in full

consciousness that what it says is incompatible with its ontologyand methodology.

For the Tractarian Wittgenstein, there are two fundamental

ontological categories, the category of objects and the category of

facts. These categories of being are radically disjoint. No object

can be a fact, no fact an object (2.01, 2.02). It is in his unstinting

insistence on the disjointedness of his two categories of being that

Wittgenstein differs so much from most other ontologists.

There is, in the pursuit of ontology, a manifest tendency to

make use of an arsenal of quite special ontological predicates-forinstance, 'being an object', 'being a property', 'being a set', 'being a

member of', 'being a fact', etc. But it is seldom discussed why

233








234 NOUS

these predicates are singled out, rather than, say, 'being a witch' or

'being a brother of'. In doing ontology this way, the philosopher has

already almost certainly been tempted part way down the path to

ontological commitment. He countenances individuals, i.e., things

that can be referred to, and furthermore seems to want to imply

that this is a category of being under which everything falls, an

ultimate ontological genus. Moreover, he may tend to believe that

these predicates represent properties, i.e., things that can be attrib-

uted. Here, then, is a further ontological move. A decision on the

question of whether everything that can be referred to can be

attributed represents yet another ontological step. This step is

usually made with a negative answer, but the answer is rarely

supported with much of a reason. Does 'is a member of' represent

anything real ? If so, our philosopher believes in relations too.

Wittgenstein's ontological undertaking is radically different.

His two categories of being are truly disjoint. One can talk about,

refer to, name objects; one can picture, describe, state facts. One

cannot picture, describe, or state objects, and one cannot talk about,

refer to, or name facts (3.221, 3.144). Wittgenstein is deadly serious

here-to the point of realizing, indeed admitting that much of his

own book is an attempt to do what on his own view cannot be done.

For Wittgenstein, there is no ultimate genus that collects both

facts and objects into it (4.1241).

Very often in ordinary conversation we seem to be doing what

Wittgenstein holds we cannot do. We seem to be referring to facts

and stating objects. 'The fact that John is an invalid won't make

things any easier', we hear people say. Don't these people seem

to be referring to facts ? And at times people will even make some

such statement as 'Ludwig Wittgenstein' (when they have, for

instance, been told to state who wrote the Tractatus Logico-

Philosophicus). To someone this might sound like stating an object.

But the locutions of ordinary language are not always the best

touchstones to the true nature of reality (3.323, 4.002). Substantives

that state objects (or facts) are just as misleading as substantives

that refer to facts.

This is why Wittgenstein takes such an interest in a perspicu-

ous language. The propositions of a perspicuous language are

constructed so as to display the ontological structure of the world.

In a truly perspicuous language, it will be impossible to form a

sentence that gives rise to the sort of misleading impressions that

we are led to by the constructions of ordinary languages, where

substantive phrases such as 'the fact that...', 'the property of...',








ONTOLOGY AND METHOD IN WITTGENSTEIN 'S TRACTATUS 235

etc., give the impression that facts and properties are individuals

that can be talked about (3.325). In a perspicuous language, the

categories of being will be displayed in its structure, will show

through its syntax (4.04, 4.121). But it also turns out, given the

Tractarian ontology, that a book like the Tractatus cannot be

written in such a language, because in the Tractatus Wittgenstein

talks about the relation between language and the world , i.e.,

treats assertions and facts as objects that could be referred to and

stand in relations.

Yet if we had a perspicuous language, on the other hand, a

book like the Tractatus would be unnecessary, since no false

impressions due to grammar would give rise to mistakes in ontology.

And it is here that much of the basis of Wittgenstein's mysticism

lies. We can easily understand why Wittgenstein says 'My propo-

sitions serve as elucidations in the following way: anyone who

understands me eventually recognizes them as nonsensical, when he

has used them- as steps-to climb up beyond them' (6.54)

II. Objects

In a perspicuous representation of a thought, each object is

referred to by one and only one name (3.2, 5.53). If a perspicuous

language is to mirror reality, each object in reality must have a

counterpart, a name, in the language. If some object fails to have

a linguistic counterpart, we can't say anything about it (4.0311,

4.0312). If some object has more than one linguistic counterpart,

the language is poetic, in a somewhat poetic sense: The question

then arises, given a thought, as to how one will put it into words

(3.3411). We have our eye on words and have to make a choice

between different ways of saying the same thing. The poet thriveson the possibilities that alternate modes of expressing the same

thing bring. But a perspicuous language is not constructed for

poetry. Rather it is constructed in such a way as to allow reality to be

described completely in the simplest possible terms, with the least

redundancy. And one-name-one-object provides one part of the

minimum necessary.

