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Salva Veritate
The literal translation of the Latin "''salva veritate''" is "with (or by) unharmed truth", using ablative of manner: "''salva''" meaning "rescue," "salvation," or "welfare," and "''veritate''" meaning "reality" or "truth". Thus, ''Salva veritate'' (or intersubstitutivity) is the logical condition by which two expressions may be interchanged without altering the truth-value of statements in which the expressions occur. Substitution ''salva veritate'' of co-extensional terms can fail in opaque contexts. Leibniz The phrase occurs in two fragments from Gottfried Leibniz's ''General Science. Characteristics'': * In Chapter 19, Definition 1, Leibniz writes: "Two terms are the same (''eadem'') if one can be substituted for the other ''without altering the truth of any statement'' (''salva veritate'')." * In Chapter 20, Definition 1, Leibniz writes: "Terms which can be substituted for one another wherever we please ''without altering the truth of any statement'' (''salva veritate''), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the Roman Republic it became the dominant language in the Italian region and subsequently throughout the Roman Empire. Even after the fall of Western Rome, Latin remained the common language of international communication, science, scholarship and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became a dead language in the modern linguistic definition. Latin is a highly inflected language, with three distinct genders (masculine, feminine, and neuter), six or seven noun cases (nominative, accusative, genitive, dative, ablative, and vocative), five declensions, four verb conjuga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giorgio Barbarelli
Giorgione (, , ; born Giorgio Barbarelli da Castelfranco; 1477–78 or 1473–74 – 17 September 1510) was an Italian painter of the Venetian school during the High Renaissance, who died in his thirties. He is known for the elusive poetic quality of his work, though only about six surviving paintings are firmly attributed to him. The uncertainty surrounding the identity and meaning of his work has made Giorgione one of the most mysterious figures in European art. Together with his younger contemporary Titian, he founded the Venetian school of Italian Renaissance painting, characterised by its use of colour and mood. The school is traditionally contrasted with Florentine painting, which relied on a more linear disegno-led style. Life What little is known of Giorgione's life is given in Giorgio Vasari's ''Lives of the Most Excellent Painters, Sculptors, and Architects''. He came from the small town of Castelfranco Veneto, 40 km inland from Venice. His name sometimes appear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clarence Irving Lewis
Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logician, he later branched into epistemology, and during the last 20 years of his life, he wrote much on ethics. ''The New York Times'' memorialized him as "a leading authority on symbolic logic and on the philosophic concepts of knowledge and value." He was the first to coin the term "Qualia" as it is used today in philosophy, linguistics, and cognitive sciences.Lewis, Clarence Irving (1929). ''Mind and the world-order: Outline of a theory of knowledge''. New York: Charles Scribner's Sons. p. 121 Biography Lewis was born in Stoneham, Massachusetts. His father was a skilled worker in a shoe factory, and Lewis grew up in relatively humble circumstances. He discovered philosophy at age 13, when reading about the Greek pre-Socratics, Anaxagoras ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Without Loss Of Generality
''Without loss of generality'' (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as ''without any loss of generality'' or ''with no loss of generality'') is a frequently used expression in mathematics. The term is used to indicate the assumption that follows is chosen arbitrarily, narrowing the premise to a particular case, but does not affect the validity of the proof in general. The other cases are sufficiently similar to the one presented that proving them follows by essentially the same logic. As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases. In many scenarios, the use of "without loss of generality" is made possible by the presence of symmetry. For example, if some property ''P''(''x'',''y'') of real numbers is known to be symmetric in ''x'' and ''y'', namely that ''P''(''x'',''y'') is equivalent to ''P''(''y'',''x''), then in proving that ''P''(''x'',''y'') holds for every ''x'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Function
In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly one truth value; and inputting the same truth value(s) will always output the same truth value. The typical example is in propositional logic, wherein a compound statement is constructed using individual statements connected by logical connectives; if the truth value of the compound statement is entirely determined by the truth value(s) of the constituent statement(s), the compound statement is called a truth function, and any logical connectives used are said to be truth functional. Classical propositional logic is a truth-functional logic, in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salva Congruitate
