Actually, while it seems like a devastating wisecrack to say that mathematics does not have enough verbs, in fact it uses the ones it has a great deal.  If one reads out most equations, they are indeed sentences that usually contain several verbs, including with the equal sign one that suggests both existence and equivalence.  But all the arithmetic operations, as well as algebraic ones and ones from calculus and differential equations, and even some involving higher mathematics that is not usually used in economics are action verbs.  To add or multiply or exponentiate are actions.  They are verbs, even if put in the form of symbols that are not spelled-out words.

J. (not "John") Barkley Rosser, Jr.
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From: Societies for the History of Economics [[log in to unmask]] on behalf of Steve Ziliak [[log in to unmask]]
Sent: Monday, November 17, 2014 11:39 AM
To: [log in to unmask]
Subject: Re: [SHOE] R: [SHOE] Mathematics and language

Michael Polanyi is insightful on the mathematics-and-language question, with implications for economic and other social science interpretation:

"Take words, graphs, maps and symbols. . . . They are never objects of our attention in themselves, but pointers towards the things they mean. If you shift your attention from the meaning of a symbol to the symbol as an object viewed in itself, you destroy its meaning. . . . The skillful use of a tennis racket can be paralyzed by watching our racket instead of attending to the ball and the court in front of us."  - Michael Polanyi, The Study of Man (Univ of Chicago Press 1958, pp. 30-31), quoted in Ziliak's and McCloskey's The Cult of Statistical Significance (Univ of Michigan Press 2008, p. 193).

In other words, even if mathematics had more "verbs" (as in the wonderful quote from Anne), the language would have more rackets than swings, more swings than hits, so
long as investigators continue to neglect the "things" our words and graphs and symbols "mean".

-Steve Ziliak




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From: Societies for the History of Economics <[log in to unmask]> on behalf of Nicola Giocoli <[log in to unmask]>
Sent: Monday, November 17, 2014 12:46 AM
To: [log in to unmask]
Subject: [SHOE] R: [SHOE] Mathematics and language

Even more pedant. I don't have the text in front of me here (so I am only half-pedant...), but I recall that in that paper Samuelson first wrote "math is A language"; then he corrected himself (and the learned physicists who said it earlier, too) into "math is language", claiming that this was the best - actually, the only - way to put it.
The latter is what I suggest to call the Samuelsonian disease!

I agree with John that many contemporary economists look more or less immune from it, but the backbone, the underlying structure of much of their empirical analysis (both in micro - RCT -and macro - DSGE) is, I guess, still largely "infected". And I suspect many of them are even unaware of that, because of their lack of methodological and historical training.

Nicola
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