Contents 1 Family 2 Career 3 Mathematical work 4 Philosophical work 4.1 Wissenschaftslehre (Theory of Science) 4.1.1 Introduction to Wissenschaftslehre 4.1.2 Metaphysics 4.1.3 Satz an Sich (proposition in itself) 4.1.4 Ideas and objects 4.1.5 Sensation and simple ideas 4.1.6 Logic 4.1.7 Truth 4.1.8 Judgments and cognitions 5 Philosophical legacy 6 Writings 6.1 Translations and compilations 7 See also 7.1 Named after Bolzano 8 Notes 9 References 10 Further reading 11 External links Family[edit]
Bolzano was the son of two pious Catholics. His father, Bernard
Pompeius Bolzano, was an Italian who had moved to Prague, where he
married Maria Cecilia Maurer who came from Prague's German-speaking
family Maurer. Only two of their twelve children lived to adulthood.
Career[edit]
Bolzano entered the University of
1. There are no true propositions (assumption) 2. 1. is a proposition (obvious) 3. 1. is true (assumed) and false (because of 1.) 4. 1. is self-contradictory (because of 3.) 5. 1. is false (because of 4.) 6. There is at least one true proposition (because of 1. and 5.) B. There is more than one truth in itself: 7. There is only one truth in itself, namely A is B (assumption) 8. A is B is a truth in itself (because of 7.) 9. There are no other truths in themselves apart from A is B (because of 7.) 10. 9. is a true proposition/ a truth in itself (because of 7.) 11. There are two truths in themselves (because of 8. and 10.) 12. There is more than one truth in itself (because of 11.) C. There are infinitely many truths in themselves: 13. There are only n truths in themselves, namely A is B .... Y is Z (assumption) 14. A is B .... Y is Z are n truths in themselves (because of 13.) 15. There are no other truths apart from A is B .... Y is Z (because of 13.) 16. 15. is a true proposition/ a truth in itself (because of 13.) 17. There are n+1 truths in themselves (because of 14. and 16.) 18. Steps 1 to 5 can be repeated for n+1, which results in n+2 truths and so on endlessly (because n is a variable) 19. There are infinitely many truths in themselves (because of 18.) Judgments and cognitions[edit] A known truth has as its parts (Bestandteile) a truth in itself and a judgment (Bolzano, Wissenschaftslehre §26). A judgment is a thought which states a true proposition. In judging (at least when the matter of the judgment is a true proposition), the idea of an object is being connected in a certain way with the idea of a characteristic (§ 23). In true judgments, the relation between the idea of the object and the idea of the characteristic is an actual/existent relation (§28). Every judgment has as its matter a proposition, which is either true or false. Every judgment exists, but not "für sich". Judgments, namely, in contrast with propositions in themselves, are dependent on subjective mental activity. Not every mental activity, though, has to be a judgment; recall that all judgments have as matter propositions, and hence all judgments need to be either true or false. Mere presentations or thoughts are examples of mental activities which do not necessarily need to be stated (behaupten), and so are not judgments (§ 34). Judgments that have as its matter true propositions can be called cognitions (§36). Cognitions are also dependent on the subject, and so, opposed to truths in themselves, cognitions do permit degrees; a proposition can be more or less known, but it cannot be more or less true. Every cognition implies necessarily a judgment, but not every judgment is necessarily cognition, because there are also judgments that are not true. Bolzano maintains that there are no such things as false cognitions, only false judgments (§34). Philosophical legacy[edit] Bolzano came to be surrounded by a circle of friends and pupils who spread his thoughts about (the so-called Bolzano Circle), but the effect of his thought on philosophy initially seemed destined to be slight.