An atomic fact is a combination of objects (2.01). So in a

perspicuous language, the true atomic proposition that states it

will contain one name for each of these objects.Since an atomic fact is a combination of objects, we can

conclude that there must be at least two objects in an atomic fact.

So in a perspicuous language, an atomic proposition cannot be








236 NOUS

composed of just one name. One way to guarantee this is to holdthat objects are of different types or forms: an atomic propositionwill be at least a pair of names 'ab' such that 'a' is drawn from oneset of names (the names of one type of object) and 'b' from anotherdisjoint set of names (the names of another type of object) (2.0233,

2.021 and 2.025, 4.122). Then 'aa' cannot turn up in an atomicproposition of a perspicuous language and be exhaustive of thenames in the proposition.

2.0131 and 2.0251 suggest the following model. An atomicproposition is a string composed of at least seven names 'abcdefg':'a' being the name of a moment in time; 'b', 'c', and 'd' being

names of indices on the X, Y, and Z dimensions of space, respec-tively; and 'e', 'f', and 'g' being names of a hue, a brilliance, and a

saturation (of color), respectively. The visual world is here re-

presented as seven dimensional, the dimensions (forms) being thoseof time, space, and color. The model fails owing to Wittgenstein'sdemand for the independence of atomic facts (2.062). If it is a factthat a certain spatial point has a certain hue at a certain time, wecan infer that it is not a fact that it has another hue at that time

(6.3751).

If a model like this is adopted, however one that does satisfythe independence requirement it is easy to give a classical seman-tics for it. Say the world is seven dimensional. The set of possibleatomic facts is the set of seventuples, S, i.e., A x B x C x D xE x F x G, such that A is the set of indices of one dimension,B another, etc. A possible world, W, is a subset (perhaps empty)of S. Where 'abcdefg' is a sentence of a perspicuous language and

?a is what 'a' designates, Obwhat 'b' designates, etc., 'abcdefg'is truein W if and only if <Oa, 0b' 0c, Od) 0e' of, Og> E W. But Wittgenstein

would not countenance this sort of semantics at least if '<Oa, Ob,

0c, Od, ?e, Oj Og>' is taken as representing a fact because in itreference is made to a fact, i.e., to what makes a proposition trueor false.

Objects, whatever they are, are simple, not complex. Whatis complex might fall apart, be destroyed, not exist. But the dual

possibilities of existence-non-existence, combination-non-combi-

nation, integration-segregation, linkage-severance, concatenation-

non-concatenation pertain to the dual possibilities in propositions:

truth and falsehood. Objects are what contribute, through theirnames, to the stability of a proposition irrespective of the vagariesof truth-value. Objects furnish and, indeed, are meanings (3.203).

This forms the basis of one of Wittgenstein's complaints








ONTOLOGY AND METHOD IN WITTGENSTEIN S TRACTATUS 237

about Frege. For Frege, a proposition has a different meaning2

when it is true than when it is false (3.143). To know what it means,

we have to know its truth-value. For Wittgenstein, propositions

picture, they don't name or designate at all. Wittgenstein objects to

Russell on similar grounds: that 'Fu' serves both as a name and as a

proposition (3.333).

What is attractive in the seven dimensional model presented

above is that moments, points in space, and, say, redness aren't

things one finds it easy to imagine destroyed-unlike chairs.

Redness is timeless (as well as colorless), just as this moment is

timeless (as well as colorless) (2.0232). The modern (or perhaps

Meinongian) view of construing the denotata of names as possibilia

rather than as the more fragile existentialia is more in line with

the view of the Tractatus. There are also some hints that items

like space-time points, masses, and the properties of whatever

particles or items physicists discuss might be the ultimate objects

(6.341-6.343). But it is not an ontologist's job to point objects

out; it is to show their categorial status and what contribution

they make to reality by showing the form of a proposition in a

perspicuous language (6.342).

