First Order Logic by Raymond M Smullyan: A Stimulating and Challenging Book on Logic and Mathematics (PDF Download)
First Order Logic by Raymond M Smullyan PDF Download
If you are interested in logic, mathematics, or puzzles, you might have heard of the book First Order Logic by Raymond M Smullyan. This book is widely considered as one of the best introductions to quantification theory and analytic methods in logic. It is also full of challenging and entertaining exercises that test your logical skills and creativity.
First Order Logic By Raymond M Smullyan Pdf Download
In this article, we will tell you everything you need to know about this book, why you should read it, how to download it in PDF format, and how to use it effectively. Whether you are a student, a teacher, a researcher, or a hobbyist, you will find this book useful and enjoyable.
What is First Order Logic?
First order logic is a branch of symbolic logic that deals with statements that involve quantifiers, such as "for all" or "there exists". For example, the statement "All humans are mortal" can be written in first order logic as:
$\forall x (Human(x) \rightarrow Mortal(x))$
First order logic allows us to express complex and abstract concepts in a precise and rigorous way. It also enables us to reason deductively and prove theorems using formal rules of inference.
First order logic is widely used in mathematics, computer science, artificial intelligence, philosophy, linguistics, and many other fields. It is also the basis for many other logics, such as modal logic, temporal logic, or fuzzy logic.
Who is Raymond M Smullyan?
Raymond M Smullyan (1919-2017) was an American mathematician, logician, philosopher, magician, musician, and author. He was known for his contributions to mathematical logic, especially in the areas of recursion theory, Gödel's incompleteness theorems, and non-classical logics. He was also famous for his books on logic puzzles, such as What Is the Name of This Book?, The Lady or the Tiger?, and To Mock a Mockingbird.
Smullyan was a professor emeritus at Indiana University and a visiting scholar at New York University. He received many honors and awards for his work, including the Guggenheim Fellowship, the Alfred P. Sloan Fellowship, and the Chauvenet Prize.
What is the book about?
The book First Order Logic was first published in 1968 by Springer-Verlag. It was reprinted in 1995 by Dover Publications with minor corrections and additions.
The book is divided into three parts. Part I covers propositional logic from the viewpoint of analytic tableaux, a method of proving validity or satisfiability of formulas using tree diagrams. Part II covers first order logic using analytic tableaux as well as other techniques, such as magic sets, Gentzen systems, and prenex tableaux. Part III discusses some advanced topics, such as interpolation, elimination, and linear reasoning.
The book is intended to serve both as an introduction to quantification theory and as an exposition of new results and techniques in analytic or cut-free methods. It is written in a clear and elegant style, with many examples and exercises. It is also self-contained, requiring only some basic knowledge of set theory and elementary logic.
Why You Should Read This Book
There are many reasons why you should read this book if you are interested in logic or mathematics. Here are some of them:
You will learn the fundamentals of first order logic, which is essential for understanding many other branches of logic and mathematics.
You will learn the analytic tableau method, which is a simple and powerful tool for proving logical statements and solving logical problems.
You will learn some new and interesting results and techniques in logic, such as magic sets, interpolation, and linear reasoning.
You will enjoy the puzzles and problems in the book, which are challenging and fun to solve.
Benefits of learning First Order Logic
First order logic is not only a fascinating subject in itself, but also a useful skill to have. By learning first order logic, you will be able to:
Express complex and abstract concepts in a precise and rigorous way.
Reason deductively and prove theorems using formal rules of inference.
Analyze the validity and consistency of arguments and statements.
Solve logical puzzles and problems using systematic methods.
Understand the foundations and limitations of mathematics and logic.
How the book teaches First Order Logic
The book teaches first order logic in a clear and elegant way, using the analytic tableau method as the main approach. The analytic tableau method is a method of proving validity or satisfiability of formulas using tree diagrams. The idea is to start with a formula or a set of formulas, and then apply logical rules to break them down into simpler subformulas, until either a contradiction or a truth assignment is reached. If a contradiction is reached, the formula or the set of formulas is invalid or unsatisfiable. If a truth assignment is reached, the formula or the set of formulas is valid or satisfiable.
