Theory of Science : Attempt at a Detailed and in the Main Novel Exposition of Logic with Constant Attention to Earlier Authors

During the earliest stages of my work on this translation, I enjoyed the co-operation and advice of my teacher, the late Henry S. Leonard. A preliminary draft of the first volume was finished in 1958, but at that time I was still thinking of a complete translation of all four volumes. I was eventually persuaded that early complaints about the unnecessary bulk of the work had their point. Kambartel's very successful attempt at shortening the first two volumes (Bernard Bolzano's Grundlegung der Logik, Hamburg, 1963) finally convinced me that an abbreviated version was not only feasible, but desirable. With the help of a Summer Research Grant from the University of Waterloo I could resume the work in the summer of 1967. A grant from the Canada Council covered most of the cost of manuscript preparation. I am deeply indebted to Professor Roderick Chisholm for reading the manuscript and making many suggestions concerning selection and translation, and to Mr. Craig Townson for his help in the preparation of the final manuscript. Thanks are also due to the Macmillan Company for allowing me to quote from N. K. Smith's translation of Kant's Critique of Pure Reason, and to the Library of the University of Manitoba for lending me their copy of the Wissenschaftslehre for almost a year. Waterloo, September 1970 ROLF GEORGE VII CONTENTS This table lists the complete contents of the first three books of the Wissenschaftslehre. Sections with \* are translated either completely or in substantial part. Unstarred sections without page numbers are omitted altogether. ACKNOWLEDGMENTS vii EDITOR'S INTRODUCTION xxiii BIBLIOGRAPHY xlviii Some Remarks about the Usual Treatment of this Subject Some Remarks concerning the Basic Laws of Thought as they are Discussed in other Handbooks BOOK TWO THEORY OF ELEMENTS 46 Purpose, Contents, and Sections of this Book PART I Of Ideas in Themselves 47 Contents and Chapters of this Part CHAPTER I Of the Concept of an Idea in Itself 48\* What the Author Means by an Idea in Itself, and an Idea which Someone has 49\* Distinction of the Concept of an Idea in Itself from some others that are Closely Related to it 50\* Justification of this Concept 51 This Concept has been Used before 52 Unsuccessful Attempts at Defining these Concepts 53 How these Two Concepts have so far been Treated CHAPTER 2 Internal Attributes of Ideas in Themselves 54 Ideas in Themselves do not have Existence 55 Ideas in Themselves are neither True nor False 56\* Parts and Content of Ideas in Themselves 57\* Of some Cases in which an Idea is only Apparently Complex 58\* The most Important Kinds of Complexity in Ideas 59\* Interpretation of some Grammatical Forms, especially the Form 'This A' 60 Concrete and Abstract Ideas 61\* There Must also be Simple Ideas xi 62 There is no Idea with Greatest Content 78 63\* Whether the Parts of an Idea are the same as the Ideas of the Parts of its Object 78 64\* Whether the Parts of an Idea are the Ideas of the Attributes of the Object of that Idea 79 65 Comparison of § § 56-64 with the Received Theory 83 66\* The Concept of the Extension of an Idea 85 67\* Ideas without Referents 88 68\* Ideas with only a Finite Number of Objects, Singular Ideas 89 69 Redundant Ideas 91 70 Consistent and Inconsistent Ideas 92 71 Two Consequences 94 72\* What the Author Means by Intuitions 94 73\* Concepts and Mixed Ideas 97 74\* Clarification of the Preceding Definitions 98 75\* Some Remarks Concerning the Different Ways in which we Designate Intuitions and Concepts 76 Justification of these Definitions 77 Review of other Positions 78 Differences between Concepts with Respect to Content and Extension 79\* Whether the Ideas of Time and Space are Intuitions or Concepts 80\* Ideas of Attributes and Relations 81 Ideas of Matter and Form 82 The Idea of a Class, in Particular the Idea of a Class of Individually Listed Objects 83 Further Ideas which have the Idea of a Class as a Part 84 Concepts of Sets and Sums 85\* The Concept of a Sequence 86\* Concepts of a Unit, of a Manifold, and of Universality 87\* The Concept of Quantity, Finite as well as Infinite 88 Exceptive Ideas 89 Affirmative and Negative Ideas 90 Symbolic Ideas CHAPTER 3 Distinctions between Ideas that Stem from their Relation to each other 91 No Two Ideas are Exactly Equal; Similar Ideas xii 93 Relations between Ideas with Respect to their Content 93 Relations between Ideas with Respect to their Scope 94\* Relations between Ideas with Respect to their Objects 95\* Special Kinds of Compatibility: a. Inclusion 96\* b. The Relation of Mutual Inclusion or Equivalence 97\* c. The Relation of Subordination g8\* d. The Relation of Overlapping or Linking 99 Ideas of Absolutely Greatest and Smallest Scope, Highest and Lowest Ideas IOO Ideas that are Adjacent in Scope or Height IOI Whether a General Concept can be Found for any Arbitrarily Selected Set of Objects I02\* No Finite Set of Units Suffices to Measure the Scopes of all Ideas 103 Special Kinds of Incompatibility among Ideas 104 Coordinated Ideas 105 Some Theorems 106 Ideas of Kinds, Species, etc. J 5i 107 Opposing Ideas 151 108\* Ways in which the Relations Considered in § §93 ff. could be Extended to Ideas that do not have Referents CHAPTER 4 Distinctions among Ideas that Result from their Relations to other Objects 109 Correct and Incorrect Ideas of an Object no\* Complete and Incomplete Ideas of an Object in\* Essential and Inessential Attributive Ideas 112\* Common and Peculiar Attributive Ideas; Indicators, Marks 113 Basic and Derived Attributive Ideas 114 Ideas of Difference APPENDIX Earlier Treatments of the Subject Matter of this Part 115 Some General Remarks concerning the Difference between the Customary Presentation and My Own 116 Some Distinctions Made by Recent Logicians xiii 117 About the Five So-Called Predicables of the Ancients 118 Concerning the Categories and Post-Predicaments of the Ancients 119 Concerning the Categories and Concepts of Reflection of Modern Philosophers 120\* Concerning the Claim that Intension and Extension Stand in an Inverse Relation PART II Of Propositions in Themselves i2i Contents and Chapters of this Part CHAPTER I General Characteristics of Propositions 122 No Proposition in Itself is Real 123 Every Proposition Necessarily Contains several Ideas 124 Every Proposition can be Viewed as Part of another Proposition, even as Part of just an Idea 125 Every Proposition is either True or False, and Remains that Way Always and Everywhere 126\* Three Parts which are Obviously Contained in a Great Number of Propositions 127\* Parts which the Author Takes all Propositions to have 128 Attempted Definitions 129 Other Theories 130 The Extension of a Proposition is always the Same as the Extension of its Subject 131 Whether the Predicate Idea of a Proposition is Taken in its Full Extension 180 CHAPTER 2 Differences between Propositions which Arise from their Internal Constitution 132 Simple and Complex Propositions 133\* Conceptual and Empirical Propositions 134 Abstract and Concrete Propositions 184 135 Propositions Containing Ideas of Classes 184 xiv 136 Propositions with Negative Ideas 137 Various Propositions about Ideas: a. Assertions that an Idea has Reference 138 b. Denials that an Idea has a Reference 139 c. Propositions which Determine the Extension of an Idea 140 d. Propositions concerning the Relations between several Ideas 141 Propositions which Deal with other Propositions 142\* Propositions Asserting Actuality 143\* Propositions which Deal with Psychological Phenomena 144 Ethical and Related Propositions 145 Interrogative Propositions 146 Referring and Non-Referring Propositions, Singular and General Propositions 147\* The Concept of the Satisfiability of a Proposition 148\* Analytic and Synthetic Propositions 149 Propositions with Transponible Parts CHAPTER 3 Distinctions among Propositions which are Based upon their Relations to each other 150 No Two Propositions are Exactly Equal; Similar Propositions 151 Relations among Propositions with Respect to their Content 152 Relations among Propositions with Respect to their Extension 1 S3 Relations among Propositions with Respect to the Extension of their Predicate Ideas 154\* Compatible and Incompatible Propositions 155\* Special Kinds of Compatibility: a. The Relation of Deducibility 156\* b. Relations of Equivalence 157\* c. The Relation of Subordination 158\* d. The Relation of Overlapping 159\* Special Kinds of Incompatibility 160 Relations among Propositions which Result from the Number of Truths and Falsehoods in a Class of Propositions 161\* The Relation of Relative Satisfiability, or Probability, of a Proposition with Respect to other Propositions XV IÔ2\* The Relation of Ground and Consequence [Abfolge] 163 Questions and Answers 245 247 CHAPTER 4 Several Types of Propositions which State Relations between other Propositions 164 Propositions which State a Relation of Compatibility 165 Propositions which State a Relation of Incompatibility 166 Propositions which State a Relation of Complementation 167 Propositions which State a Relation of Probability 168 Propositions which State a Relation of Ground and Consequence 248 CHAPTER 5 Some Propositions whose Linguistic Expression Warrants Special Comment 169 Purpose of this Chapter 170 Propositions whose Linguistic Expression has the Form 'Nothing has attribute V 250 171 Propositions of the Form 'A certain A has b' 250 172 Propositions whose Linguistic Expression Contains the Word 'it' or 'one' or other Impersonal Forms 250 173 Propositions of the Form 'Some (or many) A are B' 174 Propositions of the Form 'n A are B' 251 175 Propositions of the Form 'A has (attribute) b to an equal, larger, or smaller degree than B' 251 176 Propositions of the Form 'Only A is B' and 'A is nothing but a B' 251 177 Propositions of the Form 'A is the case because B is the case' 178 Propositions of the Form 'A, as a C, is B' 179\* Propositions with 'if' and 'then' 180\* Propositions of the Form 'A determines B' 181 Propositions with 'Either-or' and Related Propositions 182\* Propositions which Contain the Concept of Necessity, Possibility or Contingency 183\* Propositions which Contain Time Determinations 184 Expressions which Must be Interpreted as a Class of several Propositions xvi Combination of Propositions of Forms I and II Combination of Negations with Negations III. Conclusions from the Assertion that an Idea has Reference Claims that a Proposition