By Bertrand Russell

Advent to Mathematical Philosophy is a e-book that was once written by means of Bertrand Russell and released in 1919. the point of interest of the publication is at the concept of description and it provides the tips present in Principia Mathematica in a better option to comprehend. Bertrand Russell used to be a British thinker, philosopher, and mathematician. Russell was once one of many leaders within the British "revolt opposed to idealism" and he's credited for being one of many founders of analytic philosophy. In 1950 Russell obtained the Nobel Prize in Literature.

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By “successor” he means the next number in the natural order. That is to say, the successor of 0 is 1, the successor of 1 is 2, and so on. 2 He is not assuming that we know all the members of this class, but only that we know what we mean when we say that this or that is a number, just as we know what we mean when we say “Jones is a man,” though we do not know all men individually. The five primitive propositions which Peano assumes are: (1) 0 is a number. (2) The successor of any number is a number.

At the expense of a little oddity, this definition secures definiteness and indubitableness; and it is not difficult to prove that numbers so defined have all the properties that we expect numbers to have. We may now go on to define numbers in general as any one of the bundles into which similarity collects classes. A number will be a set of classes such as that any two are similar to each [page 19] other, and none outside the set are similar to any inside the set. In other words, a number (in general) is any collection which is the number of one of its members; or, more simply still: A number is anything which is the number of some class.

2) It is obvious that in practice we can often know a great deal about a class without being able to enumerate its members. No one man could actually enumerate all men, or even all the inhabitants of London, yet a great deal is known about each of these classes. This is enough to show that definition by extension is not necessary to knowledge about a class. But when we come to consider infinite classes, we find that enumeration is not even theoretically possible for beings who only live for a finite time.

### Introduction to Mathematical Philosophy by Bertrand Russell

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