III. Properties

For Wittgenstein, properties are analyzable and hence do not

form a separate category of being. Strictly speaking, it is the

material or external properties that are analyzable. But for

Wittgenstein, formal, essential, or internal properties are not

properties at all (4.126). Rather, they pertain to the form of the

world and show through the propositions of a perspicuous language.

They cannot be represented by particular symbols in it (4.122-4.1274).

How, then, is the reduction of properties accomplished? Let

us suppose that the world has three dimensions, A, B, and C, and

that we have a perspicuous language in which the name of an object

in the A dimension is an indexed 'a', the name of an object in the

B dimension is an indexed 'b', and the name of an object in the

C dimension is an indexed 'c'. An atomic proposition, then, is of

the form '...aibjck...'. We can get a propositional form by substi-

tuting a variable for one of the names in an atomic proposition,e.g., '...a5b1x...'. Such a propositional form represents a material

property (2.0231, 3.31-3.315). Wittgenstein will abbreviate this

to 'fx', where 'f' indicates what remains constant when various








238 NOUS

appropriate names are plugged into the 'x' place. We might say,

then, that C4 and C7share the same property, , when 'fc4' and 'fc7'

are both true. But such talk of properties is just afafon de parler.But there is no need to start out with an atomic proposition.

One can construct propositional forms from molecular propositions,

e.g., '...a5b1c8... & ... a3b9c4...' might become '...a5b1x... & ... yzw...'.

The latter would represent a four-term relation. It might be

abbreviated 'g(x,y,z,w)'.

Under the dimensional interpretation, not just any name can

be substituted for any variable in a propositional form, in view of

the fact that each dimension must be represented in what results,

if correct syntax is to be preserved. So we would do well to use adifferent disjoint set of variables for each different dimension of

the world.

It is easy to see, on this account of what properties are, that

two different objects might have all their properties in common.

Suppose that for all propositional forms of one variable 'x' where

'x' ranges over the objects of the A dimension, it turned out that

any such propositional form became a true proposition when 'a1'

was substituted for 'x' if and only if it became a true proposition

when 'a2' was substituted for 'x'. The objects designated by 'a1'and 'a2' would then share all their (material) properties.

The objects designated by 'a1' and 'a2' don't differ in material

properties at all. But they are different. They have different names

in a perspicuous language. We can see why Wittgenstein might

say

If two objects have the same logical form, the only distinctionbetween them, apartfrom their external properties, s that they are

different.Either a thing has properties that nothing else has, in which

case we can immediatelyuse a description o distinguish it from the

others and refer to it; or, on the other hand,thereareseveralthingsthat have the whole set of their properties n common, in which case

it is quite impossible to indicate one of them.For if there is nothing to distinguishathing,I cannotdistinguish

it, since if I do it will be distinguished after all. (2.0233-2.02331.)

In the middle sentence, we read Wittgenstein as meaning

'...there are several things that have the whole set of their propertiesin common, in which case it is quite impossible to indicate one of

them by a property in which it differsfrom the others. For if there is

no such property, I cannot distinguish it by such a property...'.









The reader is forewarned that 'y a1' does not represent a

property. There is no propositional form with two variables that

we can abbreviate to 'g(x,y)',where

'g' behaves likea

representativeof the identity relation . Indeed, for Wittgenstein, identity is not

a relation (4.241-4.243, 5.5301-5.534).

IV. Facts

Just as each different object is mirrored in a perspicuous

language by one and only one name, so each possible fact finds its

representative in one and only one proposition (5.512-5.5151).

The artificial languages to be found in logic textbooks are

not perspicuous languages. They are poetic, in that they provide

many ways of saying the same thing, e.g., 'p', 'p & p', 'p',

'p V (q & q)', etc. The addition of ' ' to 'p' is not to be

construed as an addition of some element of meaning. '', '&',

'V', etc., are not names (4.0312). Logical objects are not objects

(4.41).

