Introduction to Mathematical PhilosophyNot to be confused with the philosophy of mathematics, mathematical philosophy is the structured set of rules that govern all existence. Or, in a word: logic. While this branch of philosophy threatens to be an intimidating and abstract subject, it is one that is surprisingly simple and necessarily sensible, particularly at the pen of writer Bertrand Russell, who infuses this work, first published in 1919, with a palpable and genuine desire to assist the reader in understanding the principles he illustrates. Anyone interested in logic and its development and application here will find a comprehensive and accessible account of mathematical philosophy, from the idea of what numbers actually are, through the principles of order, limits, and deduction, and on to infinity. British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (18721970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959). 
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Review: Introduction to Mathematical Philosophy
User Review  mm  GoodreadsI was under the impression that this would be light reading... It is presented clearly, but Russell primarily uses analogy to describe some very ambitious ideas that could benefit from a diagram or two. This didn't scare me off. I'll have to take a look at Principia Mathematica. Read full review
Review: Introduction to Mathematical Philosophy
User Review  Tom Bisbee  GoodreadsStupid to read for the math, worth reading for the logic. Read full review
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aliorelative arithmetic assert assume asymmetrical asymmetrical relation author of Waverley axiom of infinity belongs called Cantor cardinal number chapter classes of classes commutative law complex numbers consider consists constituents converse domain correlation Dedekindian deduction defined example existence fact finite follows formally equivalent fractions generalised geometry greater identical implies q important inductive cardinal inductive numbers inference infinite number integers involved irrational less limit limitingpoints logical logical constants mathematical induction mathematical logic means multiplicative axiom namely natural numbers notion nullclass number of individuals number of terms object onemany relations oneone relation ordinal Peano's philosophy of mathematics possible posterity premisses primitive ideas primitive propositions progression propositional function prove real numbers reflexive relationnumbers sense serial number series of ratios set of terms similar soandso Socrates sometimes true square subclasses successor suppose symbols theory thing tion truthfunctions unicorn upper section values variable words
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Page 2  The most obvious and easy things in mathematics are not those that come logically at the beginning; they are things that, from the point of view of logical deduction, come somewhere in the middle. Just as the easiest bodies to see are those that are neither very near nor very far, neither very small nor very great, so the easiest conceptions to grasp are those that are neither very complex nor very simple (using "simple
Page 3  It must have required many ages to discover that a brace of pheasants and a couple of days were both instances of the number 2: the degree of abstraction involved is far from easy.