This work traces the development of the theory of types from its
origins in the early 20th century through its various forms until
the mid 1950s. Attention is paid to the reception of this theory
after the publication of the second edition of Whitehead and
Russell's 'Principia Mathematica'. I examine the decline of the
theory over four decades, focusing on its modification by logicians
such as Ramsey, Carnap, Church, Quine, Godel, and Tarski. Finally,
the view of the theory of types as a many-sorted first-order theory
is discussed. It is shown that a revival of the ramified theory of
types in the 1950s coincided with the consideration of cumulative
type hierarchies which substantially altered the form of the
theory. The theory was altered even more drastically in its change
from a many-sorted theory to a one-sorted theory. This final
'standardization' made it not much different from first-order
Zermelo-Fraenkel set-theory. The theory of types, whose
developments are traced in this work, therefore lost its prominence
as the foundation for mathematics and logic. This historical
analysis will be of interest primarily to those working in the
History and Philosophy of Mathematics."
General
Imprint: |
Lap Lambert Academic Publishing
|
Country of origin: |
Germany |
Release date: |
2012 |
First published: |
2012 |
Authors: |
Jordan Collins
|
Dimensions: |
229 x 152 x 8mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
128 |
ISBN-13: |
978-3-8473-2963-3 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
3-8473-2963-4 |
Barcode: |
9783847329633 |
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