W. E. Johnson, Logic: Part I (1921)
CONTENTS
PREFACE
INTRODUCTION
§ 1. Definition of Logic. Grounds for including the theory of induction
§ 2. Thinking includes perceptual judgments
§ 3. All ulterior motives of the pursuit of truth irrelevant to the analysis and criticism of thought
§ 4. Relation of Logic to the Art of Thinking
§ 5. Logic, Aesthetics and Ethics as the three normative studies
§ 6. Relation of Logic to Universal Grammar
§ 7. Logic and Mathematics. Methodology. Pure and Applied Mathematics
§ 8. Historical sketch of the problems connecting Logic with Philosophy and with Psychology. Realism, Conceptualism and Nominalism. Materialistic and Empirical Logic
§ 9. Special features of the author's treatment of Logic
CHAPTER I
THE PROPOSITION
§ 1. Sentence, assertion and proposition
§ 2. Assertion as conscious belief
§ 3. Necessity for recognising the mental attitude in logic
§ 4. Relation between grammatical and logical analysis
§ 5. Connected functioning of substantive and adjective in the proposition
§ 6. Criticism of the view that the essential nature of the proposition is a statement of identity
§ 7. The proposition regarded as characterising the fact, and its analogies with the adjective
CHAPTER II
THE PRIMITIVE PROPOSITION
§ 1. Account of the psychologically primitive form of assertion -- exclamatory or impersonal
§ 2. The need of separate presentment for the most elementary forms of judgment
§ 3. Criticism of Mr Bradley's dictum 'distinction implies difference'.
§ 4. Illustrations of less primitive forms of assertion
§ 1. Definition of compound and simple as applied to propositions
§ 2. Distinction between the different forms of compound propositions; the logical conjunctions; distinction between the enumerative and conjunctive 'and'
§ 3. The first law of thought called 'The Law of Double Negation'
§ 4. The laws of conjunctive propositions
§ 5. The four forms of composite proposition and their immediate implications
§ 6. Complementary and supplementary propositions and their rules
§ 7. Criticism of the paradoxical forms of the composite, and preliminary explanation of the solution of the paradox
§ 8. The bearing of the distinction between hypothesis and assertion upon the paradox
§ 9. Interpretation of compound propositions as expressing possible conjunctives and necessary composites. Table of all the possible relations of one proposition to another
§ 1. Definition of primary and secondary propositions and of pre-propositional adjectives
§ 2. Modal adjectives as a species of pre-propositional. The adjectives 'true' and 'false' in this connection
§ 3. The opposition of modal adjectives
§ 4. Antithesis between 'certified' and 'uncertified'
§ 5. The rule that holds universally between two antithetical modals
§ 6. Threefold meanings of 'necessary' and 'possible'
§ 7. Antithesis of 'certified' and 'uncertified' as epistemic; antithesis of 'nomic' and 'contingent' as constitutive
§ 8. Comparison of Mill's distinction between verbal and real propositions, with Kant's distinction between analytic and synthetic propositions
§ 9. Summary of the treatment of modal adjectives in connection with secondary propositions
§ 1. The nature of pure negation and its different degrees of significance
§ 2. The importance of negation determined by its relevance to a specific
purpose
§ 3. Can there be a proposition where there is nothing corresponding to the subject-term? With illustrations of elementary forms of obversion and contradiction
§ 4. An account of the incomplete proposition 'S is'
§ 5. The hypothetical element in the proposition 'S is'
§ 6. Summary: determinateness of fact contrasted with indeterminateness of knowledge
CHAPTER VI
THE PROPER NAME AND THE ARTICLE
§ 1. Distinction between the proper and the descriptive name
§ 2. Proper name explained in terms of the introductory and referential articles
§ 3. Distinction between the connotation and the etymology of a name
§ 4. Distinctions between the four kinds of article or applicatives
§ 5. The demonstrative applicatives
§ 6. Special difficulty which attaches to the notion of a proper name
§ 7. Ostensive definition
CHAPTER VII
GENERAL NAMES, DEFINITION AND ANALYSIS
§ 1. Connection between general names and the applicatives
§ 2. Distinction between connotation and comprehension. Can adjectives be predicated of abstract names?
