The phrase "to fix ideas" shows up over 800 times in the complete JSTOR  
database.  The earliest case is:  
  
Note on the Theory of the Alternate Current Dynamo  
John Hopkinson  
Proceedings of the Royal Society of London > Vol. 42 (1887), pp. 167-170  
Stable URL:  
http://links.jstor.org/sici?sici=0370-1662%281887%2942%3C167%3ANOTTOT%3E2.0.CO%3B2-9  
  
It seems to be used in a variety of sciences -- physics, mathematics,  
psychology, and anthropology, for example -- in the 19th century.  
  
Restricting attention to economics journals in JSTOR, the earliest case is:  
  
Bilateral Monopoly  
A. L. Bowley  
The Economic Journal > Vol. 38, No. 152 (Dec., 1928), pp. 651-659  
Stable URL:  
http://links.jstor.org/sici?sici=0013-0133%28192812%2938%3A152%3C651%3ABM%3E2.0.CO%3B2-X  
  
I would imagine that it predates the journals archived in JSTOR.  
  
Kevin Hoover