Whitehead’s first book, an important precursor to the landmark Principia Mathematica co-authored with Bertrand Russell.
“A Treatise on Universal Algebra constitutes Whitehead’s first book. It is largely founded on a thorough investigation of Grassmann’s calculus of extension, Hamilton’s Quaternions, Boole’s algebra of logic and Riemann’s Manifold. Furthermore, as its title displays, Leibniz’s shadow (under the guise of the ’Ars combinatoria) leads him to the quest of a ‘universal calculus to facilitate reasoning in connection with every province of thought, or of external experience. His thesis is that mathematics (in its widest signification) is not simply the science of number and quantity, but a highly efficient universal engine of investigation of the possibilities of thought and reasoning. Whitehead’s algebra avoids the restriction of variables to symbols for particular numbers to elaborate a fully fledged logic of propositions (‘the sole concern of mathematics is the inference of proposition from proposition’).” (Weber, p. 1117).
The planned second volume of Whitehead’s Universal Algebra never appeared, being replaced by the landmark Principia Mathematica (1910-13) co-authored with Bertrand Russell who had joined Trinity College, Cambridge in 1890 and subsequently followed Whitehead’s lectures. “In 1903 Russell published The Principles of Mathematics and soon discovered the possibility of a synergy between his planned second volume and the second volume of the Universal Algebra that was still in the air. As a result, the authors decided to unite their efforts” (Weber, p. 1117).
See: Michel Weber, ‘Alfred North Whitehead’, in: Dictionary of Twentieth-Century British Philosophers, Thoemmes.