A proposition is a concatenation of names, but it is not a mere

concatenation of names like a list (3.141). That is why we have

been careful to represent atomic propositions as'...aibick...'.

The

dots show that something is missing, namely, what turns a mere

concatenation of names into a proposition of a perspicuous lan-

guage.

Wittgenstein's notation is ambiguous in a crucial respect.3

He uses the letters 'p', 'q', and 'r' to indicate propositions (4.24).

He also describes the matrix:

'p q

T T T

F T T

T F

F F T

as a propositional sign (4.442). One is led to believe that by taking

off the quotation marks, one gets a proposition or at least a propo-

sitional form. Yet what do the 'p' and 'q' in this propositional sign

indicate ? Propositions ? In short, is 'p' a propositional sign, or is,

say,

3








240 NOUS

P

T T

F

a propositional sign ?

We take it to be the latter. Indeed, this notation gives a clue as

to how to construct a perspicuous language. If

_

T T

F F

is written in the alternate way that Wittgenstein suggests in 4.442,

with a slight modification, i.e., as '(TF)((TF)(p))'-where the

'(TF)' immediately before the '(p)' represent the truth-possibilities

which are represented below the 'p' in the matrix, and the '(TF)'

in the initial segment represent, respectively, agreement and

disagreement with these truth-possibilities-we can see that thereare only four different propositions we can write this way, i.e.,

(TT)((TF)(p))

(TF)((TF)(p))

(FT)((TF)(p))

(FF)((TF)(p))

This is a start toward a perspicuous language, because all we

have is four propositions concerning three possible, and one notso possible, facts. There is no redundancy. And if the world is,

say, three dimensional, and we substitute 'alb5c4' for 'p', we get,

in '(TF)((TF)(a1b5c4))', a candidate for an atomic proposition. In

the more common notations of logic texts, this would be repre-

sented in many ways, as 'p', 'p Vp', 'p &p', -' p', etc.

But when we consider other atomic propositions, we see that

a bit of poetry still lingers in our language, for '(TFTF)((TFTF)(p),

(TTFF)(q))' says precisely the same thing as '(TF)((TF)(p))'. To

drive out this last vestige of redundancy, let us begin by assumingthat there is a finite number of objects and give each a name of

its own. Then there will be a finite number, n, of permissible

concatenations of these names, lists in which the name of one and









only one object of any single dimension appears and in which all

dimensions are represented. Let 'p1', 'P2', ...,'

go short for these

lists. Then the general form of a proposition is:

(X1X2 .. X2n)((TFTF ..Tfl(pl)~ (TTFF-.FF)(PO) ... X(TTT

...FF)(Pn))~

where Xi is a T or an F, and there are 2n T's and/or F's imme-

diately preceding each pi.When the initial string of T's and F's exactly matches one of

the strings that immediately precedes a pi, we have an atomic

proposition; when it fails to do so, we have a molecular proposition.

221 is the number of propositions. There is only one true propo-sition in which one and only one T appears in the initial string.

That proposition can be called 'the world proposition'.4 It is a true

proposition from which all true propositions and only true propo-

sitions follow. In this sense it represents the world-all that is the

case (1).

In a perspicuous language, one can see immediately when one

proposition follows from a set of propositions. If whenever all the

propositions in the set have a T in their initial strings, a particular

proposition has a T in its initial string, then that propositionfollows from the set (5.11). There is only one tautology, namely

the proposition in which the initial string is composed only of T's.

This proposition is true no matter what circumstances obtain. It is

also easy to see why Wittgenstein says, 'If all objects are given,

then at the same time all possible states of affairs are also given'

(2.0124). In the general form of a proposition, all objects are indeed

given, i.e., all permissible lists of their names appear; and all

possible ways of agreeing or disagreeing with the truth-possibilities

show clearly.The case in which there are denumerably infinitely many

objects is also straightforward. We begin by giving each object its

own name. Let us assume that there are finitely many forms of

objects; so there will be denumerably infinitely many permissible

concatenations of names. Let 'p1', 'P2', ..., go short for these lists.

