Abstract
We aim at clarifying to what extent the work of the English mathematician George Boole (1815–1864) on the algebra of logic is taken into consideration and discussed in the work of early Husserl, focusing in particular on Husserl’s lecture “Über die neueren Forschungen zur deduktiven Logik” of 1895, in which an entire section is devoted to Boole. We confront Husserl’s representation of the problem-solving processes with the analysis of “symbolic reasoning” proposed by George Boole in the Laws of Thought (1854) and try to show how and why Husserl, while praising Boole’s calculus, strongly criticizes his attempt at a philosophical clarification and justification of it.
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- 1.
In Husserl (2001), Appendix, 305–328 (henceforth LV 96, App.).
- 2.
Casari 1973, 8–9.
- 3.
See Cantini 1979, 41 ff.
- 4.
- 5.
Husserl 1891, henceforth PdA (Husserliana edition) and PoA (English translation). Here PdA 222–255; PoA 335–269.
- 6.
PdA 228–233; PoA 241–246.
- 7.
PdA 257–283; PoA 270–299.
- 8.
PdA 257–259; PoA 270–274.
- 9.
Boole 1854.
- 10.
PdA 339; PoA 357.
- 11.
PoA 244; PdA 230–231.
- 12.
PoA 244; PdA 231.
- 13.
Webb 1980 observes that “Husserl’s theory of calculation has some of the flavor of Church’s calculi of λ-conversion: ‘systematic numbers’ (e.g. arabic numerals) result from a series of rule governed ‘reductions’ of ‘unsystematic numbers’ (terms compounded out of numerals with function symbols), also called ‘symbolische Bildungen’” (25).
- 14.
Cp. Hartimo 2007, 288.
- 15.
PoA 251–252; PdA 237–238.
- 16.
- 17.
PoA 271–299; PdA 256–286.
- 18.
PoA 272; PdA 257.
- 19.
PoA 273; PdA 258 (italics in the original). Cp. Hartimo 2007, 289 f.
- 20.
We borrow here terminology from Webb 1980. As Webb 1980 puts it: “Husserl … attempted a complete development of the algorithmic conception of arithmetic, which required “die logische Untersuchung des arithmetischen Algorithmus”. The notion of algorithm, Husserl felt, had to be bound up with that of a ‘mechanical process’” (24–25).
- 21.
PoA 273; PdA 258 (italics in the original). Husserl does not fail to stress how important a good choice of the system of signs is, in terms of efficiency, for all three of these phases (encoding – calculation – decoding) of the solution of a problem.
- 22.
PoA 273; PdA 258 (italics in the original).
- 23.
PoA 273; PdA 258.
- 24.
loc. cit.
- 25.
LV 96, App. 305.
- 26.
LV 96, App. 306.
- 27.
LV 96, App. 307.
- 28.
LV 96, App. 308.
- 29.
LV 96, App. 312.
- 30.
LV 96, App. 309.
- 31.
LV 96, App. 314.
- 32.
LV 96, App. 310.
- 33.
Frege 1985.
- 34.
Frege 1903.
- 35.
LV 96, App. 311.
- 36.
PdA App. 414; PoA 391.
- 37.
LV 96, App. 322–323.
- 38.
Husserl means here: “the epistemological ground of the calculatorial method”.
References
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Centrone, S., Minari, P. (2017). Husserl and Boole. In: Centrone, S. (eds) Essays on Husserl's Logic and Philosophy of Mathematics. Synthese Library, vol 384. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1132-4_5
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