[FOM] Book on the history of logic

Irving ianellis at iupui.edu
Thu Feb 17 13:34:35 EST 2011

Sam Sanders asked:

Can someone explain to me why Kneale & Kneale's account of logic is
"extremely narrow"?
If their account is indeed of such nature, what else should have been 

The short answer to that question must be that it depends on what one 
is looking for. But it is fair to say that, like a number of mid 20th 
century accounts, it is long on the Russello-Fregean history and 
comparatively short on the Boole-De Morgan-Peirce Schröder line. 
(Kneale & Kneale also devotes much more space to the medieval logicians 
than of Boole, De Morgan, Peirce, and Schröder.)
Another such example of the comparatively sparse coverage of algebraic 
logic would be Bochenski's "History of Formal Logic", which has the 
added feature of being primarily composed of a patchwork of translated 
selections taken from the authors being discussed, held together by a 
few interstitial lines of connective tissue.

Nathan Houser and I discussed this in "The Nineteenth Century Roots of 
Universal Algebra and Algebraic Logic", in Hajnal Andreka, James Donald 
Monk, Istvan Nemeti (eds.), Colloquia Mathematica Societis Janos Bolyai 
54. Algebraic Logic, Budapest (Hungary), 1988 (Amsterdam/London/New 
York: North-Holland, 1991), 1-36.

For works of the same vintage, one would do well, if adopting a work 
such as Kneale & Kneale, to supplement that book with Nikolai 
Styazhkin's "History of Mathematical Logic from Leibniz to Peano" (MIT 
Press), to fill in the details of the algebraic logicians that are 
missing from the more standard Russello-Fregean histories. (If I 
remember correctly, Elliott Mendelson was the translator of Styazkin's 

 From the standpoint of historiography, one might consider Ivor 
Grattan-Guinness's distinction (which he formulated in his writings on 
history of mathematics) between history are heritage, the former asking 
'What happened in the past?', the latter asking 'How did we get to 
where we are today?', or equivalently, 'what happened in the past that 
leads to me?' (The differences are discussed in my "Navigating History 
of Mathematics: Essay-Review of Ivor Grattan-Guinness, Routes of 
Learning: Highways, Pathways, and Byways in the History of 
Mathematics", Annals of Science  

Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
URL: http://www.irvinganellis.info

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