''Introduction to Mathematical Philosophy'' is a book (1919 first edition) by philosopher
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...
, in which the author seeks to create an accessible introduction to various topics within the
foundations of mathematics
Foundations of mathematics are the mathematical logic, logical and mathematics, mathematical framework that allows the development of mathematics without generating consistency, self-contradictory theories, and to have reliable concepts of theo ...
. According to the preface, the book is intended for those with only limited knowledge of mathematics and no prior experience with the
mathematical logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
it deals with. Accordingly, it is often used in introductory
philosophy of mathematics
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...
courses at institutions of higher education.
Background
''Introduction to Mathematical Philosophy'' was written while Russell was serving time in
Brixton Prison
HM Prison Brixton is a Category C training establishment men's prison, located in Brixton area of the London Borough of Lambeth, in inner- South London. The prison is operated by His Majesty's Prison Service. Before 2012, it was used as a loca ...
due to his anti-war activities.
Contents
The book deals with a wide variety of topics within the philosophy of mathematics and mathematical logic including the logical basis and definition of
natural numbers
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positiv ...
,
real and
complex numbers
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a ...
,
limits and
continuity, and
classes.
[Pfeiffer, G. A.]
"Russell's Introduction to Mathematical Philosophy"
''Bull. Amer. Math. Soc.'' 27 (1920), no. 2, 81–90.
Editions
* Russell, Bertrand (1919), ''Introduction to Mathematical Philosophy'', George Allen & Unwin. (Reprinted: Routledge, 1993.)
* Russell, Bertrand (1920), ''Introduction to Mathematical Philosophy'', London: George Allen & Unwin / NY: Macmillan, Second Edition, reprintings 1920, 1924, 1930.
See also
* ''
Principia Mathematica
The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by the mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1 ...
''
* ''
The Principles of Mathematics
''The Principles of Mathematics'' (''PoM'') is a 1903 book by Bertrand Russell, in which the author presented Russell's paradox, his famous paradox and argued his thesis that mathematics and logic are identical.
The book presents a view of ...
''
*
Logicism
In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or al ...
Footnotes
Logic books
Books about philosophy of mathematics
Books by Bertrand Russell
1919 non-fiction books
Allen & Unwin books
Prison writings
Philosophy textbooks
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