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'.

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.