Abstract
This chapter is devoted to the historical and epistemological analysis, on the one hand, of the genesis of the use of symbolic writings by Boole and, on the other hand, of his conception of the uninterpretable symbolic assemblages that he had produced for the needs of his theory.
The author “Michel Serfati” was deceased at the time of publication.
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Notes
- 1.
In this chapter, I will make extensive use of my previous work: \(\acute {A}\) la recherche des Lois de la pensée. Sur l’épistémologie du calcul logique et du calcul des probabilités chez Boole (The search of the Laws of thought. On the epistemology of Boole’s logical calculus and the calculus of probabilities in Boole) [8].
- 2.
On issues of mathematical symbolism, I will refer to my book, “La Révolution Symbolique” (The Symbolic Revolution) [7].
- 3.
Cf. Serfati [7, p. 384].
- 4.
See Serfati [7], Chapter XIV, p. 323, “Formes sans significations. Analogies et ‘prolongements”’ (Forms without meanings. Analogies and ‘extensions’).
- 5.
The book will be referenced Laws.
- 6.
- 7.
See Diagne [3, p. 60].
- 8.
One may appreciate Boole’s relevant response to such criticism: “In accordance with these views it has been contended that the science of Logic enjoys an immunity from those conditions of imperfection and of progress to which all other sciences are subject”, Laws, 239.
- 9.
S. Diagne, “Boole, l’oiseau de nuit en plein jour” (“An owl in daylight”).
- 10.
Sir William Hamilton’s, Discussions on philosophy and literature, education and university reform, 3rd. ed., Blackwood and Sons, Edinburgh and London, 1866, p. 705.
- 11.
See Diagne [3, p. 71].
- 12.
Cf. in Serfati [8, p. 45], the section “Calcul logique et objets interpretables”.
- 13.
On these issues, see Bourbaki’s enthusiastic comment in Serfati [8, p. 45, footnote 10].
- 14.
- 15.
See in Serfati [8, p. 49], the section “Fonctions logiques et ‘développement”’.
- 16.
See Serfati [8, p. 48].
- 17.
Cf. Serfati [8, p. 56].
- 18.
The result is actually valid. A more complete presentation can be found in E. Schröder’s, “Vorlesungen uber die Algebra der Logik”. For a modern statement and presentation within lattice theory, see [9]. Alg\(\grave {e}\)bres de Boole, avec une introduction \(\grave {a}\) la théorie algébrique des graphes orientés et aux “sous-ensembles flous”, Paris, Sedes.
- 19.
See [8, p. 51].
- 20.
See [2]: Boole devait jouer serré avec l’analogie (Boole had to play tight with analogy).
- 21.
See [8, pp. 54–55].
- 22.
By using “The calculus of heaps” and “Axioms for heap algebra”. See [10, pp. 88–113].
- 23.
Rhetorical interpretation of x.z.w = 0.
- 24.
Rhetorical interpretation of x.(1 −z).(1 −w) = 0.
- 25.
- 26.
Leibniz had also invoked the imaginary numbers to justify his infinitesimals, with slightly different designs from those of Boole. See my comments in [8, 55, footnote 54].
- 27.
See [5].
- 28.
Coumet [2, I, p. 2].
References
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M. Serfati, Introduction aux Alg \(\grave {e}\) bres de Post. Logiques \(\grave {a}\) r valeurs. Grapho \(\ddot {i}\) des orientés, Cahiers du Bureau Universitaire de Recherche Opérationnelle 21, Institut de Statistique des Universités de Paris, (1973).
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Serfati, M. (2022). Symbolism in Boole: Its Inability to be Interpreted. In: Béziau, JY., Desclés, JP., Moktefi, A., Pascu, A.C. (eds) Logic in Question. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-94452-0_5
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