The book explains the analytic tableau method in detail, with many examples and exercises. It also shows how to use the method to prove various properties of first order logic, such as completeness, compactness, consistency, decidability, and soundness. It also compares the method with other methods, such as natural deduction, resolution, and semantic tableaux.
Examples of puzzles and problems in the book
The book contains many puzzles and problems that test your logical skills and creativity. Some of them are classic logic puzzles, such as knights and knaves, liars and truth-tellers, or the barber paradox. Some of them are original puzzles invented by Smullyan himself, such as the island of blue-eyed people, the lady or the tiger, or the harpist's dilemma. Some of them are related to mathematical logic, such as Gödel's incompleteness theorems, Tarski's undefinability theorem, or Skolem's paradox.
Here are some examples of puzzles and problems from the book:
Suppose there are two islands, A and B. On island A there are only knights (who always tell the truth) and knaves (who always lie). On island B there are only normals (who sometimes tell the truth and sometimes lie). You meet two people from these islands. One says "I am from island A" and the other says "He is lying". Which island is each person from?
Suppose there are three doors in a room. Behind one door there is a lady who loves you. Behind another door there is a tiger who wants to eat you. Behind the third door there is nothing. You don't know which door leads to what. There are two guards in front of the doors. One guard always tells the truth and the other always lies. You don't know which guard is which. You can ask one question to one guard to find out which door leads to the lady. What question should you ask?
How to Download the PDF Version of the Book
If you want to read this book in PDF format, you might be wondering how to download it. There are several ways to do that, but not all of them are legal and ethical. In this section, we will discuss some of the issues and sources of downloading PDF books, and give you some tips for finding and accessing them.
Legal and ethical issues of downloading PDF books
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Therefore, you should always respect the rights and wishes of the authors and publishers, and only download PDF books from authorized sources. You should also consider buying the physical or digital copies of the books that you like, to support their creators and enjoy their full quality and features.
Sources of free and paid PDF downloads
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Google Books: Google Books is a service that allows you to search and preview millions of books from various publishers and libraries. You can also download some books in PDF format for free, if they are in the public domain or have been authorized by the copyright holders. You can access Google Books at https://books.google.com.
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Amazon Kindle Store: Amazon Kindle Store is a service that allows you to buy and read ebooks on your Kindle device or app. You can find millions of books in various genres and languages, including some by Raymond M Smullyan. You can also convert some Kindle books to PDF using third-party tools or services. You can access Amazon Kindle Store at https://www.amazon.com/Kindle-eBooks.
Tips for finding and accessing PDF files
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Use specific keywords and filters when searching for PDF files on Google or other search engines. For example, you can type "First Order Logic by Raymond M Smullyan filetype:pdf" to find only PDF files related to this book.
Use online tools or services that allow you to convert other formats to PDF or vice versa. For example, you can use Zamzar to convert DOCX files to PDF files.
Use online tools or services that allow you to merge or split PDF files. For example, you can use Ilovepdf to merge multiple PDF files into one or split one PDF file into multiple.
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How to Use the PDF Version of the Book
Once you have downloaded the PDF version of the book, you might wonder how to use it effectively. There are some advantages and disadvantages of reading a book in PDF format, and some tools and software that can help you read and annotate it. In this section, we will discuss some of these aspects and give you some advice on how to use the PDF version of the book.
Advantages and disadvantages of PDF format
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Reading a book in PDF format has some advantages, such as:
You can access the book anytime and anywhere, as long as you have a device that can open PDF files.
You can zoom in and out, rotate, or crop the pages to suit your preferences and needs.
You can search for specific words or phrases within the book using the find function.
You can bookmark, highlight, or underline important parts of the book using some PDF readers or editors.
You can save space and paper by storing and reading multiple books in one device.
However, reading a book in PDF format also has some disadvantages, such as:
You might experience eye strain or fatigue from reading on a screen for a long time.
You might miss some features or functions that are available in physical or digital books, such as page numbers, table of contents, index, glossary, or hyperlinks.
You might have difficulty reading some parts of the book that are not formatted well or have low resolution.
