Edgeworth's Admissions as Conveyed by L. von Mises  
         As Professor Joseph T. Salerno and Dr. Chris R. Tame made clear in a   
recent post to this list (HES Digest, vol. 17, Issue 17), Ludwig von Mises   
may have been a  strong fan of  F.Y. Edgeworth's economic ideas but he was a   
tough-minded skeptic about his mathematical methods of analysis.   What I learned from
this post is that when Mises was invited to prepare (in 1925) a book review of
Edgeworth's 3-volume, Papers Relating to Political Economy (PRPE),  Mises hunted down and
captured two statements that Edgeworth made against the mathematical method. As we say in
the court room,"bingo !"
          Since Edgeworth made these two statements, Mises (who was trained   
as a lawyer) gave pride of place to what lawyers call "admissions against   
interest."  It is one thing when a sixth grade drop out makes fun of quantitative methods
in economics and another thing when the editor of the Economic Journal and the major
chairholder at Oxford University does the same!
         I wish to qualify what Mises claimed in two respects.  First, the   
same PRPE  contains other (different) quotations that Mises apparently passed   
over that presents a somewhat different picture of Edgeworth's regard for his   
methods of analysis.  Second, before we castigate von Mises for a hasty   
reading of the volumes placed before him for review, we must put part of the blame on
Edgeworth himself for camouflaging one of his most important discussions of the
mathematical method.
         My first point:  On on p. 274 of the second volume (which is   
actually p. 273 of my edition), Edgeworth admitted that mathematics is "not an   
indispensable adjunct to economic studies," which I take to mean that economic   
studies can survive without using mathematics.  I think that is what Mises   
interpreted Edgeworth as stating also.  This essay was written in 1889 and was   
related to Edgeworth's Presidential Address to Section F of the British   
Assocation. The opening abstract contained the actual quotation and may have been written
much later in 1925 when Edgeworth was rushing this collection to press but the point is,
Edgeworth did make that statement.
         Clearly, Mises is correct. Edgeworth admitted that mathematical   
reasoning is not absolutely necessary to make progress in economics.  But   
these volumes contain many other essays by Edgeworth other than this early one   
that Mises cited with what appears to be a hastily added abstract to the front.     
          Certainly, after 1892 when the "Seligman-Edgeworth" debate about   
the use of modeling assumptions in price theory took center stage, Edgeworth   
repeatedly pointed to his "taxation theorem" that was subsequently utilized by   
Hotelling and others (1932) and had a profound influence on modern demand theory   
as one of  his (Edgeworth's) crowning achievements in economics.  That   
theorem was discovered by the mathematical method and was not something that had   
been discovered in other ways (praxeological reasoning perhaps) and then   
subsequently retranslated into mathematical symbolism.  
         Edgeworth was both proud of having discovered that when   
demand curves in two markets are " highly correlated" a tax in one market could   
affect the final profit-maximizing price in BOTH markets. A totally startling   
result.  Edgeworth cited this result as a counter argument to Seligman's attitude toward
the use of calculus in economics [see my article: Moss, 2003. "The Seligman-Edgeworth
Debate About the Analysis of Tax Incidence: The Advent of Mathematical Economics, 1892-
1910" History of Political Economy (Summer) :
205-240.]   
         My second point:  Edgeworth can share some of the blame for Mises   
missing these and other quotations.  Mises focused mostly on the second volume   
of Edgeworth's collected papers.  In the first volume, there is an essay   
entitled "Professor Seligman on the Theory of Monopoly."  The significance of this essay
is not so much the price theoretical material (as important as that was) but what it
reveals about Edgeworth's attitudes towards the mathematical
method. Edgeworth reprinted his 1899 EJ article with some minor deletions in his   
PRPE.  What is most puzzling is that Edgeworth changed the title of that   
article in the PRPE.  In the EJ, the article is entitled  "Professor Seligman on the
Mathematical Method in Political Economy."   Edgeworth's retitling of that
article contributed toward Mises's missing it completely.  By removing the term   
"mathematical method" Edgeworth confused his readers as to what that article   
was really about.  In legal talk, it was the "proximate cause" of Mises's   
overlooking this discussion completely and skipping forward to the second volume   
where the earlier more incriminating materials are presented.    
               Did Edgeworth get bolder and more assertive about the   
mathematical method after Marshall published in Principles in 1890?  Did Edgeworth get
bolder and more assertive about the mathematical methods after encountering one the most
prominent of the American economists refusing to use the calculus in the way prescribed by
Edgeworth and therefore reaching "special case" conclusions only?   There is so much more
to this story and I am delighted that Professors Salerno and Tame are interested in the
subject.
  
Larry Moss