Then the general form of a proposition is:

( -XlX2 ... )((--AAlA2... )(p1))(--A2A1.)P2,@

The '--' represents the real line from zero to one inclusive.To each point on the line immediately preceding each pi is assigned

1 or 0, whichever is the ith term in the binary decimal expansion

associated with that point. '.0000...' is associated with zero;








242 NOUS

'.1111...' is associated with one. In other cases where two decimal

expansions are associated with a point, we do the following: the

decimal expansion with a finite number of 1's is associated with the

point. The remaining decimal expansions, those without a finite

number of l's, are ordered alphabetically and become A1, A2,.

The series, A'A'..., is such that A' is the ith member of Ak.

Finally, with respect to the initial '(--X1X2...)', a 1 or a 0 is

arbitrarily associated with each point on the line and each Xi.Instead of associating a 1 or a 0 with each point on the line and

each Xi, we might think of each point on the line as being either

black or red and eachXi

a black or red dot. The world proposition

would be the one true proposition in which only one black point

appeared in the initial section of the proposition.

Wittgenstein's own rendering of the general form of a propo-

sition, i.e., [fi, , N(e)] (6), is unclear. In line with what he says

in 5.2522, p is the first member of a series, 6 is an arbitrarily

selected nth member, and N(e) is the (n + I)st member. The bar

over a variable indicates that it is representative of all its values

(5.501). Hence, 'p' represents all elementary propositions (4.24).

'N' represents the operation of joint denial.

But on this interpretation, '[i, 6, N(6)]' fails to represent all

propositions. Suppose that there are just two permissible con-

catenations of names, represented by 'p' and 'q'. Then we have

the two elementary propositions:

(TFTF)((TFTF)(p),(TTFF)(q))

(TTFF)((TFTF)(p),(TTFF)(q)).

So 'p' will represent these two propositions, and these will be the

first member of our series. Applying the operation of joint denial tothese gives us:

(FFFT)((TFTF)(p),(TTFF)(q)).

If we now take this proposition to be the second member of the

series, a third application of the operation will produce:

(TTTF)((TFTF)(p),(TTFF)(q)).

It is obvious that from here on out the series will switch back and

forth between the last two propositions, and not all propositions

will be generated.

If, on the other hand, we take the second member of the series

to be all the propositions produced together with all the propositions









of earlier members, i.e., the first three listed above, the second

application will yield:

(FFFF)((TFTF)(p),(TTFF)(q)),

and further applications of joint denial will get us nothing new.

The one interpretation that does seem to succeed is this:

Contrary to what Wittgenstein says, we treat 'p' as representing

the power set (less the null set) of the set of elementary propositions.

The first application of the operation of joint denial will be to

each member of f, producing:

(FTFT)((TFTF)(p),(TTFF)(q))(FFTT)((TFTF)(p),(TTFF)(q))

(FFFT)((TFTF)(p),(TTFF)(q)).

Yet we cannot consider the second member of the series to be just

the power set of the set of these three propositions, otherwise all

propositions will not be forthcoming. Rather, the second member

of the series must be considered to be the power set of the set

of all propositions that appear thus far. Each member of the series

'carries along' all propositions formed previous to it. But when[p, 5, N(6)] is interpreted this way, it does serve as the general

form of a proposition.

V. Generality

Joint denial is not meant in the Tractatus to be an operation

that is limited to taking a finite set of propositions into a propo-

sition. In 5.502 Wittgenstein writes 'So instead of (-----T)

( .,....) [the finite joint denial], I write N(6) .' This form of

words permits two interpretations. It might be taken as a stipu-lation, a definition; and that is the way it is often read. But what

Wittgenstein wants to say, we believe, is that for his purposes the

operation that takes a finite set of propositions, denies them, and

conjoins them into one proposition, i.e., the operation he symbolizes

'(--T)(.)', is not sufficient; one needs a stronger operation,

the operation he symbolizes 'N(E)', i.e., infinite joint denial. On

reading 5.502, the emphasis must be laid heavily on the word

'instead', as in 'So instead of cornstarch, I use waterchestnut flour'.

