THEORY OF GAMES, 1944

[James A. Landau]

In a message dated 4/10/01 9:32:06 AM Eastern Daylight Time, douglas at NB.NET 
writes:

<< There is also "games theory" (= "game theory" AFAIK). >>

I was not aware of the existence of the form "games theory" until I checked 
the OED on CD last night and found the entry was for "game(s) theory".  I see 
no reason to disagree with the OED that "games theory" = "game theory".

While on the subject...

the synonymous terms "theory of sets" and "set theory" have a rather zigzag 
history.

"theory of sets" was proposed in 1853 by the Irish mathematician William 
Rowan Hamilton.  This was also the first (as far as I know) use of "set" in 
mathematics.  However, what Hamilton was discussing is what we now call 
"ordered sets" or "n-tuples" and they are covered in the  branch of 
mathematics that is now called "linear algebra".  

The word "set" in English-language mathematics (other than Hamilton's) comes 
from the German word "menge" which appeared in German-language texts in the 
1850's.  "Set theory" (non-Hamilton definition) was invented by Georg Cantor 
and the term appears in 1883 in French:  Georg Cantor, "Sur divers théorèmes 
de lat théorie des ensembles de points situés dans un espace continu à n 
dimensions. Première communication." Acta Mathematica 2, pp. 409-414 (1883) 

One might assume that "théorie des ensembles" would enter English as "theory 
of sets" but the available documentary evidence does not support that 
assumption.  The OED2 on CD says that "set theory" appeared first, in 1926.

In the interests of greater confusion: I have in front of me Volume Two of 
James Pierpont _The Theory of Functions of Real Variables_ (New York: Ginn 
1912) which contains the phrase "theory of point sets" (Preface, page v, the 
book is available on-line at URL 
http://cdl.library.cornell.edu/cdl-math-browse.html).   By "theory of point 
sets" Pierpont means what we know call "theory of sets" or "set theory".  

What was happening here  was that circa 1912 the English-language terminology 
for set theory was in a state of flux, with the words "set", "class", and 
"aggregate" all being used.  In Volume One (1905) Pierpont consistently used 
"aggregate" (although he did use "set" a few times.).  In 1912 he used both 
"aggregate" and "set"---sometimes in the same sentence.  

In a message dated 4/9/01 12:01:40 PM Eastern Daylight Time, 
t.paikeday at SYMPATICO.CA writes:

<< I think the canonical form in compounds of this type
 should be the linguistically original form >>

As the preceding example shows, it can be difficult to decide just which is 
the linguistically original form.  

Is it "theory of point sets", a form that is no longer used? 

Is it "théorie des ensembles"?  If you say yes, then I ask whether the 
linguistically original form should be the German expression (I think it was 
"Mengenlehre") habitually used by the German-speaking Cantor, who happened to 
publish in a French-language journal.

                - Jim Landau