[FOM] BOOLE'S INFLUENCE ON FREGE.
kremer at uchicago.edu
Mon Aug 2 09:23:30 EDT 2004
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.
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?
>FOM mailing list
>FOM at cs.nyu.edu
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