Theory of Science : A Selection, with an Introduction

The present selection from the Wissenschaftslehre (Sulzbach 1837) of Bernard Bolzano (1781-1848) aims at giving a compact view of his main ideas in logic, semantics, epistemology and the methodology of science. These ideas are analyzed from a modern point of view in the Introduction. Furthermore, excerpts from Bolzano's correspondence are included which yield important remarks on his own work. The translation of the sections from the Wissenschaftslehre are based on a German text, which I have located in the Manuscript Department of the University Library in Prague (signature: 75 B 459). It was one of Bolzano's own copies of his printed work and contains a vast number of corrections made by Bolzano himself, thus representing the final stage of his thought, which has gone unnoticed in previous editions. The German originals of Bolzano's letters to M. J. Fesl, J. P. Romang, R. Zimmermann and F. Pi'ihonsky are in the Literary Archive of the Pamatnfk narodnfho pfsemnictvf in Prague. The original of the letter to F. Exner belongs to the Manuscript Department of the Osterreichische Nationalbibliothek in Vienna. The original of the letter to J. E. Seidel is preserved in the Museum of the City of Ceske Budejovice.

Editor’s Introduction.- I. Logic as a Theory of Science.- II. Propositions and Sentences.- III. Ideas in Themselves.- IV. The Reduction of Sentences.- V. Judgment and Knowledge.- VI. Intuition and Concept.- VII. The Notion of Variation.- VIII. Analytic and Synthetic Propositions.- IX. Consistency and Derivability.- X. Degree of Validity and Probability.- XI. The Objective Hierarchy of Propositions.- XII. Set and Continuum.- XIII. Infinite Sets.- XIV. Natural Numbers.- XV. Conclusion.- A A Selection from the Wissenschaftslehre (Sulzbach 1837, Leipzig 1914—31) [‘+A’ (‘-A’) means including (excluding) the Anmerkung(en)]: Volume One.- § 1. What the Author Understands by Theory of Science.- § 2. Justification of this Concept and Its Designation.- § 15. Plan for Carrying out Logic According to the Author’s Understanding.- One / Theory of Fundamental Truths.- One / On the Existence of Truths in Themselves.- § 19. What the Author Understands by a Proposition in Itself (+A).- § 21. That Others Have Already Made Use of this Concept.- § 24. Various Meanings of the Words: True und Truth (-A).- § 25. What the Author Understands by Truths in Themselves.- § 26. Differentiation of this Concept from Some that Are Related to It.- § 30. The Meaning of the Claim that there Are Truths in Themselves.- § 31. Proof that there Is At Least One Truth in Itself (+A).- § 32. Proof that there Are a Number of Truths, Indeed an Infinite Number (+A).- Two / On the Possibility of Knowing the Truth.- § 34. What the Author Understands by a Judgment (-A).- § 35. Examination of Other Definitions of this Concept (Subsection 5).- § 36. What Would the Author Understand by a Cognition?.- § 40. How It Can Be Proved that We Know At Least One Truth.- § 41. How It Can Be Proved that We Are Capable of Knowing an Indefinitely Large Number of Truths (+A).- Two / Theory of Elements § 46. Purpose, Content and Sections of this Part.- One / On Ideas in Themselves.- § 48. What the Author Understands by Ideas in Themselves and by Ideas Possessed.- § 49. Differentiation of the Concept of an Idea in Itself from Some Related Concepts.- § 50. Justification of this Concept.- § 51. That this Concept Is Already Encountered in Others (Subsection 1).- § 54. Ideas in Themselves Have No Existence.- § 55. Ideas in Themselves Are neither True nor False (-A).- 56. Parts and Content of an Idea in Itself (-A).- § 58. Closer Examination of the Most Notable Ways in which Ideas Are Compounded.- § 60. Concrete and Abstract Ideas (-A).- § 61. There Must also Be Simple Ideas.- § 63. Are the Parts of an Idea the Same as the Ideas of the Parts of Its Object?.- § 64. Are the Parts of an Idea the Same as the Ideas of Its Object’s Properties? (-A).- § 66. The Concept of the Extension of an Idea (-A).- § 67. There Are also Objectless Ideas (+A).- § 68. There Are also Ideas that Have Only a Finite Set of Objects, and Singular Ideas as Well (-A).- § 70. Real and Imaginary Ideas (+A).- § 71. Two Consequences (+A).- § 72. What the Author Understands by Intuitions (-A).- § 73. What Is It that the Author Calls Concepts and Mixed Ideas?.