Otherwise, how is one to interpret what Wittgenstein says twopages later in 5.52 and 5.521, 'If e has as its values all the values of a

functionfx for all values of x, then N(j) = -- (3x).fx. I dissociate

the concept all from truth-functions. Frege and Russell introduced








244 NOUS

generality in association with logical product or logical sum. This

made it difficult to understand the propositions (3x).fx and

(x).fx , in which both ideas are embedded.'?

It is also worthwhile noting that the introduction of the

generality sign in this way signals a move to poetry, for with it

we say in a different way something that already could be said

without it in a perspicuous notation. As Wittgenstein says, 'What is

peculiar to the generality-sign is first, that it indicates a logical

prototype [by the variable], and secondly, that it gives prominence

to constants [by the predicate-sign].' (5.522)

If, for instance, there are two permissible concatenations of

names 'ab, and 'ab2', then we have the following definitions:

'(FFFT)((TFTF)(abl),(TTFF)(ab2))' df '(3x)(ax)'

'(FTFT)((TFTF)(abl),(TTFF)(ab2))' df '(3Ix)(xbl)'.

It should also by now be clear that the question, 'But is that all

the facts ?', is meaningless under a Wittgensteinian ontology. There

is no such property as beingafact (4.1272), and facts are not among

the items that can be captured by the individual quantifier.

VI. Logic and Mathematics

In the perspicuous language developed earlier, the truth-values

of two propositions were visible from the symbols alone: the

proposition in which the initial section contained all T's and the

proposition in which it contained all F's. The first showed itself to

be true whatever the circumstances, the second false whatever the

circumstances. These can be said to be the two propositions of

logic. In the other propositions it was clear, because both T's and

F's appeared in their initial sections, that both truth and falsehoodwere possibilities. But the two propositions lack content in this

sense. Wittgenstein thinks of them as limiting cases, not being

full-blown truths and falsehoods (4.46-4.4661).

Logic also deals with implication and other relations . We

use scare-quotes here because for Wittgenstein there are no

relations between facts, and consequently these will not be re-

presented in a perspicuous notation. He also calls these logical

relations operations (5.131, 5.2-5.2341) or rules (5.512). Logic,

in the sense in which it deals with implication, joint denial, etc.,is not dealing with anything real (5.4-5.44).

An operation or rule is, for Wittgenstein, the generability of

one proposition from one or more propositions (5.25). As we have









seen, in a perspicuous language what implies is what shows forth

perfectly clearly. More generally, in such a language the similaritiesand differences between propositions is on the surface; what isgenerable from a given proposition is already clear in the propo-sition itself (5.442). A perspicuous language needs no primitivelogical signs apart from the general form of a proposition (5.45-5.451). In the general form of a proposition, everything is givenat once (5.515-5.5151).

For Wittgenstein, an operation or rule is what from one ormore propositions singles out a proposition, perhaps a different one.Operations give rise to series when a proper base of one or morepropositions is given. As we have seen, however, there is no needto have operation signs in a language, indeed certainly not in aperspicuous language.

Let 'n' go short for a proposition in a perspicuous language.Let us consider an operation that gives rise to the series [n, 6, j].

Now let us indulge ourselves in poetry by framing a definition,n =df 'O(n)'. Our series begins to take on a more interesting look:

[n, e, 0(f)], or at least our notation does. Yet we can say nothingabout reality that we couldn't say before.

Numbers, says Wittgenstein, are exponents of operations(6.021). We shall not find signs for numbers in a perspicuouslanguage. One reason for this is, of course, that we shall not findsigns for operations in a perspicuous language.

Because operations take propositions into propositions, thereseems to be no limit to their applications; and it is these applicationsthat have number. Hence there are no privileged numbers (5.453).

Equations in a language signal poetry-for '=' is the signfor creating a poetic language, at least as Wittgenstein uses it

(4.241-4.243, 5.534). 'a = b' says nothing whatsoever about theworld. Just as there are no logical objects referred to by operationsigns, so there are no mathematical objects referred to bynumerals. Indeed, even if one does decide to write operation signsinto a language, one can still omit exponent signs (and thusnumerals) by writing all the operations out in full.