[3] His work was rediscovered, however, by Edmund Husserl[4] and Kazimierz Twardowski,[6] both students of Franz Brentano. Through them, Bolzano became a formative influence on both phenomenology and analytic philosophy. Writings[edit] Gesamtausgabe (Collected Works), critical edition edited by Eduard Winter, Jan Berg (sv), Friedrich Kambartel, Bob van Rootselaar, Stuttgart: Fromman-Holzboog, 1969 ss. (89 vols. published). Wissenschaftslehre, 4 vols., 2nd rev. ed. by W. Schultz, Leipzig I–II 1929, III 1980, IV 1931; Critical Edition edited by Jan Berg: Bolzano's Gesamtausgabe, vols. 11–14 (1985–2000). Bernard Bolzano's Grundlegung der Logik. Ausgewählte Paragraphen aus der Wissenschaftslehre, Vols. 1 and 2, with supplementary text summaries, an introduction and indices, edited by F. Kambartel, Hamburg, 1963, 1978². Bolzano, Bernard (1810), Beyträge zu einer begründeteren Darstellung der Mathematik. Erste Lieferung (Contributions to a better grounded presentation of mathematics; Ewald 1996, pp. 174–224 and The Mathematical Works of Bernard Bolzano, 2004, pp. 83–137). Bolzano, Bernard (1817), Rein analytischer Beweis des Lehrsatzes, dass zwischen je zwey Werthen, die ein entgegengesetzes Resultat gewähren, wenigstens eine reele Wurzel der Gleichung liege, Wilhelm Engelmann (Purely analytic proof of the theorem that between any two values which give results of opposite sign, there lies at least one real root of the equation; Ewald 1996, pp. 225–48. Franz Prihonsky (1850), Der Neue Anti-Kant, Bautzen (an assessment of the Critique of Pure Reason by Bolzano, published posthumously by his friend F. Prihonsky).*Bolzano, Bernard (1851), Paradoxien des Unendlichen, C.H. Reclam (Paradoxes of the Infinite; Ewald 1996, pp. 249–92 (excerpt)). Translations and compilations[edit] Theory of Science (selection edited and translated by Rolf George, Berkeley and Los Angeles: University of California Press, 1972). Theory of Science (selection edited, with an introduction, by Jan Berg. Translated from the German by Burnham Terrell, Dordrecht and Boston: D. Reidel Publishing Company, 1973). Theory of Science, first complete English translation in four volumes by Rolf George and Paul Rusnock, New York: Oxford University Press, 2014. The Mathematical Works of Bernard Bolzano, translated and edited by Steve Russ, New York: Oxford University Press, 2004 (re-printed 2006). On the Mathematical Method and Correspondence with Exner, translated by Rolf George and Paul Rusnock, Amsterdam: Rodopi, 2004. Selected Writings on Ethics and Politics, translated by Rolf George and Paul Rusnock, Amsterdam: Rodopi, 2007. Franz Prihonsky, The New Anti-Kant, edited by Sandra Lapointe and Clinton Tolley, New York, Palgrave Macmillan, 2014. See also[edit] List of Roman
Named after Bolzano[edit] Bolzano's theorem, or "intermediate value theorem", a theorem in mathematical analysis Bolzano–Weierstrass theorem, a theorem concerning sequences in real analysis Notes[edit] ^ a b
References[edit] Boyer, Carl B. (1959), The History of the Calculus and Its Conceptual
Development, New York: Dover Publications, MR 0124178 .
Boyer, Carl B.; Merzbach, Uta C. (1991), A History of Mathematics, New
York: John Wiley & Sons, ISBN 978-0-471-54397-8 .
Ewald, William B., ed. (1996), From Kant to Hilbert: A Source Book in
the Foundations of Mathematics, 2 volumes, Oxford University
Press CS1 maint: Extra text: authors list (link) .
Künne, Wolfgang[de] (1998), "Bolzano, Bernard", Routledge
Encyclopedia of Philosophy, 1, London: Routledge,
pp. 823–827 CS1 maint: Multiple names: authors list (link)
. Retrieved on 2007-03-05
Veverková, Kamila, "Kleinere Schriften des deutschen Lehrers und
Priester Anton Krombholz[cs] (1790–1869)." In: Homiletisch –
Liturgisches Korrespondenzblatt – Neue Folge. Nr 107, Jg 28/2011,
str. 758-782. ISSN 0724-7680.
O'Connor, John J.; Robertson, Edmund F. (2005), "Bolzano", MacTutor
History of
Further reading[edit] Edgar Morscher (de) (1972), "Von Bolzano zu Meinong: Zur Geschichte des logischen Realismus." In: Rudolf Haller (ed.), Jenseits von Sein und Nichtsein: Beiträge zur Meinong-Forschung, Graz, pp. 69–102. External links[edit] Wikimedia Commons has media related to Bernard Bolzano. Morscher, Edgar. "Bernard Bolzano". In Zalta, Edward N. Stanford
Encyclopedia of Philosophy.
Šebestík[cs], Jan. "Bolzano's Logic". In Zalta, Edward N. Stanford
Encyclopedia of Philosophy. CS1 maint: Multiple names: authors
list (link)
Morscher, Edgar. "The Principles of Equality and Liberty in Bolzano's
Authority control WorldCat Identities VIAF: 24615537 LCCN: n50043118 ISNI: 0000 0001 2277 5147 GND: 118513117 SELIBR: 261171 SUDOC: 028434307 BNF: cb12027042g (data) MGP: 96330 NDL: 00433782 NKC: jk01012 |