...but look here, Doctor, I’ll have to give you a comparison if I am to make myself clear. Women and poets seem to reason mostly by comparisons. So imagine a spider... D’Alembert: Who’s that? Is that you Mademoiselle...? 1
Paul Samuelson chose as an epigraph to his 1947 book Foundations of Economic Analysis the physicist Gibb’s assertion that
Mathematics is a Language.
Read on its own, a question arises as to why this claim is in itself at all relevant to the foundations of economic analysis. It is clear that if it is to be answered, however precursorily or tentatively, the sentence cannot be detached from the work to which it serves as an epigraph. One possible attachment, and hence one possible reading, is to see it as a trope for the word foundations in the title of Samuelson’s [End Page 759] book. Lloyd Metzler’s 1948 reading is along this line. In his review, he observes that “the book...is a study of the foundations of economic method, [and] that it is the author’s [well demonstrated] contention that all of the various branches of economic analysis are unified by a small number of basic principles.” It is these principles that constitute the foundations of economic analysis, and they can be “best and most conveniently” expressed, not necessarily in the language of mathematics, a language among others, but rather in mathematics itself. It is because of these basic principles that the Foundations “is by no means a book on methodology in the customary sense [and] contains a much higher proportion of substantive economics than traditional books dealing with economic method.”
In his own re-reading, five years later, 2 of Gibb’s assertion, Samuelson explicitly poses the question as to “the conditions under which one choice of language is more convenient than another?” This is done in a section titled Differences in Convenience of Languages, and this short section of four paragraphs is the core of what is Samuelson’s most linguistically-conscious article. 3 In it, he raises the question of the indeterminacy of translation; 4 of the intrinsic convenience of a language for one purpose rather than for another; 5 of the identification of particular cultures with particular methods for tackling problems; of the sterility of a methodology that focusses on the essence of economic concepts; 6 and of the neutrality of mathematics with respect to this methodology. 7 Indeed, Samuelson’s “only” objection to his epigraph is to its length he would have reduced it by “twenty five percent” to the statement that
Mathematics is Language.
[End Page 760] “Now I mean this entirely literally,” he writes, and it is clear that he means exactly what he says. Even though the strengthened claim, when first presented, is somewhat qualified, 8 the suspicion that he may be intending the claim to be made only in the context of economic theory is decisively put to rest.
For in deepest logic and leaving out all tactical and pedagogical questions the two media are strictly identical. I simply cannot admit, [without recanting] the logical identity of words and symbols,...that a rigorous literary proof of Euler’s theorem is in principle impossible. 9
This strengthened claim is introduced in a section titled The Strict Equivalence of Mathematical Symbols and Literary Words; and the statement therein that “Geometry is a branch of mathematics in exactly the same sense that mathematics is a branch of language” is presumably to be interpreted in the sense of Mandelbroit’s fractals whereby any part has all the characteristics of the whole. 10 Indeed, Samuelson also poses the question of the affinity between methods of literary criticism and mathematics when he wonders “why a man... should be so enamored of literary theory and stop short of diagrams and symbols.”
Thus, Samuelson’s epigraph, by emphasizing that the foundations of economic analysis can be presented both in and as mathematics, gives face to these foundations. It is not the only way of giving face but the most efficient, not only in terms of “arriving at” them, as even Marshall had conceded, but...