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Bernard Bolzano. Theory of Science 428 • Philosophia Mathematica Menzel, Christopher [1991] ‘The true modal logic’, Journal of Philosophical Logic 20, 331–374. ———[1993]: ‘Singular propositions and modal logic’, Philosophical Topics 21, 113–148. ———[2008]: ‘Actualism’, in Edward N. Zalta, ed., Stanford Encyclopedia of Philosophy (Winter 2008 Edition). Stanford University. http://plato.stanford.edu/archives/win2008/entries/actualism, last accessed June 2015. Nelson, Michael [2009]: ‘The contingency of existence’, in L.M. Jorgensen and S. Newlands, eds, Metaphysics and the Good: Themes from the Philosophy of Robert Adams, Chapter 3, pp. 95–155. Oxford University Press. Downloaded from https://academic.oup.com/philmat/article/23/3/428/1449457 by guest on 30 September 2021 Parsons, Charles [1983]: Mathematics in Philosophy: Selected Essays. New York: Cornell University Press. Plantinga, Alvin [1979]: ‘Actualism and possible worlds’, in Michael Loux, ed., The Possible and the Actual, pp. 253–273. Ithaca: Cornell University Press. ———[1983]: ‘On existentialism’, Philosophical Studies 44, 1–20. Prior, Arthur N. [1956]: ‘Modality and quantification in S5’, The Journal of Symbolic Logic 21, 60–62. ———[1957]: Time and Modality. Oxford: Clarendon Press. ———[1968]: Papers on Time and Tense. Oxford University Press. Quine, W.V. [1951]: ‘Two dogmas of empiricism’, Philosophical Review 60, 20–43. ———[1969]: Ontological Relativity and Other Essays. New York: Columbia University Press. ———[1986]: Philosophy of Logic. 2nd ed. Cambridge, Mass.: Harvard University Press. Shapiro, Stewart [1991]: Foundations without Foundationalism: A Case for Second-order Logic.Oxford University Press. Stalnaker, Robert [2012]: Mere Possibilities: Metaphysical Foundations of Modal Semantics. Princeton, N.J.: Princeton University Press. Turner, Jason [2005]: ‘Strong and weak possibility’, Philosophical Studies 125, 191–217. Williamson, Timothy [2010]: ‘Modal logic within counterfactual logic’, in Bob Hale and Aviv Hoffmann, eds, Modality: Metaphysics, Logic, and Epistemology, pp. 81–96. Oxford University Press. ———[2012]: Modal Logic as Metaphysics. Oxford University Press. Zalta, Edward N. [1983]: Abstract Objects: An Introduction to Axiomatic Metaphysics. Dordrecht: D. Reidel. ——— [1993]: ‘Twenty-five basic theorems in situation and world theory’, Journal of Philosophical Logic 22, 385–428. doi:10.1093/philmat/nkv017 Advance Access publication June 26, 2015 Bernard Bolzano. Theory of Science. Volumes I–IV. Paul Rusnock and Rolf George, trans. Oxford: Oxford University Press, 2014. ISBN: 978-0-19-968438-0. Pp. 2044.† Reviewed by Jan Sebestik∗ After 177 years, thanks to Paul Rusnock and Rolf George, we finally have the com- plete English translation of Bolzano’s monumental work Theory of Science, the great †Volume I contains a general introduction and a translation of key terms; each volume has a special introduction, a bibliography, and an index of names and an index of subjects. All quotations in foreign languages are translated. ∗Institut d’Histoire et de Philosophie des Sciences de l’Université de Paris I Panthéon-Sorbonne and CNRS, UMR 8590, Paris, France. E-mail: sebestik@flu.cas.cz Critical Studies/Book Reviews • 429 unknown classical work in logic and epistemology. The translation is excellent, both in keeping the flavor of nineteenth-century books and in being eminently readable. The fundamental innovations brought about by his work were not really understood by his contemporaries, which accounts for the initial neglect of his work until, about a hundred years after its publication, logicians of the twentieth century arrived at similar concepts. Downloaded from https://academic.oup.com/philmat/article/23/3/428/1449457 by guest on 30 September 2021 1. BOLZANO’S LIFE AND WORK This author lived in a Europe shaken to its foundations by the French revolution and Napoleonic wars. At the end of the eighteenth century, his native country Bohemia was a multicultural society with Germans politically dominating the Czech majority. The third component, the mainly German-speaking Jewish community, had been settled in the Czech lands since the Middle Ages. Symbolically, his life went through revolutions, both political and philosophical. Bernard Bolzano (1781–1848) was born into a Prague Catholic family; his father was Italian, his mother German. Bolzano knew some Czech, but his native language was German and all his publications were in that language. In the same year 1781 the Austrian Emperor Joseph II initiated a series of reforms which put an end to the forced labor of peasants, modernized justice and forbade torture, abolished inactive religious orders, introduced partial religious freedom (Protestants could reopen their churches) and tolerance, resulting in the modernisation of the society and awakening of the sci- ences. Also in 1781 was published Kant’s Critique of Pure Reason which revolutionized philosophy. During his studies at the Prague Charles-Ferdinand University, Bolzano became interested in mathematics and philosophy. His mathematical notebooks are an excep- tionally