As the sign system whose grammar has determined the shape of Western culture’s techno-scientific discourse since its inception, mathematics is implicated, at a deeply linguistic level, in any form of distinctively intellectual activity; indeed, the norms and guidelines of the ‘rational’ valid argument, definitional clarity, coherent thought, lucid explication, unambiguous expression, logical transparency, objective reasoning are located in their most extreme, focused, and highly cultivated form in mathematics. The question this essay addresses what is the nature of mathematical language? should therefore be of interest to semioticians and philosophers as well as mathematicians. There are, however, certain difficulties. inherent in trying to address such disparate types of readers at the same time which it would he disingenuous not to acknowledge at the outset. Consider the mathematical reader. On the one hand it is no accident that Peirce, whose writings created the possibility of the present essay, was a mathematician: nor one that I have practiced as a mathematician; nor that Hilbert, Brouwer, and Frcge the authors of the accounts of mathematics I shall dispute were mathematicians. Mathematics is cognitively difficult, technical, abstract, and (for many) defeatingly impersonal: one needs, it seems, to have been inside the dressing room in order to make much sense of the play. On the other hand, one cannot stay too long there if the play is not to disappear inside its own performance. In this respect mathematicians confronted with the nature of their subject arc no different from anybody else. The language that textual critics, for example, use to talk about criticism will be permeatcd by precisely those features figures of ambiguity, polysemy, compression of meaning, subtlety and plurality of interpretation, rhetorical tropes, and so on which these critics value in the texts they study; likewise mathematicians will create and respond to just those discussions of mathematics that ape what attracts them to their subject matter. Where textual critics literize their rnetalanguage. mathematicians mathcmatize theirs. And since for mathematicians the principal activity is proving new theorems, what they will ask of
[1]
Justin Buchler.
The Philosophy of Peirce: Selected Writings
,
1941
.
[2]
P. Lorenzen.
Einführung in die operative Logik und Mathematik
,
1955
.
[3]
Umberto Eco,et al.
A theory of semiotics
,
1976,
Advances in semiotics.
[4]
Charles S. Peirce,et al.
The Philosophy of Peirce : Selected Writings
,
1941
.
[5]
H. Weyl,et al.
Philosophy of Mathematics and Natural Science
,
1950
.
[6]
L. Brouwer,et al.
HISTORICAL BACKGROUND, PRINCIPLES AND METHODS OF INTUITIONISM
,
1975
.