A Treatise on Universal Algebra

Abstract

Alfred North Whitehead (1861–1947) was equally celebrated as a mathematician, a philosopher and a physicist. He collaborated with his former student Bertrand Russell on the first edition of Principia Mathematica (published in three volumes between 1910 and 1913), and after several years teaching and writing on physics and the philosophy of science at University College London and Imperial College, was invited to Harvard to teach philosophy and the theory of education. A Treatise on Universal Algebra was published in 1898, and was intended to be the first of two volumes, though the second (which was to cover quaternions, matrices and the general theory of linear algebras) was never published. This book discusses the general principles of the subject and covers the topics of the algebra of symbolic logic and of Grassmann's calculus of extension.

On the Homogeneous Model of Euclidean Geometry

“…The k-blades of W correspond to (k−1)-dimensional subspaces of RP n . All multiples of the same k-blade represent the same projective subspace, and differ only by intensity ( [Whi98], §16-17). 1-blades correspond to points; 2-blades to lines; 3-blades to planes, etc.…”

“…In such situations terms such as weighted point or "point with intensity" will be used. See [Whi98], Book III, Ch. 4.…”

Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics.

“…Russell learnt the doctrine through Whitehead's Universal Algebra, and the peculiarity of Russell's presentation can be explained by this genealogy. I have analysed in detail the relation between [Whitehead, 1898] and [Russell, 1899b] elsewhere 35 . But the following quotation of Whitehead's book should suffice, I think, to show the relevance of this comparing:…”

“…If ρ+σ = υ, then (P ρ P σ ) is a mere number and can be considered either as progressive or regressive. ( [Whitehead, 1898], p. 191).…”

Chapter Two : Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole��s Footsteps, as Something the Brain Does

“…Or, the 8 sequences that yield no car need to be eliminated. They are sequences 4,8,12,16,20,24,28, and 32. In the list below, the 8 sequences in question have been removed.…”