- At the very beginning of The mathematical analysis of logic (the reference is given in footnote 3 below) Boole stated that he was moved to resume his enquiries about an algebra of logic by the controversy between Hamilton and De Morgan. Besides having been the external stimulus which moved Boole to pursue his enquiries, the controversy may have had another kind of influence on Boole; it seems that several of the ideas interchanged in the controversy confirmed and clarified Boole's own ideas, and that probably the latter stated his philosophy of mathematics in the introduction to The mathematical analysis of logic as a response to Hamilton's ideas about the same subject.
- Mary Everest Boole Boole's wife, referred in many places in her writings (which are cited in footnote 16 below) to the existence of a mystico-pedagogico-psychological background and aim of Boole's logic. According to her, the equation x 2 = x was the expression of a dualistic philosophy which claimed that the Eternal Unity of God could be reached from the contemplation of all opposite opinions and facts; (1—x) was the opposite of x, and (1—x) + x = 1. Such conception involved a psychological theory of the mind and had pedagogical implications. Several historians of logic have despised Mary Everest's claim, but in fact, it seems that she was basically right. It would take too long to prove it here; I have examined Mary Everest's claims in ‘A study of the genesis of Boolean logic’, a doctoral dissertation submitted to the Graduate School of the University of Notre Dame. This dissertation was directed by Professor Michael J. Crowe. Among the psychological implications of Boole's—probably existing—metaphysical conception was that God works directly through some hidden resort of the human mind, so that the latter does not need to be continuously conscious of its operations. In pedagogy, this idea materializes in the stress on the importance of using symbols which only at determinate steps of the argument need to have meaning, in the processes of learning and teaching. One interesting problem is to know the possible influence on Mary Everest (and Boole too?) of a symbolical school which developed in the early and mid-nineteenth century (for references to secondary literature on this theme, see footnote 46 below).
- Boole , G. 1847 . The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning Cambridge and London repr. 1958, New York). Also in G. Boole, Studies in logic and probability (ed. R. Rhees; 1952, London), 49–124. This work is cited hereafter as ‘MAL’.
- MAL , 17 – 18 .
- This view that Boole's logic was applied mathematics of a universal calculus of symbols supports Russell's view that ‘Pure mathematics was discovered by Boole’ Mysticism and logic London 1917 repr. 1963), 59), precisely because of the universal meaning attributed by Boole to the word ‘analysis’. Nevertheless, Russell's assertion was too exclusive: even though it seems that Boole grasped by himself the existence of a universal calculus capable of embodying several known and possible fields, this idea was already at least implicitly contained in the works of the French mathematicians of the immediately prior period, and in those of Peacock, Herschel, Hamilton, Gregory, De Morgan and others. In mathematics it is often misleading to assign a particular discovery to a particular person. Russell himself retracted somewhat his comment on Boole discovering pure mathematics. (I owe the last information to Dr. Ivor Grattan-Guinness, who cites Russell's letter in Proc. Roy. Irish Acad., 57 (A) (1954–56), 28.)
- Boole , G. 1841 . Researches on the theory of analytical transformations, with a special application to the reduction of the general equation of the second order . Cambridge mathematical journal , 2 : 64 – 73 .
- Boole , G. 1841 . Researches on the theory of analytical transformations, with a special application to the reduction of the general equation of the second order . Cambridge mathematical journal , 2 : 64 – 64 .
- Boole , G. 1841 . Researches on the theory of analytical transformations, with a special application to the reduction of the general equation of the second order . Cambridge mathematical journal , 2 : 65 – 65 .
- Boole , G. 1841 . Researches on the theory of analytical transformations, with a special application to the reduction of the general equation of the second order . Cambridge mathematical journal , 2
- Boole , G. 1841 . Researches on the theory of analytical transformations, with a special application to the reduction of the general equation of the second order . Cambridge mathematical journal , 2
- Boole , M. Everest . 1931 . Collected works Edited by: Cobham , E.M. and Dummer , E.S. Vol. 1 , 4 – 4 . London 4 vols.5, 35
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 97 – 102 .
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 97 – 97 .
- See, for instance Cambridge mathematical journal 1841 2 64 73 (p. 64); 2 (1841), 114–119 (p. 115); 3 (1843), 1–20 (p. 2); and Cambridge and Dublin mathematical journal, 2 (1847), 7–12 (p. 7).
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 99 – 99 .
