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Existential Fallacy
The existential fallacy, or existential instantiation, is a formal fallacy. In the existential fallacy, one presupposes that a class has members when one is not supposed to do so; i.e., when one should not assume existential import. Not to be confused with the 'Affirming the consequent', as in "If A, then B. B. Therefore A". One example would be: "''Every unicorn has a horn on its forehead''". It does not imply that there are any unicorns at all in the world, and thus it cannot be assumed that, if the statement were true, somewhere there is a unicorn in the world (with a horn on its forehead). The statement, if assumed true, implies only that if there were any unicorns, each would definitely have a horn on its forehead. Overview An existential fallacy is committed in a medieval categorical syllogism because it has two universal premises and a particular conclusion with no assumption that at least one member of the class exists, an assumption which is not established by the prem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Instantiation
In predicate logic, existential instantiation (also called existential elimination) is a rule of inference which says that, given a formula of the form (\exists x) \phi(x), one may infer \phi(c) for a new constant symbol ''c''. The rule has the restrictions that the constant ''c'' introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof. It is also necessary that every instance of x which is bound to \exists x must be uniformly replaced by ''c''. This is implied by the notation P\left(\right), but its explicit statement is often left out of explanations. In one formal notation, the rule may be denoted by :\exists x P \left(\right) \implies P \left(\right) where ''a'' is a new constant symbol that has not appeared in the proof. See also * Existential fallacy * Universal instantiation In predicate logic, universal instantiation (UI; also called universal specification or universal eliminat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Fallacy
In logic and philosophical logic, philosophy, a formal fallacy is a pattern of reasoning rendered validity (logic), invalid by a flaw in its logical structure. propositional calculus, Propositional logic, for example, is concerned with the meanings of sentences and the relationships between them. It focuses on the role of logical operators, called propositional connectives, in determining whether a sentence is true. An error in the sequence will result in a deductive argument that is invalid. The argument itself could have true premises, but still have a false logical consequence, conclusion. Thus, a formal fallacy is a fallacy in which deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic. While a logical argument is a ''non sequitur'' if, and only if, it is invalid, the term "non sequitur" typically refers to those types of invalid arguments which do not constitute formal fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Import
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book '' Prior Analytics''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concerne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affirming The Consequent
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the antecedent is true. It takes on the following form: :: If ''P'', then ''Q''. :: ''Q''. :: Therefore, ''P''. which may also be phrased as : P \rightarrow Q (P implies Q) : \therefore Q \rightarrow P (therefore, Q implies P) For example, it may be true that a broken lamp would cause a room to become dark. It is not true, however, that a dark room implies the presence of a broken lamp. There may be no lamp (or any light source). The lamp may also be off. In other words, the consequent (a dark room) can have other antecedents (no lamp, off-lamp), and so can still be true even if the stated antecedent is not. Converse errors are comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Syllogism
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book '' Prior Analytics''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concerne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic philosophy.Stanford Encyclopedia of Philosophy"Bertrand Russell", 1 May 2003. He was one of the early 20th century's prominent logicians and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore, and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against British idealism, idealism". Together with his former teacher Alfred North Whitehead, A. N. Whitehead, Russell wrote ''Principia Mathematica'', a milestone in the development of classical logic and a major attempt to reduce the whole of mathematics to logic (see logicism). Russell's article "On Denoting" has been considered a "paradigm of philosophy". Russell was a Pacifism, pacifist who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giuseppe Peano
Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much Mathematical notation, notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin. He also created an international auxiliary language, Latino sine flexione ("Latin without inflections"), which is a simplified version of Classical Latin. Most of his books and papers are in Latino sine flexione, while others are in Italian. Biography Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Piedmont, Italy. He attended the Liceo classico Cavour in Turin, and enrolled at the Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enthymeme
An enthymeme (, ''enthýmēma'') is an argument with a hidden premise. Enthymemes are usually developed from premises that accord with the audience's view of the world and what is taken to be common sense. However, where the general premise of a syllogism is supposed to be true, making the subsequent deduction necessary, the general premise of an enthymeme is merely probable, which leads only to a tentative conclusion. Originally theorized by Aristotle, there are four types of enthymeme, at least two of which are described in Aristotle's work. Aristotle referred to the enthymeme as "the body of proof", "the strongest of rhetorical proofs...a kind of syllogism" (''Rhetoric'' I, 1.3,11). He considered it to be one of two kinds of proof, the other of which was the paradeigma. Maxims, Aristotle thought, were a derivative of enthymemes. (''Rhetoric'' II.XX.1). Aristotle discusses two types of enthymemes: demonstrative 'deiktika''and refutative 'elentika'' or ''rézoi'' (ῥέζοι) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogism
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book '' Prior Analytics''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first-order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. The most commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as duals; in classical logic: each can be defined in terms of the other using negation. They can also be used to define more complex quantifiers, as in the formula \neg \exists x P(x) which expresses that nothing has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuous Truth
In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied. It is sometimes said that a statement is vacuously true because it does not really say anything. For example, the statement "all cell phones in the room are turned off" will be true when no cell phones are present in the room. In this case, the statement "all cell phones in the room are turned ''on''" would also be vacuously true, as would the conjunction of the two: "all cell phones in the room are turned on ''and'' turned off", which would otherwise be incoherent and false. More formally, a relatively well-defined usage refers to a conditional statement (or a universal conditional statement) with a false antecedent. One example of such a statement is "if Tokyo is in Spain, then the Eiffel Tower is in Bolivia". Such statements are considered vacuous truths becau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogistic Fallacies
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of Argument, logical argument that applies deductive reasoning to arrive at a Logical consequence, conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book ''Prior Analytics''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Term logic, Aristotelian syllogism and Stoic logic, Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
