These heterogeneous semantic statuses do not affect computation which, as a formal process,
operates independently of significations. In his Tractatus, Wittgenstein affirms in the same
vein that if we are to avoid the errors attached to polysemy, we require a language that comes fully
equipped with some sort of logical syntax (3.325, p.29); one condition, however: "In logical syntax the meaning of a sign should never play a rôle" (3.33, p.31).
(iii) The symbol and the linguistic sign
In principle, it is possible to manipulate logical symbols without taking their contents into
account. From a Saussurian point of view __ for Saussure the two sides of
the sign cannot be dissociated __ they are not signs, because their content is
dissociated from their expression; and all the more so because their content is not theirs proper (it
can call on another language or another plane of reality). Besides, Hjelmslev distinguishes between
symbolic systems and semiotic systems (1971a, p.142). Only the first systems
are defined by a term-to-term relationship between content and expression. More accurately, the
symbolic systems are monoplanar: they consist of a plane of expression, and their plane of content
is not configured by a system. As such, symbols are non-semiotic interpretable orders. Formal
languages are not semiotics, and post-Russellian logistics turns out to have been misguided in
generalizing their properties (1971a, p.142).
Let us briefly recall, even if it means returning to a semiotics
of the sign and factional issues for one moment, how linguistic signs differ from symbols:
a) The signifiers of linguistic signs have a twofold articulation, symbols do not. First-level
units (letters), as a matter of fact, are often used as logical symbols.1
b) Linguistic signs are neither constants nor variables.
c) Symbols are strictly counted as they are put in circulation. There are an indefinite number
of signs in a natural language.2
d) Symbols strictly come up with their signification through syntactic rules, whereas
linguistic signs do not abide by the compositionality principle. That is particularly clear at the level
of text. In other words, the relationship between symbol and computation is the same as between the
element and the whole; the relationship between the sign and the text is that of local to
e) Their meaning can vary indefinitely according to occurrence. The types of meaning, or
signification, and even their syntactic rules, differ according to the social practices in which they are
implemented. On the other hand, symbols keep the same reference, even if unknown, over the same
The signification of symbols is extrinsic to themselves. It is instituted from outside by their
interpretation within another symbolic field or within an ontology of sorts. On the other hand, the
meaning of signs is determined in a practice where they themselves play a part. And usage can
reconfigure it indefinitely.
All things considered, whereas symbols have only one signification, but no meaning, because
meaning is a contextual and textual phenomenon, signs do make sense, but their signification remains
a problematic construct (as the debates surrounding polysemy prove it).
f) Symbols are not subjected to diachrony, neither within a
same computational process (diachrony has nothing to do with the succession of an algorithm), nor
from one process to the next. Unlike linguistic signs, they have no history but that of their original
g) Linguistic signs are suitable for metalinguistic use, symbols are not.3 In other words, natural languages might experience hermeneutic
circularity, but not other languages.
h) Their hermeneutic modes differ, as much actually for the identification of their signifier
as for the identification of their signified.
1. One can also use second-level units, such as words, and
Lewis Carroll blithely does so in his Game of Logic. But then their use is actually
2. Symbols in a language are initially stipulated in a list. The
list of the words in a natural language is constantly overhauled, because it depends on variable
standards which allow us to create interpretable neologisms at any time. [RETURN]
3. More precisely, a formal language cannot, without
modification in its vocabulary or structure, be interpreted in terms of itself. [RETURN]