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 101 – 101 .
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 97 – 97 .
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 98 – 98 .
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 98 – 98 .
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 101 – 102 .
- MAL , 49 – 50 . 52, 64, 77
- Boole , G. 1841 . On certain theorems in the calculus of variations . Cambridge mathematical journal , 2 : 98 – 98 .
- Boole , G. 1841 . On the integration of linear differential equations with constant coefficients . Cambridge mathematical journal , 2 : 114 – 119 .
- Boole , G. 1841 . On the integration of linear differential equations with constant coefficients . Cambridge mathematical journal , 2 : 115 – 115 .
- Boole , G. 1841 . On the integration of linear differential equations with constant coefficients . Cambridge mathematical journal , 2 : 119 – 119 .
- Boole , G. 1841 . Analytical geometry . Cambridge mathematical journal , 2 : 179 – 188 .
- Boole , G. 1841 . Analytical geometry . Cambridge mathematical journal , 2 : 180 – 180 .
- Boole , G. 1841 . Analytical geometry . Cambridge mathematical journal , 2 : 182 – 182 .
- Boole , G. 1843 . Exposition of a general theory of linear transformations . Cambridge mathematical journal , 3 : 1 – 20 . 106–119 (pp. 6–7)
- Boole , G. 1843 . Exposition of a general theory of linear transformations . Cambridge mathematical journal , 3 : 8 – 8 .
- MAL , 73 – 73 .
- MAL , 70 – 70 .
- Boole , G. 1844 . On a general method in analysis . Philosophical transactions of the Royal Society of London , 134 : 225 – 282 .
- Boole , G. 1844 . On a general method in analysis . Philosophical transactions of the Royal Society of London , 134 : 225 – 225 .
- Gregory , D.F. 1841 . Examples of the processes of the differential and integral calculus Cambridge and London
- Gregory , D.F. 1841 . Examples of the processes of the differential and integral calculus 235 – 235 . Cambridge and London
- Gregory , D.F. 1841 . Examples of the processes of the differential and integral calculus 235 – 235 . Cambridge and London
- Herschel , J. 1814 . Considerations on various points in analysis . Philosophical transactions of the Royal Society of London , 104 : 440 – 468 .
- These important developments still await the historical study that they deserve, but interim information can be recovered from: S. Pincherle Pour la bibliographie de la théorie des opérations distributives Bibl. math. 1899 13 2 13 18 his ‘Funktionale Operationen und Gleichungen’, Enc. math. Wiss., Bd. 2, Teil A (1903–21, Leipzig), 761–824; H. Burkhardt, ‘Entwicklungen nach oscillierenden Funktionen …’, Jber. Dtsch. Math.-Ver., 10, pt. 2 (1901–08), esp. ch. 13; E. Koppelman, ‘The calculus of operations and the rise of abstract algebra’, Arch. hist. exact sci., 8 (1972), 155–242; and I. Grattan-Guinness and J. R. Ravetz, Joseph Fourier 1768–1830 … (1972), Cambridge, Mass.), esp. pp. 464–466.
- Boole , G. 1844 . On a general method in analysis . Philosophical transactions of the Royal Society of London , 134 : 225 – 225 .
- MAL , 15 – 18 .
- Boole , G. 1844 . On a general method in analysis . Philosophical transactions of the Royal Society of London , 134 : 282 – 282 .
- Boole , G. 1845 . On the inverse calculus of definite integrals . Cambridge mathematical journal , 4 : 82 – 87 . (p. 87)
- Boole , G. 1846 . On the equations of Laplace's functions . Cambridge and Dublin mathematical journal , 1 : 10 – 22 . (p. 22)
- Boole , G. 1847 . On a certain symbolical equation . Cambridge and Dublin mathematical journal , 2 : 7 – 12 . (p. 7)
- Boole , G. 1846 . On the equations of Laplace's functions . Cambridge and Dublin mathematical journal , 1 : 11 – 11 .
- Boole , G. 1846 . On the equations of Laplace's functions . Cambridge and Dublin mathematical journal , 1 : 11 – 11 . 13, 20
- MAL , 70 – 72 .
- Boole , G. 1845 . On the theory of developments . Cambridge mathematical journal , 4 : 214 – 223 . (p. 219)
- MAL , 60 – 60 .
- MAL ,
- MAL , 60 – 61 .
Annals of Science
Volume 34, 1977 - Issue 2
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