sion either includes everything, or at least has as many terms as if it included everything...

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Ludzie pragną czasami się rozstawać, żeby móc tęsknić, czekać i cieszyć się z powrotem.

And a collection has as
many terms as if it included everything, when there is a rela-
tion which every possible term, without exception, has to
one and only one term of the given collection, provided
that to every term of the given collection some term has
the given relation”. (cit. in [3]: 359).
From the quotations we see that, apart from its declared agnosti-
cism, Russell hesitated between two possible ways of explication of the
concept of the logical constant in terms of the proof theory and in
terms of semantics or ontology. In fact, almost all further investigations
on the subject concentrated on the two mentioned approaches.
Carnap
The notion of logical constant and the criteria of logicality con-
stituted an unsolved problem in Carnap's main works where he tried to
explicate the concept of analyticity. The division between analytical and non-analytical sentences, in the strict, explicated sense of these terms, presupposes the division between logical and extra logical constants. In
his The Logical Syntax of Language ([4]), he adopts a pure syntactical
criterion. As logical constants, or rather logical expressions, he reck-
oned numerical constants, numerical variables, individual variables, sentential connectives, parenthesis, and some operation symbols. In his Introduction to Semantics ([5]), he admitted that his previous criterion
was inadequate and the proper criterion should be a semantical one. In
fact Carnap was sceptical on the existence of an adequate criterion for
logicality of symbols. The idea of logicality was unclear and supported
by the rather vague intuition that logical symbols were meaningless and
they had no meaning independent of the context. Moreover, some signs
seemed “more logical” than others. In Meaning and Necessity, Carnap
writes:
T ARSKI ON LOGICAL ENTITIES
135
“Only (declarative) sentences have a (designative) meaning
in the strictest sense, a meaning of the highest degree of in-
dependence. All other expressions derive what meaning they
have from the way in which they contribute to the meaning
of the sentences they occur. One might perhaps distinguish -
in a vague way - different degrees of independence of this
derivative meaning. Thus, for instance, I should attribute a
very low degree to '(', somewhat more independence to '∨',
still more to '+' (...). And where to make the cut between
expressions with no or little independence of meaning
('syncategorematic' in traditional terminology) and those
with a high degree of independence, to be taken as designa-
tors, seem more or less matter of convention.” ([6]: 7).
Presented intuition cannot be treated as an adequate criterion of
logicality. Earlier, in Introduction to Semantics, Carnap claimed that though the division of expressions into logical and extra logical
(descriptive) can be established in a particular language, there are no
general criteria of logicality of constants:
“So far we have discussed the distinction between logical and
descriptive expressions only in a form in which it appears
when we have to do with a particular semantical system, in
other words, as a question of special semantics. The problem
is more difficult in the form it takes in general semantics.
Here it is the question whether and how 'logical' and 'descrip-
tive' can be defined on the basis of the other semantical
terms, e.g. 'designation' and 'true', so that the application of
the general definition to any particular system will lead to a
result which is in accordance with the intended distinction.
The satisfactory solution is not yet known.” ([5]: 59).
Reichenbach
In his approach to natural language, Reichenbach used the standard
functor-argument technique of formal logic, very far from the syntax of
natural language. Nevertheless, his results were not trivial. For Reichen-
bach the problem of the criteria of logicality of expressions in natural
language is even more important than in formal logic, where it is solved
arbitrarily.
His analysis of natural language, (cf. [25]) starts with a criticism
of traditional grammar. In Reichenbach's opinion, the right division of
136
LUIS VILLEGAS-FORERO, JANUSZ MACIASZEK
parts speech should be the following: argument terms, functional terms,