Logic, Vol. 2

by Alexander Bain

Explore how mathematics moves from numbers to symbols and shapes, and why proofs stay grounded in experience.
This edition surveys the logic behind algebra and geometry, showing how arithmetic rules extend to algebraic quantities. It explains why signs and operations must be justified, and how solving equations reveals deeper structure in numbers and terms. The text traces the shift from concrete diagrams to abstract formulas, and it discusses Euclid, Descartes, and the birth of algebraic geometry. It also highlights the limits of symbol use and the need to verify results against real objects and experiments.



How arithmetic rules become rules for algebra and why they matter.
How equations are formed, transformed, and solved while preserving equality.
How geometry evolves into algebra through coordinates and formulas.
The role of diagrams, intuition, and verification in mathematical reasoning.

Ideal for readers curious about the foundations of mathematics, logic, and the history of ideas.

Kindle Edition

Published August 24, 2018

About the author

Alexander Bain was a Scottish philosopher and educationalist in the British school of empiricism and a prominent and innovative figure in the fields of psychology, linguistics, logic, moral philosophy and education reform. He founded Mind, the first ever journal of psychology and analytical philosophy, and was the leading figure in establishing and applying the scientific method to psychology. Bain was the inaugural Regius Chair in Logic and Professor of Logic at the University of Aberdeen, where he also held Professorships in Moral Philosophy and English Literature and was twice elected Lord Rector of the University of Aberdeen.