You might encounter compatibility or security issues with some PDF files or readers.
You might violate the copyright laws or the ethical principles of the author or the publisher if you download or share the book without permission.
Tools and software for reading and annotating PDF files
To read and annotate PDF files effectively, you need to have a good tool or software that can open and edit them. There are many tools and software that can do that, but not all of them are reliable and user-friendly. Here are some examples of tools and software that we recommend for reading and annotating PDF files:
Adobe Acrobat Reader: Adobe Acrobat Reader is a free and popular software that allows you to view, print, sign, and comment on PDF files. It has many features and functions that can enhance your reading experience, such as text-to-speech, night mode, read mode, fill and sign, sticky notes, highlighter, and more. You can download Adobe Acrobat Reader at https://get.adobe.com/reader.
Foxit Reader: Foxit Reader is another free and popular software that allows you to view, print, sign, and comment on PDF files. It has a similar interface and features as Adobe Acrobat Reader, but it is faster and lighter. It also has some additional features, such as cloud storage, collaboration tools, security options, and more. You can download Foxit Reader at https://www.foxitsoftware.com/pdf-reader.
Sumatra PDF: Sumatra PDF is a free and simple software that allows you to view PDF files. It has a minimalistic interface and features that focus on speed and performance. It is ideal for users who want a fast and easy way to read PDF files without any distractions or complications. You can download Sumatra PDF at https://www.sumatrapdfreader.org.
Xodo PDF Reader & Editor: Xodo PDF Reader & Editor is a free and versatile software that allows you to view, print, sign, comment, edit, merge, split, convert, compress, organize, and share PDF files. It has a user-friendly interface and features that can help you manage your PDF files efficiently and effectively. You can download Xodo PDF Reader & Editor at https://www.xodo.com.
In this article, we have given you an overview of the book First Order Logic by Raymond M Smullyan, why you should read it, how to download it in PDF format, and how to use it effectively. We hope that you have found this article useful and informative, and that you will enjoy reading this book and learning more about logic and mathematics.
If you have any questions or feedback, please feel free to contact us or leave a comment below. We would love to hear from you and help you with your queries.
Thank you for reading this article and happy learning!
References and further reading
Smullyan, R. M. (1995). First-order logic. Dover Publications.
Enderton, H. B. (2001). A mathematical introduction to logic. Academic Press.
Huth, M., & Ryan, M. (2004). Logic in computer science: modelling and reasoning about systems. Cambridge University Press.
Pelletier, F. J. (Ed.). (2000). Philosophy of mathematics: selected readings. Cambridge University Press.
Smullyan, R. M. (1978). What is the name of this book?: The riddle of Dracula and other logical puzzles. Prentice-Hall.
Frequently Asked Questions
Q: What is the difference between first order logic and propositional logic?
A: Propositional logic is a branch of symbolic logic that deals with statements that are either true or false, such as "It is raining" or "It is not raining". First order logic is a branch of symbolic logic that deals with statements that involve quantifiers, such as "for all" or "there exists", such as "All humans are mortal" or "There exists a unicorn". First order logic is more expressive and powerful than propositional logic, but also more complex and difficult.
Q: What are some applications of first order logic?
A: First order logic has many applications in various fields, such as mathematics, computer science, artificial intelligence, philosophy, linguistics, and more. For example, first order logic can be used to:
Define and prove theorems in mathematics using axioms and rules of inference.
Specify and verify the properties and behaviors of software systems using formal methods.
Represent and reason about knowledge and beliefs using ontologies and semantic web.
Analyze and evaluate arguments and statements using critical thinking and logic puzzles.
Model and understand natural languages using syntax and semantics.
Q: What are some challenges or limitations of first order logic?
A: First order logic also has some challenges or limitations that make it difficult or impossible to express or solve some problems or questions. For example, first order logic:
Is undecidable, which means that there is no algorithm that can determine whether a given formula is valid or satisfiable in general.
Is incomplete, which means that there are some true statements that cannot be proved from a given set of axioms in general.
Is not expressive enough to capture some concepts or phenomena that require higher-order or non-classical logics, such as modality, vagueness, uncertainty, or paradoxes.