[FOM] BOOLE'S INFLUENCE ON FREGE.

[Michael Kremer]

In reply to John Corcoran:

Certainly Frege knew of Boole and knew of the work of Schroeder.  Schroeder 
reviewed Begriffsschrift and claimed there was no advance there over 
Boole.  Frege then wrote a long reply which was never published, in which 
he argued that his Begriffsschrift was fundamentally different from Boole's 
logical notation.  It is the second piece in Posthumous Writings.  In that 
essay Frege cites as a main influence Leibniz's idea of a "universal 
characteristic" and claims that his BS is a universal characteristic, that 
is, a language of thought, whereas Boole's logic is a mere "calculus 
ratiocinator" (a system of uninterpreted markers for calculating without 
thinking -- see the beginning of Whitehead's Universal Algebra for an 
account of this conception).

The influence of Leibniz on Frege is discussed by Hans Sluga in his book on 
Frege.  Sluga points to an essay by Trendelenburg on the idea of a 
universal characteristic as the source of the influence.  It is not clear 
whether Frege read Boole before writing BS or only after composing his 
reply to Schroeder.

On the idea of truth-values as objects and the meanings of sentences, Sluga 
has an essay ("Frege on Meaning," in The Rise of Analytic Philosophy, H.J. 
Glock, ed. (Oxford: Blackwell, 1997)) pointing out that the term 
"truth-value" ("Wahrheitswert") probably derives from the neo-Kantian 
Windelband. Sluga's work here builds on work of Gottfried Gabriel on the 
influence of neo-Kantianism on Frege (beginning with "Frege als 
Neukantianer," Kantstudien 77 (1986), 84-101).  (I think Sluga goes too far 
in coming close to saying the whole sense-meaning distinction derives from 
Windelband, but that their is a connection seems highly plausible.)

Frege also wrote a critical piece about Schroeder's Lectures on the Algebra 
of Logic, published in 1895, which can be found in his Collected Papers.

--Michael Kremer


At 04:48 PM 8/1/04 -0400, you wrote:
>1 What is known about Boole's immediate or mediated influence on Frege?
>How can people be so sure that Boole's idea of laws of thought was not
>one of the contributing influences on what Frege calls laws of thought
>in the opening two pages of 1879?
>2 The so-called algebraic tradition (which becomes even more
>scholasticized with Schroeder) lived on albeit on death's door, in
>WHITEHEAD, LOWENHEIM and even SKOLEM. Did any Boolean influence reach
>Frege through the algebraic tradition? 3. Could the idea of truth-values
>have been inspired by Boole's zero and one in his hypothetical logic?
>Could it have come to Frege through Peirce or Schroeder?
>
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