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Logical Quality
In many philosophies of logic, statements are categorized into different logical qualities based on how they go about saying what they say. Doctrines of logical quality are an attempt to answer the question: "How many qualitatively different ways are there of saying something?" Aristotle answers, two: you can affirm something of something or deny something of something. Since Frege, the normal answer in the West, is only one, assertion, but what is said, the content of the claim, can vary. For Frege asserting the negation of a claim serves roughly the same role as denying a claim does in Aristotle. Other Western logicians such as Kant and Hegel answer, ultimately three; you can affirm, deny or make merely limiting affirmations, which transcend both affirmation and denial. In Indian logic, four logical qualities have been the norm, and Nāgārjuna is sometimes interpreted as arguing for five. Aristotle's two logical qualities In Aristotle's term logic there are two logical qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy. However, they are considered separate academic disciplines in the modern sense of the term. Influential traditions in the history of philosophy include Western philosophy, Western, Islamic philosophy, Arabic–Persian, Indian philosophy, Indian, and Chinese philosophy. Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the Spirituality, spiritual problem of how to reach Enlightenment in Buddhism, enlighten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gentzen
Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Czech prison camp in Prague in 1945. Life and career Gentzen was a student of Paul Bernays at the University of Göttingen. Bernays was fired as "non-Aryan" in April 1933 and therefore Hermann Weyl formally acted as his supervisor. Gentzen joined the Sturmabteilung in November 1933, although he was by no means compelled to do so. Nevertheless, he kept in contact with Bernays until the beginning of the Second World War. In 1935, he corresponded with Abraham Fraenkel in Jerusalem and was implicated by the Nazi teachers' union as one who "keeps contacts to the Chosen People." In 1935 and 1936, Hermann Weyl, head of the Göttingen mathematics department in 1933 until his resignation under Nazi pressure, made strong efforts to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turnstile (symbol)
In mathematical logic and computer science the symbol ⊢ (\vdash) has taken the name turnstile because of its resemblance to a typical turnstile. It is also referred to as tee and is often read as "yields", "proves", "satisfies" or "entails". Interpretations The turnstile represents a binary relation. It has several different interpretations in different contexts: * In epistemology, Per Martin-Löf (1996) analyzes the \vdash symbol thus: "... e combination of Frege's , judgement stroke and , content stroke �� came to be called the assertion sign." Frege's notation for a judgement of some content ::\vdash A :can then be read ::''I know is true''. :In the same vein, a conditional assertion ::P \vdash Q :can be read as: ::''From , I know that '' * In metalogic, the study of formal languages; the turnstile represents syntactic consequence (or "derivability"). This is to say, that it shows that one string can be derived from another in a single step, according to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metalanguage
In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quotation marks, or writing on a separate line. The structure of sentences and phrases in a metalanguage can be described by a metasyntax. For example, to say that the word "noun" can be used as a noun in a sentence, one could write ''"noun" is a ''. Types of metalanguage There are a variety of recognized types of metalanguage, including ''embedded'', ''ordered'', and ''nested'' (or ''hierarchical'') metalanguages. Embedded An ''embedded metalanguage'' is a language formally, naturally and firmly fixed in an object language. This idea is found in Douglas Hofstadter's book, ''Gödel, Escher, Bach'', in a discussion of the relationship between formal languages and number theory: "... it is in the nature of any formalization of number theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Consequence
Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statement (logic), statements that hold true when one statement logically ''follows from'' one or more statements. A Validity (logic), valid logical argument is one in which the Consequent, conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises?Beall, JC and Restall, Greg, Logical Consequence' The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is logical truth, necessary and Formalism (philosophy of mathematics), formal, by wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequent
In mathematical logic, a sequent is a very general kind of conditional assertion. : A_1,\,\dots,A_m \,\vdash\, B_1,\,\dots,B_n. A sequent may have any number ''m'' of condition formulas ''Ai'' (called " antecedents") and any number ''n'' of asserted formulas ''Bj'' (called "succedents" or " consequents"). A sequent is understood to mean that if all of the antecedent conditions are true, then at least one of the consequent formulas is true. This style of conditional assertion is almost always associated with the conceptual framework of sequent calculus. Introduction The form and semantics of sequents Sequents are best understood in the context of the following three kinds of logical judgments: Unconditional assertion. No antecedent formulas. * Example: ⊢ ''B'' * Meaning: ''B'' is true. Conditional assertion. Any number of antecedent formulas. Simple conditional assertion. Single consequent formula. * Example: ''A1'', ''A2'', ''A3'' ⊢ ''B'' * Meaning: IF ''A1'' AND ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mūlamadhyamakakārikā