Much of what so exercises Wittgenstein in his later writingscan be seen to originate in difficulties that he finds in his Tractarianviews concerning logic and mathematics. For example, in the

propositions of a perspicuous language, everything is said to be onthe surface, given at once. In fact, however, many of the internalrelations among these propositions are not all that clear. It issimply not immediately obvious that joint denial does serve to








246 NOUS

generate all propositions from the set of elementary propositions-even in the case in which there are assumed to be but two elemen-

tary propositions. This takes showing, some sort of proof. And here

we come face to face with some difficulties already:

(1) What is shown in cases like this does not have the form of aproposition in a perspicuous language; yet it does have content,for otherwise it would be obvious enough not to need proof. Nor

does it seem to be translatable into any proposition in a perspicuouslanguage, not, that is, without losing its content. In this sense,

operation signs are like token reflexives, for the content introducedinto propositions by token reflexives does not seem to be easily

translatable away either.5 What is this thing that is proved when it

is proved that joint denial does serve to generate all propositionsout of the set of elementary propositions ? Is it a proposition ? Inhis later writings, Wittgenstein toys with a number of answers to

this question. It is a command. It is a rule. It is a construction

without application. It is like a position in a game.

(2) We prove that certain propositions have certain formal

properties by appealing to other formal properties . In the case

above, we start with the set of elementary propositions. Being

elementary is a formal property that some propositions have and

others do not. Suppose that to someone it isn't obvious that

(TFTF)((TFTF)(p),(TTFF)(q)) is an elementary proposition, just

as it is not obvious to us that joint denial does serve to generate all

propositions from the set of elementary propositions. He'll require

proof. Is the notion of proof an epistemological one ?Is a proof just a

way of convincing someone who can't see it ? If not, why do we

prove things ? If proofs are just there for the discovering, what istheir ontological status ? (Where are they for the discovering ?)

We believe that difficulties like these led Wittgenstein to giveup the perspicuous language methodology and adopt instead the

view that no language mirrors reality better or worse than any

other. It is still language that gives philosophers problems, that

misleads them, but what will put them straight again is not a

translation into a different, more perspicuous language, but a

broader and clearer view of the original language itself. In a sense,all languages are perspicuous when seen clearly against the back-

ground of the various uses to which they are put. The problem is

less one of seeing through a disguise than it is of seeing all the sides.It is less a job for a magnifying glass and more one of stepping far

enough back to see what a thing looks like. The new method is to

step back and get rid of the false impressions that too narrow a








PRAGMATICALLY NECESSARY STATEMENTS 247

view gives. With the adoption of this new method, the importance

of ontology for Wittgenstein lessens. All philosophical problems,

not merely ontological ones, are amenable to the new kind of

linguistic cure.

NOTES

The quotations herein are taken from the Pears and McGuinness translationof the Tractatus.

2 We here use 'meaning' in Wittgenstein's sense, not in Frege's.3This ambiguity has been noticed also by Roger Dexter.

4We adopt this phrase from Nino Cocchiarella, in whose ontology a similar'world proposition' plays a role.

5 With respect to token reflexives, see Hector-Neri Castafieda, Indicators

and Quasi-Indicators , American Philosophical Quarterly (1967), and Charles B.

Daniels, Reference and Singular Referring Terms , J7ournal of PhilosophicalLogic 1 (1972).

Pragmatically Necessary Statements

GRAHAM NERLICH

UNIVERSITY OF SYDNEY

A robust idea of necessary statements has been nurtured in

many traditions in philosophy. The distinction between necessary

and non-necessary statements favoured by classical empiricism isseveral shades more pallid than that favoured by classical ration-

alism. But both ideas count as strong since they agree at least in

this: the distinction is an absolute one, dividing statements

exhaustively into exclusive classes. Now, however, these classical

ideas of necessary statements have come upon lean times and are in

wide disfavour. True, W. V. Quine allows that some statements

are, at any rate, more necessary than others, thus giving the idea of

necessary statements a foot in the door. But this apparent opening

affords no real entry. It merely enables Quine to hold off the mainsubstance of the classical idea more effectively. Quine's distinc-

tion (it is intended as a hollow one) is pragmatic, for it makes a

statement more (or less) necessary if it is more (or less) useful in

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Ontology and Method in Wittgenstein's Tractatus.pdf