Bộ sách luyện thi ETS 2023 LC&RC
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This is the first book focused on the
logico-philosophical aspects of the lambda-calculus since the inception
of the field in 1932 in the pioneering work of Alonzo Church. The book
starts a new field called “lambda-philosophy”: a branch of logic-based
analytic philosophy in the tradition of Frege and Russell, directly
constructed from the lambda-calculus. Another innovation of the book is a
new graphical and intuitive logico-mathematical notation for the
lambda-calculus called “the container notation”.
The book covers in
detail some episodes of the history of the subject, including three
comparative studies of the lambda-calculus with Viète's algebra,
Descartes' analytic geometry, and Wittgenstein’s Tractatus. A didactic
approach to the logico-mathematical aspects of the lambda-calculus,
partially based on cognitive science, provides the technical basis for
the analysis. In this way, the book provides a systematic and coherent
treatment of diverse logico-philosophical aspects and applications of
the lambda-calculus as part of the platform offered by
lambda-philosophy.
The book includes the a detailed treatment of the
ambiguities of the concept of function (under the traditional or
Euler’s notation); an elucidation of the notion of transformative
philosophical analysis; an account of Church’s methodology which shows
that the lambda-calculus is an adequate solution to the problem of a
philosophical analysis of functions as rules of computation; a didactic
treatment of the formal aspects of the lambda-calculus through the
container notation; and diverse arithmetical and logical examples of the
container notation. The book questions a dogma of algorithmic thinking
by arguing that the lambda-calculus is more intuitive and natural than
Turing machines.
The Logic, Philosophy, and History of the
Lambda-Calculus is essential reading for all scholars and researchers of
the history of analytic philosophy and especially those focussing on
logic-based analytic philosophy.
Categories:Mathematics - Others
Content Type:Books
Year:2025
Edition:1
Language:english
Pages:274
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