- § 75. Some Remarks on the Difference between the Ways in which Intuitions and Concepts Are Designated.- § 78. Differences among Concepts with Respect to Content and Extension (+A 1–2, to p. 356,1. 12, of the German text).- § 80. Ideas of Qualities and Relations (-A).- § 84. Concepts of Sets and Sums (-A).- § 86. Concepts of Unity, Plurality and Universality.- § 87. Concepts of Quantity, Both Finite and Infinite (-A).- § 90. Symbolic Ideas (-A).- § 91. There Are No Two Completely Identical Ideas. Similar Ideas (+ A 1–2).- § 92. Relations among Ideas with Respect to Their Content (-A).- § 93. Relations among Ideas with Respect to Their Breadth (-A).- § 94. Relations among Ideas with Respect to Their Objects (-A).- § 95. Special Kinds of Compatibility: (a) Inclusion (+A).- § 96. (b) The Relationship of Mutual Inclusion, or Equivalence (-A).- § 97. (c) The Relationship of Subordination (-A).- § 98. (d) The Relationship of Intersection or Concatenation (-A).- § 102. No Finite Set of Standards Is Sufficient to Measure the Breadths of All Ideas.- § 103. Particular Kinds of Incompatibility among Ideas (-A).- § 108. How the Relationships Discussed in §§93ff Can Be Extended to Objectless Ideas as Well (+A).- § 120. On the Rule that Content and Extension Stand in an Inverse Relationship.- Volume Two.- Two / On Propositions in Themselves.- § 122. No Proposition in Itself Is an Existent.- § 123. Every Proposition Necessarily Contains Several Ideas. Its Content (-A).- § 124. Every Proposition Is Capable of Being Considered as a Component of Another Proposition, or Even of a Mere Idea.- § 125. Every Proposition Is either True Or False and True or False in All Times and at All Places.- § 126. Three Components that Are Undeniably Found in a Large Number of Propositions.- § 127. Which Components Does the Author Assume for All Propositions?.- § 130. The Extension of a Proposition Is Always the Same as the Extension of Its Base (-A).- § 133. Conceptual Propositions and Empirical Propositions (+A).- § 137. Various Propositions about Ideas: (a) Assertions of the Denotative Character of an Idea.- § 138. (b) Denials of the Denotative Character of an Idea (-A).- § 139. (c) Further Propositions that Define the Extension of an Idea More Closely.- § 146. Objectless and Denotative, Singular and General Propositions.- § 147. The Concept of the Validity of a Proposition.- § 148. Analytic and Synthetic Propositions (+A).- § 154. Compatible and Incompatible Propositions (-A).- § 155. Special Types of Compatibility: (a) The Relation of Derivability (+A).- § 156. (b) The Relation of Equivalence (+A).- § 157. (c) The Relationship of Subordination.- § 158. (d) The Relationship of Concatenation.- § 159. Special Types of Incompatibility (-A).- § 160. Relations among Propositions Resulting from Consideration of How Many True or False Propositions there Are in a Set (+A).- § 161. The Relationship of Comparative Validity or the Probability of a Proposition with Respect to Other Propositions (+A2 from p. 189, 1. 10, of the German text).- § 162. The Relation of Ground and Consequence.- § 167. Propositions which Assert a Relation of Probability.- § 168. Propositions which Assert a Relation of Ground and Consequence (Subsection 3).- § 174. Propositions of the Form: n A are B (+A).- § 179. Propositions with If and Then (+A).- §182. Propositions Containing the Concept of Necessity, Possibility or Contingency (-A).- Three / On True Propositions.- § 198. The Concept of a Ground-Consequence Relationship between Truths (-A).- § 199. Can the Inference Rule also Be Counted among the Partial Grounds of a Conclusion? (-A).- § 200. Is the Relation of Ground and Consequence Subordinate to that of Derivability?.- § 203. Only Truths Are Related as Ground and Consequence (Subsection 1).- § 204. Can Something Be Ground and Consequence of Itself? (-A).- § 205. Are Ground and Consequence in Each Case only a Single Truth or a Set of Several Truths?.- § 206. Can One Ground Have a Variety of Consequences or One Consequence a Variety of Grounds?.- § 207. Can One Regard the Consequence of a Part as the Consequence of the Whole?.- § 209. Can a Truth or a Whole Set of Truths Be both Ground and Consequence in One and the Same Relation? (-A).- § 210. Can a Set of Several Grounds Be Regarded as the Ground of a Set of Several Consequences?.- §211. Is there a Rank Order among the Parts of the Ground or of the Consequence?.