Tractatus Logico-Philosophicus | Page 5

The meanings of primitive signs can be explained by means of
elucidations. Elucidations are propositions that stood if the meanings of
those signs are already known.
3.3 Only propositions have sense; only in the nexus of a proposition
does a name have meaning.
3.31 I call any part of a proposition that characterizes its sense an
expression (or a symbol). (A proposition is itself an expression.)
Everything essential to their sense that propositions can have in
common with one another is an expression. An expression is the mark
of a form and a content.
3.311 An expression presupposes the forms of all the propositions in
which it can occur. It is the common characteristic mark of a class of
propositions.
3.312 It is therefore presented by means of the general form of the
propositions that it characterizes. In fact, in this form the expression

will be constant and everything else variable.
3.313 Thus an expression is presented by means of a variable whose
values are the propositions that contain the expression. (In the limiting
case the variable becomes a constant, the expression becomes a
proposition.) I call such a variable a 'propositional variable'.
3.314 An expression has meaning only in a proposition. All variables
can be construed as propositional variables. (Even variable names.)
3.315 If we turn a constituent of a proposition into a variable, there is a
class of propositions all of which are values of the resulting variable
proposition. In general, this class too will be dependent on the meaning
that our arbitrary conventions have given to parts of the original
proposition. But if all the signs in it that have arbitrarily determined
meanings are turned into variables, we shall still get a class of this kind.
This one, however, is not dependent on any convention, but solely on
the nature of the pro position. It corresponds to a logical form--a logical
prototype.
3.316 What values a propositional variable may take is something that
is stipulated. The stipulation of values is the variable.
3.317 To stipulate values for a propositional variable is to give the
propositions whose common characteristic the variable is. The
stipulation is a description of those propositions. The stipulation will
therefore be concerned only with symbols, not with their meaning. And
the only thing essential to the stipulation is that it is merely a
description of symbols and states nothing about what is signified. How
the description of the propositions is produced is not essential.
3.318 Like Frege and Russell I construe a proposition as a function of
the expressions contained in it.
3.32 A sign is what can be perceived of a symbol.
3.321 So one and the same sign (written or spoken, etc.) can be
common to two different symbols--in which case they will signify in

different ways.
3.322 Our use of the same sign to signify two different objects can
never indicate a common characteristic of the two, if we use it with two
different modes of signification. For the sign, of course, is arbitrary. So
we could choose two different signs instead, and then what would be
left in common on the signifying side?
3.323 In everyday language it very frequently happens that the same
word has different modes of signification--and so belongs to different
symbols-- or that two words that have different modes of signification
are employed in propositions in what is superficially the same way.
Thus the word 'is' figures as the copula, as a sign for identity, and as an
expression for existence; 'exist' figures as an intransitive verb like 'go',
and 'identical' as an adjective; we speak of something, but also of
something's happening. (In the proposition, 'Green is green'--where the
first word is the proper name of a person and the last an
adjective--these words do not merely have different meanings: they are
different symbols.)
3.324 In this way the most fundamental confusions are easily produced
(the whole of philosophy is full of them).
3.325 In order to avoid such errors we must make use of a
sign-language that excludes them by not using the same sign for
different symbols and by not using in a superficially similar way signs
that have different modes of signification: that is to say, a
sign-language that is governed by logical grammar--by logical syntax.
(The conceptual notation of Frege and Russell is such a language,
though, it is true, it fails to exclude all mistakes.)
3.326 In order to recognize a symbol by its sign we must observe how
it is used with a sense.
3.327 A sign does not determine a logical form unless it is taken
together with its logico-syntactical employment.
3.328 If a sign is useless, it is meaningless. That is the point of Occam's

maxim. (If everything behaves as if a sign had meaning, then it does
have meaning.)