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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 Nagarjuna 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 (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universiti ... [...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 Soviet prison camp in Prague in 1945, having been interned as a German national after the Second World War. 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 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one in which the 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 necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to be a logical conse ... [...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 ''A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mūlamadhyamakakārikā
The ''Mūlamadhyamakakārikā'' ( sa, मूलमध्यमककारिका, ''Root Verses on the Middle Way''), abbreviated as ''MMK'', is the foundational text of the Madhyamaka school of Mahāyāna Buddhist philosophy. It was composed by the Indian philosopher Nāgārjuna (approximately around 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 (somewher ... [...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''). 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 evaluate to false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called "truthy" and "falsy" / "false". Classical logic In classical logic, with its intended semantics, the truth values are ''true'' (denoted by ''1'' or the verum ⊤), and '' untrue'' or '' false'' (denoted by ''0'' or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of log ... [...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''. 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 Corpus is today composed of: * ''Divine Names'' ('); * '' Celestial Hierarchy'' ('')''; * ''Ecclesiastical Hierarchy'' ('); * ''Mystical Theology'' ('), "a brief but powerful wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Gregg Bury
Robert Gregg Bury (22 March 1869 – 11 February 1951) was an Irish 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 ( grc-gre, Σέξτος Ἐμπειρικός, ; ) was a Ancient Greece, Greek Pyrrhonism, Pyrrhonist philosopher and Empiric school physician. 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 philosophy, Hellenistic philosophies, they are also a major source of information about those philosophies. 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. Little is known about Sextus Empiricus. He likely lived in Alexandria, Rome, or Athens. The ''Suda,'' a 10th-century Byzantine encyclopedia, states that he was the same person as Sextus of Chaeronea, as do other pre-modern sources, but this identification is commonly doubted. Writings Diogenes Laërtius ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Interpretatione
''De Interpretatione'' or ''On Interpretation'' (Greek: Περὶ Ἑρμηνείας, ''Peri Hermeneias'') is the second text from Aristotle's ''Organon'' and is among the earliest surviving philosophical works in the Western tradition to deal with the relationship between language and logic in a comprehensive, explicit, and formal way. The work is usually known by its Latin title. The work begins by analyzing simple ''categoric'' propositions, and draws a series of basic conclusions on the routine issues of classifying and defining basic linguistic forms, such as ''simple terms'' and ''propositions'', nouns and verbs, negation, the ''quantity'' of simple propositions (primitive roots of the quantifiers in modern symbolic logic), investigations on the ''excluded middle'' (which to Aristotle is not applicable to future tense propositions—the problem of future contingents), and on modal propositions. The first five chapters deal with the terms that form propositions. Chapter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
