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The Logical Grammar of Kant's Twelve Forms of Judgment : a Formalized Study of Kant's Table of Judgments

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University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations 1896 - February 2014 1-1-1972 The logical grammar of Kant's twelve forms of judgment : a formalized study of Kant's table of judgments. Kirk Dallas Wilson University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_1 Recommended Citation Wilson, Kirk Dallas, "The logical grammar of Kant's twelve forms of judgment : a formalized study of Kant's table of judgments." (1972). Doctoral Dissertations 1896 - February 2014. 2172. https://scholarworks.umass.edu/dissertations_1/2172 This Open Access Dissertation is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations 1896 - February 2014 by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. THE LOGICAL GRAMMAR OF KANT'S TWELVE FORMS OF JUDGMENT- A FORMALIZED STUDY OF KANT'S TABLE OF JUDGMENTS A Dissertation Presented By Kirk Dallas Wilson Submitted to the Graduate School of the University of Massachusetts in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY February, 1972 Philosophy Kirk Dallas Wilson All Rights Reserved ) ) ) IHE LOGICAL GRAMMAR OF ICANT’S TWELVE FORMS OF JUDGMENT A FORMALIZED STUDY OF KANT'S TABLE OF JUDGMENTS A Dissertation By Kirk Dallas Wilson Approved as to style and content by: irman of Committee) ^Head of Department) (Member (Member) ^Member (Month (Year acknowledgments My deepest gratitude and thanks is extended to Professor Leonard H. Ehrlich whose incisive questions and criticisms forced me to think hard about the topics explored in this dissertation. His help was also invaluable with regard to the translations of Kant that appear in the text, I thank Professor Bruce Aune for his comments on all aspects of the dissertation. AlsOj I thank Professors Gareth Matthews and V. C. Chappell for their comments and much appreciated encouragement and assurances. Special gratitude for his encouragement and understanding goes to the late Professor Joseph W. Swanson whose death prohibited him from serving on my dissertation committee until its end. His loss is felt deeply by all who knew him as friend and teacher. CONTENTS CHAPTER I Formalism and Kant’s Table of Logical Functions 1 § - 1 On the Character of Kant’s Logic of Judgment 1 i 2 - Some Modem Puzzles 5 § 3 - A Method of Investigation 13 CHAPTER II The Logical Functions of the Traditional Categorical Judgment 20 § 1 - The Universal and Particular Quantifiers 21 § 2 - Quality and the Copula 28 § 3 - The Meaning of Quantification and the Theory of Extension 38 CHAPTER III Singular Quantity, Infinite Quality, and "Complex" Judgments 51 § 1 - The Logic of Singular Quantification 51 1. Singular Quantification 51 2. The Problem of Proper Names 54 3. The Interrelationship of Universal and Singular Judgments 59 § 2 - The Infinite Judgment: An Alleged Subtlety in General Logic 66 1. The Unity of the Infinite Judgment 66 2. The "Subtlety" of the Infinite Judgment 72 3. An Assessment of This Subtlety: The Logical Importance of the Infinite Judgment 75 § 3 - The Hypothetical and Disjunctive Judgments 78 1. The Hypothetical Judgment 81 2. The Disjunctive Judgment 85 § 4 - On Conjunction 89 IV V CHAPTER IV The Logic of Modality § 1 - The Role of Logical Modalities in Judgment 96 - § 2 The Syntax of Modal Forms 101 — § 3 The Unities of the Modal Forms 110 1. The Problematic Judgment HI 2. The Assertoric Judgment II5 3. The Apodictic Judgment II9 § 4 - Negative Modalities and Contraposition 122 1. The Judgments of Negative Modality 122 2. Contraposition 127 CHAPTER V The Certainty of Judgment: Judgment’s Subjective Side 133 § 1 - Assent and the Theory of Certainty 134 § 2 - Opinion, Belief, and Knowledge 142 CHAPTER VI Kant’s Theory of the Forms of Judgment: Some Final Comments 155 § 1 - The Problem of Completeness 155 § 2 - A Point About Logical Theory 162 i 3 - A Concluding Assessment 170 FOOTNOTES 174 WORKS CITED 190 SUMMARY OF SYMBOLS AND FORMULAS 194 SUMMARY OF TABLES 195 CHAPTER I FORMALISM AND KANT’S TABLE OF LOGICAL FUNCTIONS - § 1 On the Character of Kant’s Logic of Judgments Kant’s general logic is a logic of judgments, rather than of sentences or of propositions in the modern sense of hypostatized meanings. A judgment, according to Kant, is a representation of unity in a cognition. Judgment involves bringing concepts or other judgments into a set of relations in order to represent how they belong to one another in an objective unity. Therefore, in all cases judgment is the mediate knowledge of one representation (a concept or a judgment) by means of another. In a subject-predicate judgment, for example, the knowledge of the subject is mediated by means of the predicate. The relation through which this mediation takes place is the form of the judgment.