By Alfred North Whitehead
Alfred North Whitehead (1861-1947) used to be both celebrated as a mathematician, a thinker and a physicist. He collaborated along with his former scholar Bertrand Russell at the first variation of Principia Mathematica (published in 3 volumes among 1910 and 1913), and after a number of years instructing and writing on physics and the philosophy of technology at collage collage London and Imperial collage, was once invited to Harvard to coach philosophy and the speculation of schooling. A Treatise on common Algebra was once released in 1898, and was once meant to be the 1st of 2 volumes, although the second one (which used to be to hide quaternions, matrices and the final thought of linear algebras) used to be by no means released. This e-book discusses the overall ideas of the topic and covers the subjects of the algebra of symbolic good judgment and of Grassmann's calculus of extension.
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Additional info for A Treatise on Universal Algebra: With Applications
MANIFOLDS. The idea of a manifold was first explicitly stated by Riemann*; Grassmann"f" had still earlier defined and investigated a particular kind of manifold. Consider any number of things possessing any common property. That property may be possessed by different things in different modes : let each separate mode in which the property is possessed be called an element. The aggregate of all such elements is called the manifold of the property. Any object which is specified as possessing a property in a given mode corresponds to an element in the manifold of that property.
Bradley*. In this connexion a demonstration is to be defined as a process of combining a complex of facts, the data, into a whole so that some new fact is evident. Inference is an ideal combination or construction within the mind of the reasoner which results in the intuitive evidence of a new fact or relation between the data. But in the use of a calculus this process of combination is externally performed by the combination of the concrete symbols, with the result of a new fact respecting the symbols which arises for sensuous perception-)-.
1. SIGNS. Words, spoken or written, and the symbols of Mathematics are alike signs. Signs have been analysed* into (a) suggestive signs, (/3) expressive signs, (7) substitutive signs. A suggestive sign is the most rudimentary possible, and need not be dwelt upon here. An obvious example of one is a knot tied in a handkerchief to remind the owner of some duty to be performed. In the use of expressive signs the attention is not fixed on the sign itself but on what it expresses; that is to say, it is fixed on the meaning conveyed by the sign.
A Treatise on Universal Algebra: With Applications by Alfred North Whitehead