- § 213. Can the Consequence of the Consequence Be Considered a Consequence of the Ground? (-A).- § 214. Can Every Truth Be Regarded not only as Ground but also as Consequence of Others? (-A).- § 215. Is there More than One Basic Truth? (+A).- § 216. Does the Process of Mounting up from Consequences to Its Grounds Have to Come to an End for Every Given Truth?.- § 217. What the Author Understands by Subsidiary Truths.- § 218. No Truth Can Be a Subsidiary Truth of Itself.- § 220. What Kind of Pictorial Representation Can Be Given for the Relationship that Prevails between Truths with Respect to Ground and Consequence?.- § 221. Some Criteria for Determining whether Certain Truths Have the Relationship of Dependence (+A).- Four / On Inferences.- § 223. Content and Purpose of this Chapter (+A).- § 224. Some Rules by which Conclusions to Given Premises Can Be Sought out.- § 243. Continuation [Assertions about Numbers].- Volume Three.- Three / Theory of Knowledge.- One / On Ideas.- § 270. Concept of an Idea in the Subjective Sense (-A).- § 271. There Is an Idea in Itself Attached to Every Subjective Idea (+A).- § 272. Every Subjective Idea Is Something Real, but only as an Attribute of a Substance.- § 285. Naming Our Ideas (Subsections 1–2).- Two / On Judgments.- § 290. The Concept of a Judgment.- § 291. Some Properties that Belong to All Judgments (-A).- § 292. What We Call a Single Judgment, and when We Say of Several Judgments that They Are Like or Unlike.- § 294. Classifications of Judgments that Arise from Classifications of Propositions with the Same Names.- § 298. Does Every Judgment Leave a Trace of Itself behind after It Has Passed away?.- § 300. Mediation of a Judgment by Other Judgments (-A).- § 303. How We Do Arrive at Our Most General Empirical Judgments and how We Can Arrive at Them (-A).- § 306. Survey of the Most Noteworthy Activities and States of Our Mind that Concern the Business of Making Judgments (-A).- Three / The Relationship of our Judgments to the Truth.- § 307. More Precise Definition of the Concepts: Knowledge, Ignorance and Error (-A).- § 309. What Is the Basis of the Possibility of Error and what Circumstances Promote Our Errors’ Occurrence?.- § 314. Are there Definite Limits to Our Capacity for Knowledge? (+A).- Volume Four.- Five / Theory of Science Proper.- One / General Theory.- § 395. The Supreme Principle of All Theory of Science (-A).- § 401. A Proper Scholarly Treatise Must also Indicate the Objective Connection between Truths, as far as Possible.- Four / On the Propositions which should Occur in a Scholarly Treatise.- § 525. Explaining a Truth’s Objective Ground (-A).- § 530. Proofs by Reduction to Absurdity (Subsection 1).- § 557. How to Prove a Statement Specifying the Composition of an Idea.- § 558. How the Proof that a Definition of a Given Proposition Is Correct Must Be Carried out (-A).- B Excerpts from Bolzano’s Correspondence.- Letter to J. E. Seidel, 26 January 1833 (Manuscript in Krajské muzeum v Ceských Bud?jovicích; transcription by Jan Berg).- Letter to M. J. Fesl, 8 February 1834 (Manuscript in Literární ar chív Památníku národního písemnictví v Praze; published in Wissenschaft und Religion im Vormärz. Der Briefwechsel Bernard Bolzanos mit Michael Josef Fesl (ed. by E. Winter and W. Zeil), Berlin 1965, p. 58,1. 4 – 1. 3 f.b.).- Letter to F. Exner, 22 November 1834 (Manuscript in Österreichische Nationalbibliothek Wien; published in Der Briefwechsel B. Bolzano’s mit F. Exner (ed. by E. Winter), Bernard Bolzano’s Schriften, vol. 4, Prague 1935, p. 62,1. 32 - p. 67, 1. 38).- Letter to J. P. Romang, 1 May 1847 (Manuscript in the same archive as Letter to M. J. Fesl (above); published in Philosophisches Jahrbuch der Görresgesellschaft, vol. 51, Fulda 1938, p. 50,1. 5f.b. - p. 53, 1. 16).- Letter to R. Zimmermann, 9 March 1848 (Manuscript in the same archive as Letter to M. J. Fesl (above); transcription by Jan Berg).- Letter to F. P?íhonský, 10 March 1848 (Manuscript in the same archive as Letter to M. J. Fesl (above); published in E. Winter: Der Böhmische Vormärz in Brief en B. Bolzanos an F. P?ihonskí, Berlin 1956, p. 285,1. 1 – 1. 16).- A. Works by Bolzano.- 1. Works on Logic, Epistemology and Methodology of Science.- 2. Works on Mathematics.- B. Works on Bolzano.- 1. General Works.- 2. Biographies.- 3. Logic.- 4. Mathematics.- 5. Metaphysics.- 6. Theology.- 7. Social Philosophy.- 8. Aesthetics.- Name Index.