§ 3. The nature of the analysis involved in definition. Definition by means
of substitution of phrase. The indefinable
§ 4. Analytic and synthetic modes of definition
§ 5. Partition, resolution and analysis
CHAPTER VIII
ENUMERATIONS AND CLASSES
§ 1. The relation 'comprising' as defining the nature of an enumeration and
an item. The three operators for enumerations
§ 2. Enumerations of different orders
§ 3. Distinction between ' comprised' and 'included'
§ 4. Connection between enumerations and classes and the question whether
'class' is a genuine entity
§ 5. The nature and reality of the class as determined by the type of adjective significantly predicable of it
§ 6. Attempted proof of the genuineness of 'class' by the so-called principle of Abstraction. Charge of petitio principii and ignoratio elenchi against
the alleged proof
CHAPTER IX
THE GENERAL PROPOSITION AND ITS IMPLICATIONS
§ 1. Pure general propositions. Thing
§ 2. Analysis of the general proposition, showing how adjectives alone function in the predicate
§ 3. Different interpretations of the universal and particular proposition, and the resultant modifications in their relations of implication and opposition
§ 4. Comparison with traditional scheme
§ 5. Development of the immediate implications of the universal proposition as ordinarily interpreted; with tables of immediate inferences
§ 6. Development of the analogies between universals and particulars on the one side and necessary composites and possible conjunctions on the other
§ 7. Formulation of general propositions in terms of classes. The principle underlying Euler's and Venn's diagrams
§ 8. Summary
CHAPTER X
EXISTENTIAL, SUBSISTENTIAL AND NARRATIVE PROPOSITIONS
§ 1. The proper principle for the Classification of Propositions
§ 1. Philosophical distinction between Existential and Subsistential
§ 3. The so-called existential formulation of Propositions : Two meanings of the Universe of Discourse
§ 4. The interpretation of mythical propositions as elliptically secondary
§ 5. The Narrative Proposition
§ 6. Distinction between fictitious and historical narratives
§ 7. The relation between the existence of a class and the existence of an individual
CHAPTER XI
THE DETERMINABLE
§ 1. The fundamentum divisionis, for which the name Determinable is to stand. The analogy and distinction between the relation of an individual to its class and that of an adjectival determinate to its determinable
§ 2. Can abstracts be divided into singular and general? The corresponding distinction is properly between the comparatively determinate and the comparatively indeterminate. The notion of a determinable as generating its determinates
§ 3. The increase of intension that determines a decrease of extension to be supplemented by the superdeterminateness of adjectival characterisation. Classification as starting from a summum genus constituted by mere determinables and terminating in an ultima species constituted by absolute determinates. Illustration from Botany
§ 4. Relations between determinates under a given determinable. Incompatibility. Order of qualitative betweenness, continuous or discrete. Complex determinables
§ 5. Important consequences of the distinction between the absolutely determinate and the comparatively indeterminate
CHAPTER XII
THE RELATION OF IDENTITY
§ 1. Identity goes along with Otherness, the two being co-opponent relations. Verbal and Factual Identification involve the same kind of identity, the nature of the propositions only differing
§ 2. False sense in which identity has been said to imply difference
§ 3. Relations like and unlike; similar and dissimilar; agreeing and disagreeing
§ 4. Adjectives comparable and disparate. Distensive magnitude. Difference properly adjectival
§ 5. Adjectival comparison implies substantival otherness. False view of the notion of 'numerical' difference
§ 6. Criticism of the Leibnizian dictum: the identity of indiscernibles
§ 7. Can identity be defined? Identity carries co-implication and substitutability. Exception for secondary proposition
§ 8. Identity and the Continuant, psychical or physical. Relation of Occurrent to Continuant. The causal bond that constitutes the unity of Experience
CHAPTER XIII
RELATIONS OR TRANSITIVE ADJECTIVES
§ 1. Monadic, diadic, triadic, etc. adjectives and propositions. Every relative implies its correlative
§ 2. The substantive-couple characterised by an adjective-couple
§ 3. Illustrations of 'analogy' extending beyond arithmetical ratio
§ 4. The coupling-tie and the characterising-tie, expressed in the grammatical rules of governance and accordance
§ 5. The paradox of relation. Distinction between tie and relation. The relation 'characterised' as unit relation entering into all adjectives and relations
§ 6. How adjectives, relations and propositions may function as substantives
§ 7. Relational propositions of triadic and higher orders. The cognates of a relation: permutations and bracketing. Relations between terms and possibilia
§ 8. The problem of the relation of assertion to the proposition. How ideas are involved in propositions
CHAPTER XIV
LAWS OF THOUGHT
§ 1. The logical meaning of consistency as distinguished from truth. The Laws of Thought may possibly be not enumerable as independents
§ 2. The value and functions of truisms
§ 3. In what sense are the principles of logic imperatives? The distinction between normative and positive sciences dealing with psychological material
§ 4. The fundamental formulae as used implicitly in building up the logical
system itself
§ 5. The three laws of identity: Transitive, Symmetrical, Reflexive
§ 6. The four Principles of Propositional Determination; and their import. Expression of the same for Adjectival Determination. These in generalised form. The distinction between false and not-true, true and not-false. These compared with male and female
§ 7. Defence of the first Principle of Propositional Determination. Truth as temporally unalterable and as capable of only one meaning
§ 8. The four Principles of Adjectival Determination, as bringing out the relation of an adjective to its determinable. Postulate of the absolutely determinate character of the real. Substantival Categories distinguished by the Adjectival Determinables by which they are characterisable. The possibility of exhaustively comprehending the range of variation of a determinable. Summary
§ 9. The four Principles of Connectional Determination. These embody the purely formal properties of the causal relation. Its complementary aspects -- Agreement and Difference. The fundamental postulate involved in the existence of Laws of Nature. The plurality and uniqueness both of cause and of effect
§ 10. The bearing of these principles upon the problem of internal and external relations
INDEX