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Qualitative Logic
An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's ''Collected Papers''. Peirce wrote of this system in an 1897 ''Monist'' article titled "The Logic of Relatives", although he had mentioned logical graphs in an 1882 letter to O. H. Mitchell. The syntax is: * The blank page; * Single letters, phrases; * Dashes; * Objects (subgraphs) enclosed by a simple closed curve called a ''cut''. A cut can be empty. The semantics are: * The blank page denotes False; * Letters, phrases, subgraphs, and entire graphs can be True or False; * To surround objects with a cut is equivalent to Boolean complementation. Hence an empty cut denotes Truth; * All objects within a given cut are tacitly joined by disjunction. * A dash ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagram
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term " illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, represen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars. The earliest mathematical texts available are from Mesopotamia and Egypt – '' Plimpton 322'' ( Babylonian c. 2000 – 1900 BC), the ''Rhind Mathematical Papyrus'' ( Egyptian c. 1800 BC) and the '' Moscow Mathematical Papyrus'' (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most anci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Logic
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in Indian logic, India, Logic in China, China, and Greek philosophy, Greece. Greek methods, particularly Aristotelian logic (or term logic) as found in the ''Organon'', found wide application and acceptance in Western science and mathematics for millennia.Boehner p. xiv The Stoicism, Stoics, especially Chrysippus, began the development of predicate logic. Christian philosophy, Christian and Logic in Islamic philosophy, Islamic philosophers such as Boethius (died 524), Ibn Sina (Avicenna, died 1037) and William of Ockham (died 1347) further developed Plato's logic in the Medieval philosophy#High Middle Ages, Middle Ages, reaching a high point in the mid-fourteenth century, with Jean Buridan. The period between the fourteenth century and the beginning of the nineteenth century saw largely decline and neglect, and at least one historian of l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagrams
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term "illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, representat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Chronological Edition
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguish it fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Weiss (philosopher)
Paul Weiss (; May 19, 1901 – July 5, 2002) was an American philosopher. He was the founder of ''The Review of Metaphysics'' and the Metaphysical Society of America. Early life and education Paul Weiss grew up on the Lower East Side of New York City. His father, Samuel Weiss (d. 1917), was a Jewish emigrant who moved from Europe in the 1890s. He worked as a tinsmith, a coppersmith, and a boilermaker. Paul Weiss's mother, Emma Rothschild (Weiss) (d. 1915), was a Jewish emigrant who worked as a servant until she married Samuel. Born into a Jewish family, Paul lived among other Jewish families in a working-class neighborhood in the Yorkville section of Manhattan. Originally given the Hebrew name "Peretz," Weiss says in his autobiography that the name "Paul" was his "registered name" and "part of his mother's attempt to move upward in the American world."Weiss, Paul. The Philosophy of Paul Weiss. Ed. Lewis Hahn. Chicago : Open Court, 1995. He had three brothers, two older and one y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Hartshorne
Charles Hartshorne (; June 5, 1897 – October 9, 2000) was an American philosopher who concentrated primarily on the philosophy of religion and metaphysics, but also contributed to ornithology. He developed the neoclassical idea of God and produced a modal proof of the existence of God that was a development of Anselm of Canterbury's ontological argument. Hartshorne is also noted for developing Alfred North Whitehead's process philosophy into process theology. Early life and education Hartshorne (pronounced harts-horn) was born in Kittanning, Pennsylvania, and was a son of Reverend Francis Cope Hartshorne (1868-1950) and Marguerite Haughton (1868-1959), who were married on April 25, 1895, in Bryn Mawr, Montgomery County, Pennsylvania. Rev. F. C. Hartshorne, who was a minister in the Protestant Episcopal Church, was rector of St. Paul's Episcopal Church in Kittanning from 1897 to 1909, then rector of St. Peter's Episcopal Church in Phoenixville, Pennsylvania for 19 years ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce Bibliography
This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and . For an extensive chronological list of Peirce's works (titled in English), see the (Chronological Overview) on the (Writings) page for Charles Sanders Peirce. Abbreviations Click on abbreviation in order to jump down this page to the relevant edition information. Click on the abbreviation appearing with that edition information in order to return here. Main editions (posthumous) Other Primary literature Bibliographies and microfilms Other bibliographies of primary literature * Burks, Arthur W. (1958). "Bibliography of the Works of Charles Sanders Peirce." CP 8:260–321. * Cohen, Morris R. (1916). "Charles S. Peirce and a Tentative Bibliography of His Published Writings." ''The Journal of Philosophy, Psychology, and Scientific Methods'' 13(26):726–37. *Fisch, Max H. (1964). "A First Supplement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laws Of Form
''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems: * The "primary arithmetic" (described in Chapter 4 of ''LoF''), whose models include Boolean arithmetic; * The "primary algebra" (Chapter 6 of ''LoF''), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus; * "Equations of the second degree" (Chapter 11), whose interpretations include finite automata and Alonzo Church's Restricted Recursive Arithmetic (RRA). "Boundary algebra" is Meguire's (2011) term for the union of the primary algebra and the primary arithmetic. ''Laws of Form'' sometimes loosely refers to the "primary algebra" as well as to ''LoF''. The book The preface states that the work was first explored in 1959, and Spencer Brown cites Bertrand Russell as being supportive of his endeav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Modal Logic
In logic, a normal modal logic is a set ''L'' of modal formulas such that ''L'' contains: * All propositional tautologies; * All instances of the Kripke schema: \Box(A\to B)\to(\Box A\to\Box B) and it is closed under: * Detachment rule (''modus ponens''): A\to B, A \in L implies B \in L; * Necessitation rule: A \in L implies \Box A \in L. The smallest logic satisfying the above conditions is called K. Most modal logics commonly used nowadays (in terms of having philosophical motivations), e.g. C. I. Lewis's S4 and S5, are normal (and hence are extensions of K). However a number of deontic and epistemic logic Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applica ...s, for example, are non-normal, often because they give up the Kripke schema. Every normal modal logic is regular and hen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (mathematics)
In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is , then the dual of is . Such involutions sometimes have fixed points, so that the dual of is itself. For example, Desargues' theorem is self-dual in this sense under the ''standard duality in projective geometry''. In mathematical contexts, ''duality'' has numerous meanings. It has been described as "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics". Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, ''linear algebra duality'' corresponds in this way to bilinear maps from pairs of vecto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
