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 Tractatus Author(s): Charles B. Daniels and John Davison Source: Noûs, Vol. 7, No. 3 (Sep., 1973), pp. 233-247 Published 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 PM All use subject to JSTOR Terms and Conditions
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7/22/2019 Ontology and Method in Wittgenstein's Tractatus.pdf
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
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-
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
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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
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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
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