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Contraposition (traditional Logic)
In traditional logic, contraposition is a form of immediate inference in which a proposition is inferred from another and where the former has for its subject the contradictory of the original logical proposition's predicate. In some cases, contraposition involves a change of the former's quality (i.e. affirmation or negation). For its symbolic expression in modern logic, see the rule of transposition. Contraposition also has philosophical application distinct from the other traditional inference processes of conversion and obversion where equivocation varies with different proposition types. Traditional logic In traditional logic, the process of contraposition is a schema composed of several steps of inference involving categorical propositions and classes. A categorical proposition contains a subject and predicate where the existential impact of the copula implies the proposition as referring to a class ''with at least one member'', in contrast to the conditional form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traditional Logic
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge. Term logic revived in medieval times, first in Islamic logic by Alpharabius in the tenth century, and later in Christian Europe in the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even if eclipsed by newer logical systems, term logic still plays a significant role in the study of logic. Rather than radically breaking with term logic, modern logics typically expand it, so to understand the newer systems, one must be acquainted with the earlier one. Aristotle's system Aristotle's logical work is collected in the six texts that are collectively known as the ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material Conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language. Notation In l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contraposition
In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as Proof by contrapositive, proof by contraposition. The contrapositive of a statement has its Antecedent (logic), antecedent and consequent Inverse (logic), inverted and Conversion (logic), flipped. Material conditional, Conditional statement P \rightarrow Q. In Logical connective, formulas: the contrapositive of P \rightarrow Q is \neg Q \rightarrow \neg P . If ''P'', Then ''Q''. — If not ''Q'', Then not ''P''. ''"''If ''it is raining,'' then ''I wear my coat" —'' "If ''I don't wear my coat,'' then ''it isn't raining."'' The law of contraposition says that a conditional statement is true if, and only if, its contrapositive is true. The contrapositive ( \neg Q \rightarrow \neg P ) can be compared with three other statements: ;Inverse (logic), Inversion (the inverse), \neg P \rightarrow \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Proposition
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the ''subject term'') are included in another (the ''predicate term''). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called ''A'', ''E'', ''I'', and ''O''). If, abstractly, the subject category is named ''S'' and the predicate category is named ''P'', the four standard forms are: *All ''S'' are ''P''. (''A'' form, \forall _\rightarrow P_xequiv \forall neg S_\lor P_x/math>) *No ''S'' are ''P''. (''E'' form, \forall _\rightarrow \neg P_xequiv \forall neg S_\lor \neg P_x/math>) *Some ''S'' are ''P''. (''I'' form, \exists _\land P_x/math>) *Some ''S'' are not ''P''. (''O'' form, \ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Of Opposition
In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle's tractate ''On Interpretation'' and its distinction between two oppositions: contradiction and contrariety. However, Aristotle did not draw any diagram. This was done several centuries later by Apuleius and Boethius. Summary In traditional logic, a proposition (Latin: ''propositio'') is a spoken assertion (''oratio enunciativa''), not the meaning of an assertion, as in modern philosophy of language and logic. A '' categorical proposition'' is a simple proposition containing two terms, subject () and predicate (), in which the predicate is either asserted or denied of the subject. Every categorical proposition can be reduced to one of four logical forms, named , , , and based on the Latin ' (I affirm), for the affirmative propositions and , and ' (I deny), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum and the wider Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was born in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Susan Stebbing
Lizzie Susan Stebbing (2 December 1885 – 11 September 1943) was a British philosopher. She belonged to the 1930s generation of analytic philosophy, and was a founder in 1933 of the journal ''Analysis.'' Stebbing was the first woman to hold a philosophy chair in the United Kingdom, as well as the first female President of Humanists UK. Biography Born in North Finchley, Middlesex, ''Susan'' Stebbing (as she preferred to be called), was the youngest of six children born to Alfred Charles Stebbing and Elizabeth (née Elstob), and was orphaned at an early age. Stebbing was educated at James Allen's Girls' School, Dulwich, until she went, in 1904, to Girton College, Cambridge, to read history (though Cambridge did not award degrees or full University membership to women at the time). Having come across F. H. Bradley's ''Appearance and Reality'' she became interested in philosophy and stayed on to take part I of the Moral Sciences tripos in 1908. This was followed by a University of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irving Copi
Irving Marmer Copi (; né Copilovich or Copilowish; July 28, 1917 – August 19, 2002) was an American philosopher, logician, and university textbook author. Biography Copi studied under Bertrand Russell while at the University of Chicago. In 1948 he contributed to the calculus of relations with his article using logical matrices. Copi taught at the University of Illinois, the United States Air Force Academy, Princeton University, and the Georgetown University Logic Institute, before teaching logic at the University of Michigan, 1958–69, and at the University of Hawaii at Manoa, 1969–90. Assigned to teach logic, Copi reviewed textbooks available and decided to write his own. The manuscript was split into ''Introduction to Logic'' and ''Symbolic Logic''. A reviewer noted that it had an "unusually comprehensive chapter on definition" and "The author accounts for the seductive nature of informal fallacies." The textbooks proved popular, and a reviewer of the third edition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Logic
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Explanation Logical connectives are found in natural languages. In English for example, some examples are "and" (conjunction), "or" (disjunction), "not" (negation) and "if" ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. Logical equivalences In logic, many common logical equivalences exist and are often listed as laws or properties. The following tables illustrate some of these. General logical equivalences Logical equivalences involving conditional statements :#p \implies q \equiv \neg p \vee q :#p \implies q \equiv \neg q \implies \neg p :#p \vee q \equiv \neg p \implies q :#p \wedge q \equiv \neg (p \implies \neg q) :#\neg (p \implies q) \equiv p \wedge \neg q :#(p \implies q) \wedge (p \implie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conversion (logic)
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication ''P'' → ''Q'', the converse is ''Q'' → ''P''. For the categorical proposition ''All S are P'', the converse is ''All P are S''. Either way, the truth of the converse is generally independent from that of the original statement.Robert Audi, ed. (1999), ''The Cambridge Dictionary of Philosophy'', 2nd ed., Cambridge University Press: "converse". Implicational converse Let ''S'' be a statement of the form ''P implies Q'' (''P'' → ''Q''). Then the converse of ''S'' is the statement ''Q implies P'' (''Q'' → ''P''). In general, the truth of ''S'' says nothing about the truth of its converse, unless the antecedent ''P'' and the consequent ''Q'' are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal." The converse of that statement is "If I am mortal, then I am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particular
In metaphysics, particulars or individuals are usually contrasted with universals. Universals concern features that can be exemplified by various different particulars. Particulars are often seen as concrete, spatiotemporal entities as opposed to abstract entities, such as properties or numbers. There are, however, theories of ''abstract particulars'' or '' tropes''. For example, Socrates is a particular (there's only one Socrates-the-teacher-of-Plato and one cannot make copies of him, e.g., by cloning him, without introducing new, distinct particulars). Redness, by contrast, is not a particular, because it is abstract and multiply instantiated (for example a bicycle, an apple, and a given woman's hair can all be red). In nominalist view everything is particular. Universals in each moment of time from point of view of an observer is the collection of particulars that participates it (even a void collection). Overview Sybil Wolfram Sybil Wolfram, ''Philosophical Logic'', Routledge, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