The ''Mūlamadhyamakakārikā'' (), abbreviated as ''MMK'', is the foundational text of the Madhyamaka school of Mahāyāna Buddhist philosophy. It was composed by the Indian philosopher Nāgārjuna (around roughly 150 CE).Siderits and Katsura (2013), p. 1. The MMK makes use of reductio arguments to show how ''all'' phenomena ('' dharmas'') are empty of '' svabhava'' (which has been variously translated as essence, own-being, or inherent existence). The MMK is widely regarded as one of the most influential and widely studied texts in the history of Buddhist philosophy. The MMK had a major impact on the subsequent development of Buddhist thought, especially in Tibetan Buddhism and East Asian Buddhism. Background The MMK is the work of Nāgārjuna, an Indian Buddhist monk and philosopher writing in Sanskrit. Very little is known about this figure, including exactly where he lived (somewhere in the Indian subcontinent), exactly what time (some time around the 2nd or 3rd century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth-values
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Truth values are used in computing as well as various types of logic. Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null are treated as false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called falsy and truthy. For example, in Lisp, nil, the empty list, is treated as false, and all other values are treated as true. In C, the number 0 or 0.0 is false, and all other values are treated as true. In JavaScript, the empty string (""), null, undefined, NaN, +0, −0 and false are sometim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critique Of Pure Reason
The ''Critique of Pure Reason'' (; 1781; second edition 1787) is a book by the German philosopher Immanuel Kant, in which the author seeks to determine the limits and scope of metaphysics. Also referred to as Kant's "First Critique", it was followed by his ''Critique of Practical Reason'' (1788) and ''Critique of Judgment'' (1790). In the preface to the first edition, Kant explains that by a "critique of pure reason" he means a critique "of the faculty of reason in general, in respect of all knowledge after which it may strive ''independently of all experience''" and that he aims to decide on "the possibility or impossibility of metaphysics". Kant builds on the work of Empiricism, empiricist philosophers such as John Locke and David Hume, as well as Rationalism, rationalist philosophers such as René Descartes, Gottfried Wilhelm Leibniz and Christian Wolff (philosopher), Christian Wolff. He expounds new ideas on the nature of Philosophy of space and time, space and time, and trie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudo-Dionysius The Areopagite
Pseudo-Dionysius the Areopagite (or Dionysius the Pseudo-Areopagite) was a Greek author, Christian theologian and Neoplatonic philosopher of the late 5th to early 6th century, who wrote a set of works known as the ''Corpus Areopagiticum'' or ''Corpus Dionysiacum''. Through his writing in ''Mystical Theology'', he has been identified as the "progenitor of apophatic or negative theology." The author pseudepigraphically identifies himself in the corpus as "Dionysios", portraying himself as Dionysius the Areopagite, the Athenian convert of Paul the Apostle mentioned in Acts 17:34. Historic confusions In the early sixth century, a series of writings of a mystical nature, employing Neoplatonic language to elucidate Christian theological and mystical ideas, was ascribed to the Areopagite. They have long been recognized as pseudepigrapha, and their author is now called "Pseudo-Dionysius the Areopagite". Corpus Works The surviving corpus comprises: * ''Divine Names'' (') ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Gregg Bury
Robert Gregg Bury (; 22 March 1869 – 11 February 1951) was an Irish Anglican clergyman, classicist, philologist, and a translator of the works of Plato and Sextus Empiricus into English. Early life and education Born in Clontibret, County Monaghan, Ireland, Bury was the son of Edward John Bury, the canon of Clogher, and the brother of John Bagnell Bury, an Irish historian, classical scholar, Medieval Roman historian and philologist. It was pleasantly claimed by neighbors that the only language spoken in the Clontibret presbytery was Greek.Auguste Diès"Robert Gregg Bury (1869–1951)" In: ''Bulletin de l'Association Guillaume Budé'', No. 1, March 1952. p. 66. He studied classics under Professor Henry Jackson at Trinity College, Cambridge, winning the Browne Medal Scholar in 1889 and graduating with first-class honours in classics in 1890. He graduated as M.A. in 1893 and received a Litt.D. in 1910. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sextus Empiricus
Sextus Empiricus (, ; ) was a Greek Pyrrhonist philosopher and Empiric school physician with Roman citizenship. His philosophical works are the most complete surviving account of ancient Greek and Roman Pyrrhonism, and because of the arguments they contain against the other Hellenistic philosophies, they are also a major source of information about those philosophies. Life Little is known about Sextus Empiricus. He likely lived in Alexandria, Rome, or Athens. His Roman name, Sextus, implies he was a Roman citizen. The ''Suda,'' a 10th-century Byzantine encyclopedia, states that he was the same person as Sextus of Chaeronea,Suda, Sextos σ 235. as do other pre-modern sources, but this identification is commonly doubted. In his medical work, as reflected by his name, tradition maintains that he belonged to the Empiric school in which Pyrrhonism was popular. However, at least twice in his writings, Sextus seems to place himself closer to the Methodic school. Philosophy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