does not have a Referent 235-Combination of Propositions of Forms I and III 236 Combination of Propositions of Forms II and III Combination of Propositions of Form III with each other IV. Conclusions from the Assertion that an Idea is a Singular Idea 240-Combination of several Propositions of Previously Considered Forms V. Conclusions from the Assertion that an Idea is General VI. Conclusions from Determinations of the Scope of an Idea VII. Conclusions from Propositions which Assert a Relation between Ideas VIII. Conclusions from Propositions which State a Relation of Compatibility between other Propositions 248-IX. Conclusions from Propositions which State a Relation of 249 Ground and Consequence between other Propositions X. Conclusions from Propositions which State a Relation of Equivalence between others XI. Conclusions from Propositions which State a Relation of Contradiction between others XII. Conclusions from Propositions which State a Relation of Complementation between others XIII. Conclusions from Propositions which State a Relation of Probability APPENDIX Earlier Treatments of the Subject Matter of this Part Concerning the Distinction between Matter and Form of an Argument Concerning the Division of Arguments into Direct and Indirect 256-Immediate Inferences with Respect to Quantity, Quality, 259 Relation and Modality Immediate Inference by Rephrasing of Judgments Other Presentations of this Doctrine The Syllogism in the Received Logic xix 263 The First Principle of all Syllogisms 264 Division of Syllogisms into Categorical, Hypothetical, and Disjunctive 265-Categorical, Hypothetical, and Disjunctive Syllogisms 267 268 Inferences of the Faculty of Judgment BOOK THREE THEORY OF KNOWLEDGE 269 Purpose, Contents, and Divisions of this Book 303 PART I Of Ideas 270 Concept of an Idea in its Subjective Sense 304 271 To every Subjective Idea Belongs an Objective one 304 272 Every Subjective Idea is Real, but only as an Attribute of a Being 304 273 What we Call a Single Subjective Idea, and when we Say of several that they are or are not the Same 274 Whether several Equal Ideas can Occur Simultaneously in the same Being 275 Strength or Vividness of Subjective Ideas 276 Distinctions Among Subjective Ideas which Rest upon Corresponding Distinctions among Objective Ideas 277 We have Simple as well as Complex Ideas 278 We have Intuitions as well as Concepts 279 Sensible and Supersensible Ideas 280 Clear and Obscure Ideas 281 Distinct and Confused Ideas 282 Whether each of our Ideas has a Beginning and an End 283 Whether every Idea Leaves a Certain Trace after it has Disappeared 284 Effects which Result from the Traces of our Ideas 285\* Signs for our Ideas 286\* Description of the most Important Ways in which Ideas Originate 287 Opinions of Others on this Point 288 How the Lack or Cessation of an Idea is to be Understood xx 289 Survey of the most Important Activities and States of our Mind Connected with Ideas PART II Of Judgments 290 The Concept of a Judgment 291 Some Attributes Common to all Judgments 292 Individual Judgments; when we Say of several Judgments that they are the Same or not the Same 293\* Strength or Vividness of Judgments, and Confidence in a Judgment 294 Distinction between Judgments, Derived from Parallel Distinctions between Propositions 295 Clear and Obscure Judgments 296 Distinct and Confused Judgments 297 Whether every Judgment has a Beginning and an End 298 Whether every Judgment Leaves a Trace after it Disappears 299 Effects of These Traces of our Judgments 300\* Mediation of a Judgment by other Judgments 301 The Generation of Judgments by the Relation of Probability 302 How we Obtain our Immediate Judgments 303\* How we Arrive at, or could Arrive at, our most General Judgments of Experience 304\* Other Opinions on this Subject 305 The Doctrine of Critical Philosophy concerning this Point 306 Survey of the most Important Activities and States of Mind which Concern the Business of Judging PART III Of the Relation between our Judgments and Truth 307 More Precise Determination of the Concepts: Knowledge, Ignorance, and Error 308 Grounds for the Possibility of Ignorance in Man 309 Grounds for the Possibility of Error, and Circumstances which Promote Error 310 Other Treatments of the same Subject 311 Origin of True Judgments-Understanding and Reason 312 Whether we can Recognize a Truth without Recognizing its Grounds xxi 313 Grounds for the Recognition of Truth 314 Whether there is a Definite Limit to our Knowledge 35a 315\* The Doctrine of Critical Philosophy on this Subject 316 Survey of the most Important Distinctions between Judgments, Based on their Truth Values PART IV Of Certainty, Probability, and Confidence in Judgments 317\* Definition of the Concepts of Certainty and Probability with Respect to Thinking Beings 318\* Circumstances which Determine the Confidence of our Judgments 319 The most Important Levels of our Confidence 320\* How the Various Degrees of Confidence can be Represented Numerically 321\* Knowledge and Belief BOOK FOUR HEURETIC 329\* Tentative Acceptance or Indirect Procedure 379\* The Discovery of Causes for Given Effects 384 The Discovery of Effects of Given Causes BOOK FIVE THEORY OF SCIENCE PROPER This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.