^ The form of the judgment rests upon what Kant calls the logical function of the understanding involved in making the judgment. In the "Transcendental Analytic’’ of the Critique of Pure Reason, ^ Kant displays these logical functions, grouped under four headings, by means of a table (B95): Quantity Quality Un iversal Affirmative Particular Negative Singular Infinite 1 2 Relation Modality Categorical Problematic H^^pothetical Assertoric Disjunctive Apodictic A function is ”the unity of the act of bringing various representations under one common representation" (B93). A function then, much like a function in mathematics,^ is an operation ("act") upon arguments (for Kant these arguments are either concepts or other judgments) which is law-governed in uniquely determining a value for those arguments. For Kant, this value is a unity of a specific kind consisting in the relation which is thought between the arguments. Each kind of unity is called a moment of unity. For instance, the logical function of universal quantification yields the moment of unity thought between two concepts by uniting them in a universal judgment. This unity is expressed by the relation of the predicate’s pertaining to the whole extension of the subject without exception. Similarly, the logical functions of particular and singular quantification yield, respectively, the unity of the predi- cate’s pertaining to some of the extension of the subject (the particular judgment) and that of the predicate’s pertaining to an individual (the singular judgment). The other logical functions yield unity in judgments in a similar manner. The moment of unity of the affirmative judgment is represented by the function of affirming the relation between the subject and predicate; that of the negative judgment, by the function of denying this relation; and tliat of the infinite judgment, by the function of a negative predicate in an affirmative judgment. Tlie unity 3 of the categorical judgment is represented by joining tnvo concepts together in the relationship of subject and predicate by the copu- lative function (the copula); that of the hypothetical, by joining two judgments in a conditional relation by the function ’if. ..then and that of the disjunctive, by joining two or more judgments by the function ’either... or ’. (One should not think of these last tv-70 functions as the corresponding truth-functional connec- tives of the modem propositional calculus. Kant defines the functions of the hypothetical and disjunctive judgments as yielding a specific kind of unity in consciousness, a way of thinking the judgments to be related, and not as yielding a truth-value. ) Finally, the unity of the problematic judgment is represented by a function expressing the possibility of the cognition; that of the assertoric, by a function expressing the actuality (truth) of the cognition; and that of the apodictic, by a function expressing the necessity of the cognition. A judgment is a unity constituted by the moments of unity resulting from each logical function comprising the judgment. How the unity of the whole judgment is constructed from these moments will be, in a broad sense, the topic of this dissertation. Kant believes that this set of logical functions corresponds to the logical forms appropriate for a general, or formal, logic. The table itself is based upon Kant’s own v7ork and lectures on general logic. In presenting the table in the Critique , Kant claims that it does not differ ”in any essential respects” from the classificatory table of judgments commonly provided by logicians (695-96).“^ General 4 logic IS formal in the sense that it treats relationships between concepts in a judgment or beliveen judgments themselves in inferences irrespective of the content of that which is related. Kant says, General logic . abstracts from all content of knowledge . and considers only the logical form in the relation of any knowledge to other knowledge (B79). Moreoever, general logic has universal applicability to all areas of thought. In characterizing general logic, Kant maintains, The sphere of logic is quite precisely delimited; its sole concern is to give an exhaustive exposition and a strict proof of the formal rules of all thought (Bix). Thus, general logic deals in a precise manner with the traditional question of logic, "What is correct reasoning?" Kant, in following the practice of his own day, divides general logic into two separate disciplines: the Analytic, which deals with the principles of the formal assessment and criticism of all reasoning, and the Dialectic, which exposes dialectical illusion (fallacy) in reasoning. Hence, by the analytic of general logic Kant intends to mark off what is considered today as the domain of elementary formal logic; namely, the specification of logical forms and of the formal principles of valid inference. Hence, we can interpret each function as a logical constant of a possible judgment.^ Where a modern logician would speak of trans- lating a sentence into a symbolic notation to reveal what he wishes to consider its logical form, Kant would speak of classifying a judgment according to the table of logical functions.
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