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An Introduction To Non-Classical Logic
''An Introduction to Non-Classical Logic'' is a 2001 mathematics textbook by philosopher and logician Graham Priest, published by Cambridge University Press. The book provides a systematic introduction to non-classical propositional logics, which are logical systems that differ from standard classical propositional logic. It covers a wide range of topics including modal logic, intuitionistic logic, many-valued logic, relevant logic, and fuzzy logic. Editions The book has been published in two editions by Cambridge University Press. The first edition, published in 2001, was titled simply ''An Introduction to Non-Classical Logic''. In 2008, Priest published a substantially expanded and revised second edition under the title ''An Introduction to Non-Classical Logic: From If to Is''. The second edition more than doubled the length of the original text, expanding from 242 to 613 pages. This expansion reflected both revisions to existing content, such as the chapter on fuzzy logic whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graham Priest
Graham Priest (born 1948) is a philosopher and logician who is distinguished professor of philosophy at the CUNY Graduate Center, as well as a regular visitor at the University of Melbourne, where he was Boyce Gibson Professor of Philosophy and also at the University of St Andrews. Life Priest was educated at St John's College, Cambridge and the London School of Economics. His thesis advisor was John Lane Bell. He also holds a DLitt from the University of Melbourne. Priest was elected a corresponding fellow of the Australian Academy of the Humanities in 1995. In addition to his work in philosophy and logic, Priest practised karate-do. He is 3rd dan, International Karate-do Shobukai; 4th dan, shitō-ryū, and an Australian National kumite referee and kata judge. Presently, he practices tai chi. Philosophical work Priest is known for his defence of dialetheism, his in-depth analyses of the logical paradoxes (holding the thesis that there is a uniform treatment for many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stewart Shapiro
Stewart Shapiro (; born 1951) was O'Donnell Professor of Philosophy at the Ohio State University until his retirement, and is also distinguished visiting professor at the University of Connecticut. He is a leading figure in the philosophy of mathematics where he defends the abstract variety of structuralism. Education and career Shapiro studied mathematics and philosophy as an undergraduate at Case Western Reserve University in 1973. He earned his M.A. in mathematics at the State University of New York at Buffalo in 1975. He transferred to the University at Buffalo Philosophy Department, where three years later he received a Ph.D. His doctoral supervisor was John Corcoran. He was elected a Fellow of the American Academy of Arts & Sciences in 2021. Publications Books * ''Philosophy of Mathematics: Structure and Ontology''. Oxford University Press, 1997. * ''Thinking about Mathematics: The Philosophy of Mathematics''. Oxford University Press, 2000. * ''Foundations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English-language Non-fiction Books
English is a West Germanic language that developed in early medieval England and has since become a global lingua franca. The namesake of the language is the Angles, one of the Germanic peoples that migrated to Britain after its Roman occupiers left. English is the most spoken language in the world, primarily due to the global influences of the former British Empire (succeeded by the Commonwealth of Nations) and the United States. English is the third-most spoken native language, after Mandarin Chinese and Spanish; it is also the most widely learned second language in the world, with more second-language speakers than native speakers. English is either the official language or one of the official languages in 57 sovereign states and 30 dependent territories, making it the most geographically widespread language in the world. In the United Kingdom, the United States, Australia, and New Zealand, it is the dominant language for historical reasons without being explicitl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press Books
Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 United Kingdom census, the population of the City of Cambridge was 145,700; the population of the wider built-up area (which extends outside the city council area) was 181,137. (2021 census) There is archaeological evidence of settlement in the area as early as the Bronze Age, and Cambridge became an important trading centre during the Roman Britain, Roman and Viking eras. The first Town charter#Municipal charters, town charters were granted in the 12th century, although modern city status was not officially conferred until 1951. The city is well known as the home of the University of Cambridge, which was founded in 1209 and consistently ranks among the best universities in the world. The buildings of the university include King's College Chap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2008 Non-fiction Books
8 (eight) is the natural number following 7 and preceding 9. Etymology English ''eight'', from Old English '', æhta'', Proto-Germanic ''*ahto'' is a direct continuation of Proto-Indo-European '' *oḱtṓ(w)-'', and as such cognate with Greek and Latin , both of which stems are reflected by the English prefix oct(o)-, as in the ordinal adjective ''octaval'' or ''octavary'', the distributive adjective is '' octonary''. The adjective ''octuple'' (Latin ) may also be used as a noun, meaning "a set of eight items"; the diminutive '' octuplet'' is mostly used to refer to eight siblings delivered in one birth. The Semitic numeral is based on a root ''*θmn-'', whence Akkadian ''smn-'', Arabic ''ṯmn-'', Hebrew ''šmn-'' etc. The Chinese numeral, written ( Mandarin: ''bā''; Cantonese: ''baat''), is from Old Chinese ''*priāt-'', ultimately from Sino-Tibetan ''b-r-gyat'' or ''b-g-ryat'' which also yielded Tibetan '' brgyat''. It has been argued that, as the cardinal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2001 Non-fiction Books
1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, a determiner for singular nouns, and a gender-neutral pronoun. Historically, the representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In digital technology, 1 represents the "on" state in binary code, the foundation of computing. Philosophically, 1 symbolizes the ultimate reality or source of existence in various traditions. In mathematics The number 1 is the first natural number after 0. Each natural numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Books
Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google that searches the full text of books and magazines that Google has scanned, converted to text using optical character recognition (OCR), and stored in its digital database.The basic Google book link is found at: https://books.google.com/ . The "advanced" interface allowing more specific searches is found at: https://books.google.com/advanced_book_search Books are provided either by publishers and authors through the Google Books Partner Program, or by Google's library partners through the Library Project. Additionally, Google has partnered with a number of magazine publishers to digitize their archives. The Publisher Program was first known as Google Print when it was introduced at the Frankfurt Book Fair in October 2004. The Google Books Library Project, which scans works in the collections of library partners and adds them to the digital inventory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first-order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. The most commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as duals; in classical logic: each can be defined in terms of the other using negation. They can also be used to define more complex quantifiers, as in the formula \neg \exists x P(x) which expresses that nothing has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof By Induction
Mathematical induction is a method for proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for n = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case n = k, ''then'' it must also hold for the next case n = k + 1. These two steps establish that the statement holds for every natural number n. The base case does not necessarily begin with n = 0, but often with n = 1, and possibly with any fixed natural number n = N, establishing the truth of the statement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set-builder Notation
In mathematics and more specifically in set theory, set-builder notation is a notation for specifying a set by a property that characterizes its members. Specifying sets by member properties is allowed by the axiom schema of specification. This is also known as set comprehension and set abstraction. Sets defined by a predicate Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to ''true'' for an element of the set, and ''false'' otherwise. In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the separator, and a rule on the right of it. These three parts are contained in curly brackets: :\ or :\. The vertical bar (or colon) is a separator that can be read as "such that", "for which", or "with the property that". The formula is said to be the ''rule'' or the ''predicate''. All values of for which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prolegomenon
In an essay, article, or book, an introduction (also known as a prolegomenon) is a beginning section which states the purpose and goals of the following writing. This is generally followed by the body and conclusion. Common features and techniques The introduction typically describes the scope of the document and gives a brief explanation or a summary of the document. It may also explain certain elements that are important to the document. The readers can thus have an idea about the following text before they actually start reading it. The University of Toronto provides advice about how to write essays: A good introduction should identify your topic, provide essential context, and indicate your particular focus in the essay. It also needs to engage your readers’ interest. Some authors write their introduction first, while others prefer to leave it for a later stage in the writing process; another option is to start with a rough draft introduction, and then come back to fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
