|
Showing 1 - 6 of
6 matches in All Departments
|
Logic, Language, Information, and Computation - 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings (Paperback, 1st ed. 2017)
Juliette Kennedy, Ruy J. G. B De Queiroz
|
R2,800
Discovery Miles 28 000
|
Ships in 10 - 15 working days
|
Edited in collaboration with FoLLI, the Association of Logic,
Language and Information this book constitutes the refereed
proceedings of the 24th Workshop on Logic, Language, Information
and Communication, WoLLIC 2017, held in London, UK, in August 2017.
The 28 contributed papers were carefully reviewed and selected from
61 submissions. They cover interdisciplinary research in pure and
applied logic, aiming at interactions between logic and the
sciences related to information and computation.
Is mathematics 'entangled' with its various formalisations? Or are
the central concepts of mathematics largely insensitive to
formalisation, or 'formalism free'? What is the semantic point of
view and how is it implemented in foundational practice? Does a
given semantic framework always have an implicit syntax? Inspired
by what she calls the 'natural language moves' of Goedel and
Tarski, Juliette Kennedy considers what roles the concepts of
'entanglement' and 'formalism freeness' play in a range of logical
settings, from computability and set theory to model theory and
second order logic, to logicality, developing an entirely original
philosophy of mathematics along the way. The treatment is
historically, logically and set-theoretically rich, and topics such
as naturalism and foundations receive their due, but now with a new
twist.
This Element takes a deep dive into Goedel's 1931 paper giving the
first presentation of the Incompleteness Theorems, opening up
completely passages in it that might possibly puzzle the student,
such as the mysterious footnote 48a. It considers the main
ingredients of Goedel's proof: arithmetization, strong
representability, and the Fixed Point Theorem in a layered fashion,
returning to their various aspects: semantic, syntactic,
computational, philosophical and mathematical, as the topic arises.
It samples some of the most important proofs of the Incompleteness
Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as
newer proofs, also of other independent statements, due to H.
Friedman, Weiermann and Paris-Harrington. It examines the question
whether the incompleteness of e.g. Peano Arithmetic gives
immediately the undecidability of the Entscheidungsproblem, as
Kripke has recently argued. It considers set-theoretical
incompleteness, and finally considers some of the philosophical
consequences considered in the literature.
Is mathematics 'entangled' with its various formalisations? Or are
the central concepts of mathematics largely insensitive to
formalisation, or 'formalism free'? What is the semantic point of
view and how is it implemented in foundational practice? Does a
given semantic framework always have an implicit syntax? Inspired
by what she calls the 'natural language moves' of Goedel and
Tarski, Juliette Kennedy considers what roles the concepts of
'entanglement' and 'formalism freeness' play in a range of logical
settings, from computability and set theory to model theory and
second order logic, to logicality, developing an entirely original
philosophy of mathematics along the way. The treatment is
historically, logically and set-theoretically rich, and topics such
as naturalism and foundations receive their due, but now with a new
twist.
The logician Kurt Goedel (1906-1978) published a paper in 1931
formulating what have come to be known as his 'incompleteness
theorems', which prove, among other things, that within any formal
system with resources sufficient to code arithmetic, questions
exist which are neither provable nor disprovable on the basis of
the axioms which define the system. These are among the most
celebrated results in logic today. In this volume, leading
philosophers and mathematicians assess important aspects of
Goedel's work on the foundations and philosophy of mathematics.
Their essays explore almost every aspect of Godel's intellectual
legacy including his concepts of intuition and analyticity, the
Completeness Theorem, the set-theoretic multiverse, and the state
of mathematical logic today. This groundbreaking volume will be
invaluable to students, historians, logicians and philosophers of
mathematics who wish to understand the current thinking on these
issues.
|
You may like...
Midnights
Taylor Swift
CD
R425
Discovery Miles 4 250
|