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Set Theory: Boolean-Valued Models and Independence Proofs

John L. Bell

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This is the third edition of a well-known graduate textbook on Boolean-valued models of set theory. The aim of the first and second editions was to provide a systematic and adequately motivated ... More


BOOLEAN AND HEYTING ALGEBRAS: THE ESSENTIALS

John L. Bell

in Set Theory: Boolean-Valued Models and Independence Proofs

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter provides a brief account of the theory of Boolean and Heyting algebras, including the basic representation theorems and their connections with logic.


Introduction to Supervaluational Approaches to Paradox

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter examines the simplest supervaluationist fixed points, and the ‘internal’ fixed-point theories based on them. These are not gap theories; they are ‘weakly classical’ theories in that they ... More


Boolean-valued structures

Tim Button and Sean Walsh

in Philosophy and Model Theory

Published in print:
2018
Published Online:
May 2018
ISBN:
9780198790396
eISBN:
9780191863424
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198790396.003.0013
Subject:
Philosophy, Logic/Philosophy of Mathematics

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin ... More


Logic: a new beginning

Pieter A. M. Seuren

in The Logic of Language: Language From Within Volume II

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199559480
eISBN:
9780191721144
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559480.003.0002
Subject:
Linguistics, Semantics and Pragmatics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics

Entailment, contrariety, and contradiction stand in a triangular relation. Given negation of the predicate and given the duality of all and some, two isomorphic triangles arise, together forming an ... More


Classical Mereology

A. J. Cotnoir and Achille C. Varzi

in Mereology

Published in print:
2021
Published Online:
September 2021
ISBN:
9780198749004
eISBN:
9780191811647
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198749004.003.0002
Subject:
Philosophy, Philosophy of Mind

The aim of this chapter is to provide a comprehensive introduction to classical mereology. It examines this theory by providing a clear and perspicuousaxiom system that isolates several important ... More


Boolean Algebra

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0004
Subject:
Mathematics, History of Mathematics

This chapter discusses how Boole cast logic into algebraic form. Boole was interested in symbolic analysis years before he wrote his Laws of Thought. In fact, others before him—in particular, the ... More


Synthesis and the Principle of Addition

Kurt Smith

in Matter Matters: Metaphysics and Methodology in the Early Modern Period

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199583652
eISBN:
9780191723155
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199583652.003.0010
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

This chapter studies the mathematical concept of a group, early ancestors of the concept found in the works of Descartes and Leibniz. Here, it is shown exactly how the four conditions expressed by a ... More


Introduction

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0002
Subject:
Mathematics, History of Mathematics

This introductory chapter considers the work of mathematician George Boole (1815–1864), whose book An Investigation of the Laws of Thought (1854) would have a huge impact on humanity. Boole's ... More


 Mid-plural logic

Alex Oliver and Timothy Smiley

in Plural Logic

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199570423
eISBN:
9780191755866
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570423.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

Plural formal logic comes in two phases. This chapter develops mid-plural logic, got by adding three logical items to the singular base of the previous chapter: plural variables, a predicate ... More


The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Paul J. Nahin

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.001.0001
Subject:
Mathematics, History of Mathematics

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use—from our computers and cars, to home appliances. How did a system of mathematics ... More


Mid-plural logic

Alex Oliver and Timothy Smiley

in Plural Logic: Second Edition, Revised and Enlarged

Published in print:
2016
Published Online:
February 2017
ISBN:
9780198744382
eISBN:
9780191843877
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198744382.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

Plural formal logic comes in two phases. This chapter develops mid-plural logic, got by adding three logical items to the singular base of the previous chapter: plural variables, a predicate ... More


Logic Switching Circuits

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0005
Subject:
Mathematics, History of Mathematics

Today's digital circuitry is built with electronic technology that the telephone engineers of the 1930s and the pioneer computer designers of the 1940s would have thought to be magic. The first real ... More


George Boole and Claude Shannon: Two Mini-Biographies

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0003
Subject:
Mathematics, History of Mathematics

This chapter presents brief biographical sketches of George Boole and Claude Shannon. George was born in Lincoln, a town in the north of England, on November 2, 1815. His father John, while simple ... More


What You Need to Know to Read This Book

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0001
Subject:
Mathematics, History of Mathematics

This chapter details the background knowledge needed to read this book. Specifically, it assumes some knowledge of mathematics and electrical physics and an appreciation for the value of analytical ... More


Beyond Boole and Shannon

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0010
Subject:
Mathematics, History of Mathematics

Boole and Shannon never studied the physics of computation. Obviously Boole simply could not have, as none of the required physics was even known in his day, and Shannon was nearing the end of his ... More


Epilogue: For the Future: The Anti-Amphibological Machine

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0011
Subject:
Mathematics, History of Mathematics

This chapter present the author's vision of the sort of logical problem that may soon be one that even a quantum computer would find a struggle to deal with—the decipherment of entangled legalese, ... More


Boole, Shannon, and Probability

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0006
Subject:
Mathematics, History of Mathematics

George Boole and Claude Shannon shared a deep interest in the mathematics of probability. Boole's interest was, of course, not related to the theory of computation—he was a century too early for ... More


Characteristic Analysis as an Oil Exploration Tool

H. A. F. Chaves

in Computers in Geology - 25 Years of Progress

Published in print:
1994
Published Online:
November 2020
ISBN:
9780195085938
eISBN:
9780197560525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195085938.003.0013
Subject:
Computer Science, Software Engineering

Characteristic analysis is well known in mineral resources appraisal and has proved useful for petroleum exploration. It also can be used to integrate geological data in sedimentary basin analysis ... More


Turing Machines

Paul J. Nahin

in The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691176000
eISBN:
9781400844654
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691176000.003.0009
Subject:
Mathematics, History of Mathematics

This chapter discusses Turing machines. A Turing machine is the combination of a sequential, finite-state machine plus an external read/write memory storage medium called the tape (think of a ribbon ... More


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