Venn, best known for his diagrams for set theory, primarily studied logic and probability theory. The present book is a study of the principles of logic, with special emphasis on inference and induction.

From the Preface to the First Edition (1889): "As many readers will probably perceive, the main original guiding influence with me--as with most of those of the middle generation, and especially with most of those who approached logic with previous mathematical or scientific training--was that of Mill ... I still continue to regard the general attitude towards phenomena, which Mill took up as a logician, to be the soundest and most useful for scientific study ... "

From the Preface to the Second Edition (1907): "Though thus leaving the main outlines unaltered I have done what I could to improve the work, and to try to bring it up to date ... A number of paragraphs have been altered, others have been re-written, and many hundreds of minor alterations, additions and corrections inserted ... "

Readership

Graduate students and research mathematicians.

Table of Contents

• The physical foundations of inference, or the world as the logician regards it: an exposition of the principal assumptions demanded for the establishment of a material or objective system of logic
• The foundations of logic considered more in detail, and especially in respect of what is demanded for inference; (I) Sequences of phenomena, or laws of causation
• Continuation of the previous subject in respect of (II) Co-existences; and comparison of these with sequences through the same three stages of advancing precision and completeness
• The uniformity of nature; or that wide conception of regularity in the external world, which is the objective counterpart of inferribility
• The subjective foundations of induction, or the principal postulates demanded on the mental side
• Language: a discussion of the principal questions involved in its reference, functions, medium, and varieties
• Terms; as interpreted and subdivided in logic
• Propositions: their general nature and composition
• The schedule of propositions: the various ways in which they may be arranged and subdivided for logical purposes
• Hypothetical and disjunctive judgments; their distinctive characteristics, and the circumstances of their origin
• Definition; in logic and in science
• Division, in its old interpretation: the simple analysis of the denotation of terms
• Division scientifically considered: further analysis and development
• Induction; or the process of generalizing an attribute, observed in certain objects, over the whole class to which they belong
• The syllogism in relation to induction: modified acceptance of Mill's view
• Analysis and synthesis, regarded as correlated applications of the general process of hypothesis
• Inductive methods: the analysis of the antecedents, and exclusion of all but the cause
• Standards and units, as applicable to physical objects or events
• Standards and units as applied directly to psychical data
• Geometrical data: discussion of some of the difficulties commonly felt in their realization
• Explanation and verification, as steps towards the methodization and establishment of our knowledge of nature
• A universal or perfect language
• Extensions of our general powers of observation; or the nature and limits of our control over space and time
• The ideal of logic and methodology; or the degree and kind of knowledge at which induction may legitimately aim
• Speculation and action; or the logical and scientific view of the world as modified by our practical tendencies