This unified approach to the foundations of mathematics in the theory of sets covers both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of "natural number" and "set". The book contains an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, and the analysis of proof by induction and definition by recursion. The book should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.
FREE Two-Day Shipping for students on millions of items. Learn more |
| |||||||||||||||
Book Description
Editorial Reviews
Review
"...an invigorating call to foundational arms..." Notre Dame Journal of Formal Logic
"...this book is thought provoking...a distinctive approach to the twin issues of mathematical ontology and mathematical foundations..." Australasian Journal of Philosophy
"...I also think that it is one of the more philosophically significant books to have been written on this topic in some time. It provides much food for thought... this should certainly be acknowledged as an important piece of conceptual analysis, one which suggests interesting avenues for further exploration." Mary Tiles, Philosophia Mathematica
"...a very lively book, filled with striking theses..." The Bulletin of Symbolic Logic
"...this book is thought provoking...a distinctive approach to the twin issues of mathematical ontology and mathematical foundations..." Australasian Journal of Philosophy
"...I also think that it is one of the more philosophically significant books to have been written on this topic in some time. It provides much food for thought... this should certainly be acknowledged as an important piece of conceptual analysis, one which suggests interesting avenues for further exploration." Mary Tiles, Philosophia Mathematica
"...a very lively book, filled with striking theses..." The Bulletin of Symbolic Logic
Book Description
This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
(learn more)
First Sentence:
Mathematics differs from all the other sciences in requiring that its propositions be proved. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
numerical species, global quantifiers, level global function, proper subpluralities, finite plurality, finite pluralities, simple numerical equations, plurality composed, finitist assumptions, formalised proofs, global recursion, order logical consistency, natural number arithmetic, finiteness principle, bound class variables, decimal algorithms, infinite species, formal axiomatic theory, global quantification, ordinal function, numeration base, number whose units, cardinal equivalence, general set theory, cumulative hierarchy Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Brouwer's Principle, Proof Let, Weak Hierarchy Principle, Cantor's Axiom, Axiom of Comprehension, Principle of Regularity, Axiom of Choice, Axiom of Foundation, Red Rum, Strong Hierarchy Principle, Corollary Let, Mahlo's Principle, Axiom of Euclidean Finiteness, Axiom of Replacement, One Point Extension Induction, Philosophy of Mathematics, Strong Closure Principle, Hierarchy Principles, Common Notion, Incompleteness Theorems, Proof Suppose, Well-ordering Theorem, Zorn's Lemma, Axiom of Infinity New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Mathematics differs from all the other sciences in requiring that its propositions be proved. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
numerical species, global quantifiers, level global function, proper subpluralities, finite plurality, finite pluralities, simple numerical equations, plurality composed, finitist assumptions, formalised proofs, global recursion, order logical consistency, natural number arithmetic, finiteness principle, bound class variables, decimal algorithms, infinite species, formal axiomatic theory, global quantification, ordinal function, numeration base, number whose units, cardinal equivalence, general set theory, cumulative hierarchy Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Brouwer's Principle, Proof Let, Weak Hierarchy Principle, Cantor's Axiom, Axiom of Comprehension, Principle of Regularity, Axiom of Choice, Axiom of Foundation, Red Rum, Strong Hierarchy Principle, Corollary Let, Mahlo's Principle, Axiom of Euclidean Finiteness, Axiom of Replacement, One Point Extension Induction, Philosophy of Mathematics, Strong Closure Principle, Hierarchy Principles, Common Notion, Incompleteness Theorems, Proof Suppose, Well-ordering Theorem, Zorn's Lemma, Axiom of Infinity New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 38
books:
See all 38 books this book cites
12
books
cite this book:
See all 12 books citing this book
- Frege: Philosophy of Mathematics by Michael Dummett on 6 pages
- Proof Theory (Studies in Logic and the Foundations of Mathematics) by Gaisi Takeuti on 5 pages
- Elements of Intuitionism (Oxford Logic Guides) by Michael Dummett on 4 pages
- Greek Mathematical Thought and the Origin of Algebra (Dover Books on Mathematics) by Jacob Klein on 4 pages
- Introduction to Metamathematics (Bibliotheca Mathematica) by S.C. Kleene on page 212, Back Matter (1), and Back Matter (2)
See all 38 books this book cites
- Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications) by Alexei Kushner in Front Matter
- Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications) by George Gasper in Front Matter
- Set Theory and Its Philosophy: A Critical Introduction by Michael Potter in Back Matter
- Solving Polynomial Equation Systems II: Macaulay's Paradigm and Gröbner Technology (Encyclopedia of Mathematics and its Applications) (v. 2) by Teo Mora in Front Matter
- An Algebraic Introduction to K-Theory (Encyclopedia of Mathematics and its Applications) by Bruce A. Magurn in Front Matter
See all 12 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
So You'd Like to...
Look for Similar Items by Category
- Books > Education & Reference > Encyclopedias > Antiques & Collectibles
- Books > Education & Reference > Encyclopedias > Medical
- Books > Medical Books
- Books > New & Used Textbooks > Medicine & Health Sciences > Medicine > General
- Books > New & Used Textbooks > Science & Mathematics > Mathematics
- Books > Science & Math > Mathematics