''Salva congruitate'' is a Latin scholastic term in logic, which means "without becoming ill-formed", '' salva'' meaning ''rescue'', ''salvation'', ''welfare'' and '' congruitate'' meaning ''combine'', ''coincide'', ''agree''. Salva Congruitate is used in logic to mean that two terms may be substituted for each other while preserving grammaticality in all contexts. Remarks on ''salva congruitate'' Timothy C. Potts Timothy C. Potts describes ''salva congruitate'' as a form of replacement in the context of meaning. It is a replacement which preserves semantic coherence and should be distinguished from a replacement which preserves syntactic coherence but may yield an expression to which no meaning has been given. This means that supposing an original expression is meaningful, the new expression obtained by the replacement will also be meaningful, though it will not necessarily have the same meaning as the original one, nor, if the expression in question happens to be a pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Replacement
In logic, a rule of replacementMoore and Parker is a transformation rule that may be applied to only a particular segment of an logical expression, expression. A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for Well-formed formula, logical expressions in the system. Whereas a rule of inference is always applied to a whole logical expression, a rule of replacement may be applied to only a particular segment. Within the context of a logical proof, logically equivalent expressions may replace each other. Rules of replacement are used in propositional logic to manipulate propositions. Common rules of replacement include de Morgan's laws, Commutative property, commutation, Associative property, association, Distribution (logic), distribution, double negation, Transposition (logic), transposition, Material implication (rule of inference), material implication, logical equivalence, Exportation (logic), exportation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Referential Opacity
An opaque context or referentially opaque context is a linguistic context in which it is not always possible to substitute "co-referential" expressions (expressions referring to the same object) without altering the truth of sentences. The expressions involved are usually grammatically singular terms. So, substitution of co-referential expressions into an opaque context does not always preserve truth. For example, "Lois believes x is a hero" is an opaque context because "Lois believes Superman is a hero" is true while "Lois believes Clark Kent is a hero" is false, even though 'Superman' and 'Clark Kent' are co-referential expressions. Usage The term is used in philosophical theories of reference, and is to be contrasted with referentially transparent context. In rough outline: *Opacity: "Mary believes that Cicero is a great orator" gives rise to an opaque context; although Cicero was also called 'Tully',Tully is anglicised historic name from Tullius, sourceKate Kearns: Semanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Attitude
A propositional attitude is a mental state held by an agent toward a proposition. Linguistically, propositional attitudes are denoted by a verb (e.g. "believed") governing an embedded "that" clause, for example, 'Sally believed that she had won'. Propositional attitudes are often assumed to be the fundamental units of thought and their contents, being propositions, are true or false from the perspective of the person. An agent can have different propositional attitudes toward the same proposition (e.g., "S believes that her ice-cream is cold," and "S fears that her ice-cream is cold"). Propositional attitudes have directions of fit: some are meant to reflect the world, others to influence it. One topic of central concern is the relation between the modalities of assertion and belief, perhaps with intention thrown in for good measure. For example, we frequently find ourselves faced with the question of whether or not a person's assertions conform to his or her beliefs. Disc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobriquet
A sobriquet ( ), or soubriquet, is a nickname, sometimes assumed, but often given by another, that is descriptive. A sobriquet is distinct from a pseudonym, as it is typically a familiar name used in place of a real name, without the need of explanation, and it often becomes more familiar than the original name. The term ''sobriquet'' may apply to the nickname for a specific person, group of people, or place. Examples are "Emiye Menelik", a name of Emperor Menelik II of Ethiopia, who was popularly and affectionately recognized for his kindness ("emiye" means "mother" in Amharic); "Genghis Khan", who now is rarely recognized by his original name Temüjin; and Mohandas Gandhi, who is better known as "Mahatma" Gandhi ("mahatma" means "great soul" in Sanskrit). Well-known places often have sobriquets, such as New York City, often referred to as the "Big Apple". Etymology The modern French spelling is . Two early variants of the term are found: and . The first early spelling varian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Essence
Essence ( la, essentia) is a polysemic term, used in philosophy and theology as a designation for the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Essence is contrasted with accident: a property that the entity or substance has contingently, without which the substance can still retain its identity. The concept originates rigorously with Aristotle (although it can also be found in Plato), who used the Greek expression ''to ti ên einai'' (τὸ τί ἦν εἶναι, literally meaning "the what it was to be" and corresponding to the scholastic term quiddity) or sometimes the shorter phrase ''to ti esti'' (τὸ τί ἐστι, literally meaning "the what it is" and corresponding to the scholastic term haecceity) for the same idea. This phrase presented such difficulties for its Latin translators that they coined the word ''essentia'' (English "essence") to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
