The work opens by establishing that science arises from discovering identity amidst diversity, where all reasoning rests upon the fundamental laws of thought: identity, contradiction, and duality. The author demonstrates that induction is simply the inverse process of deduction, requiring prior knowledge of deductive rules to interpret the results of experience correctly. Formal logic forms the necessary foundation for all complex scientific inquiry, allowing the complete development of consequences from any given premises through the principle of substitution. The discussion then moves into the principles of number, variety, and the theory of probability, highlighting the inverse method of probabilities as the true foundation of inductive conclusions.
Since no inductive result can attain absolute certainty, probability theory is essential for determining the logical value of every inference. Subsequent sections analyze the exact measurement of phenomena, standards of measurement, and methods for eliminating error and approximating natural laws. The final books investigate observation, experiment, generalisation, analogy, and classification, showing how complex phenomena are resolved into rational laws. The treatise concludes with philosophical reflections on the limits of scientific method, arguing against a purely negative philosophy that presumes to encompass existence while ignoring mental phenomena.