rich source for the history of mathematics: they show his extensive knowledge of the literature of the seventeenth and eighteenth centuries, contain entries about cur- rent mathematical problems, and also reflections about methodology and critique of some fundamental concepts. In 1800, he decided to study theology, but at the same time he prepared his first publication on the Euclidean postulate of parallels (published in 1804). Having finished his studies, he participated in the contest for the chair of the ‘science of [the Catholic] religion’, newly founded by the Emperor Franz II to fight atheism and the ideals of the French revolution, and also for the chair of mathemat- ics. He won both and the commission appointed him to the ‘science of religion’. As a university professor of this discipline, he had to be a Catholic priest. Bolzano did not perceive the larger political context and thought that this chair could provide a forum for spreading his own ideas on the reform of society in the spirit of tolerance and equal- ity of all citizens. At the end of 1819, the contradiction between the intentions of the Emperor and Bolzano’s own representation of an ideal society led to his dismissal from the University. At the same time, he was deprived of the right to publish even scientific articles and his name was not to be mentioned in the Austrian press. Nevertheless, the Prague Royal Society of Sciences did not suspend his membership, and whenever he was in Prague he attended its meetings, where in the 1840s he presented his set theory and his theory of real numbers. With the help of his friends, he succeeded in publishing his works in Germany, mainly in Bavaria, sometimes without mention of their author. When he died, he left important mathematical manuscripts, and his young friend Robert Zimmermann was supposed to publish them. Instead he simply transferred 430 • Philosophia Mathematica them to the Viennese Imperial Library so that, except for Bolzano’s last and best known mathematical work The Paradoxes of the Infinite (1851), his set theory, his theory of real numbers and of (real) functions, which are parts of the great treatise of mathematics called The Theory of Magnitudes, were published only in the twentieth century. During his tenure as professor of religion he continued his work on mathematics. In 1810, he published a small book Contributions to a Better Founded Presentation of Mathematics which contains his first sketch of logic and of the methodology of mathe- Downloaded from https://academic.oup.com/philmat/article/23/3/428/1449457 by guest on 30 September 2021 matics. In 1817, four years before Cauchy’s Cours d’analyse, there appeared one of his best works, Purely Analytical Proof of the Intermediate Value Theorem.Init,heelabo- rated a sequence of concepts and theorems necessary to prove it, those of the limit of a sequence and of continuity of real functions and demonstrated the Bolzano-Cauchy criterion of convergence of sequences and the least-upper-bound theorem. All this can be found in Cauchy’s Cours, and this circumstance gave birth to a controversy whether Cauchy plagiarized Bolzano. In a way, his forced departure from the University was a blessing both for his sci- entific work and for his personal life. He had a chance to become the friend of the Hoffmanns, who lived on their estate in the countryside and who invited him to stay with them, first for summers, then between 1827 and 1842 for the whole time, interrupted only by several weeks’ sojourns in Prague. An extraordinary friendship developed between the priest Bolzano and Mrs Anna Hoffmann, his ‘benefactress and so to speak savior (Lebenserhalterin)’, who became his secretary, taking care of his correspondence with friends (Bolzano always was watched by the police). It was in the small village of Techobuzˇ that he wrote the Theory of Science and the unfinished and unpublished Theory of Magnitudes. But neither his logic nor his mathematics was understood during his lifetime. Once during his life, he met somebody who did his best to understand his logical theories and who partly understood them: Franz Exner, a professor of philosophy at the University in Prague. When Bolzano learned about his living in Prague, he sent him the manuscript of On the Mathematical Method,a summary of his logic extracted from the Introduction to the Theory of Magnitudes (it was probably the first time in the history of mathematics that a long chapter on logic became part of a mathematical treatise). A lively correspondence followed, and they became friends, but Bolzano did not succeed in convincing Exner of the soundness of his theory of propositions in themselves. After the death of the Emperor Franz in 1835, censorship decreased and Bolzano was able to publish scientific articles. In the meantime, his manuscripts circulated among friends and the general public, especially his lectures on religion and his social utopia On the Best State, published only in the twentieth century. These were the happiest years of his life. In 1842 Anna Hoffmann died and Bolzano returned to Prague, a living shadow.
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