7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 1/16
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
Stable URL: http://www.jstor.org/stable/2214349 .
Accessed: 25/10/2013 16:51
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact [email protected].
.
Wiley is collaborating with JSTOR to digitize, preserve and extend access to Noûs.
http://www.jstor.org
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 2/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 3/16
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...',
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 4/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 5/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 6/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 7/16
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...'.
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 8/16
ONTOLOGY AND METHOD IN WITTGENSTEIN S TRACTATUS 239
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 9/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 10/16
ONTOLOGY AND METHOD IN WITTGENSTEIN 'S TRACTATUS 241
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;
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 11/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 12/16
ONTOLOGY AND METHOD IN WITTGENSTEIN 'S TRACTATUS 243
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 13/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 14/16
ONTOLOGY AND METHOD IN WITTGENSTEIN S TRACTATUS 245
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 15/16
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
This content downloaded from 200.21.217.136 on Fri, 25 Oct 2013 16:51:53 PMAll use subject to JSTOR Terms and Conditions
7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
http://slidepdf.com/reader/full/ontology-and-method-in-wittgensteins-tractatuspdf 16/16
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