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Illicit Minor
Illicit minor is a formal fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion. This fallacy has the following argument form: :All A are B. :All A are C. :Therefore, all C are B. ''Example:'' : All cats are felines. : All cats are mammals. : Therefore, all mammals are felines. The minor term here is mammal, which is not distributed in the minor premise "All cats are mammals", because this premise is only defining a property of possibly some mammals (i.e., that they're cats.) However, in the conclusion "All mammals are felines", mammal ''is'' distributed (it is talking about all mammals being felines). It is shown to be false by any mammal that is not a feline; for example, a dog. ''Example:'' : Pie is good. : Pie is unhealthy. : Thus, all good things are unhealthy. See also * Illicit major * Syllogistic fallacy A syllogism ( grc-gre, συλλογισμός, ''syl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Fallacy
In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic.Harry J. Gensler, ''The A to Z of Logic'' (2010) p. 74. Rowman & Littlefield, It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where 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 fallacies covered by particular terms (e.g., affirming the consequent). In other words, in practice, "''non s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Syllogism
A syllogism ( grc-gre, συλλογισμός, ''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 BCE book ''Prior Analytics''), a 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 ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Validity (logic)
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas (also called ''wffs'' or simply ''formulas''). The validity of an argument can be tested, proved or disproved, and depends on its logical form. Arguments In logic, an argument is a set of statements expressing the ''premises'' (whatever consists of empirical evidences and axiomatic truths) and an ''evidence-based conclusion.'' An argument is ''valid'' if and only if it would be contradictory for the conclusion to be false if all of the premises are true. Validity doesn't require the truth of the premises, inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minor Term
A syllogism ( grc-gre, συλλογισμός, ''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 BCE book ''Prior Analytics''), a 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 ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution Of Terms
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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minor Premise
A syllogism ( grc-gre, συλλογισμός, ''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 BCE book ''Prior Analytics''), a 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 ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argument Form
In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language. The logical form of an argument is called the argument form of the argument. History The importance of the concept of form to logic was already recognized in ancient times. Aristotle, in the ''Prior Analytics'', was probably the first to employ variable letters to represent valid inferences. Therefore, Jan Łukasiewicz claims that the introduction of variables was "one of Aristotle's greatest inventions." According ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mammal
Mammals () are a group of vertebrate animals constituting the class Mammalia (), characterized by the presence of mammary glands which in females produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur or hair, and three middle ear bones. These characteristics distinguish them from reptiles (including birds) from which they diverged in the Carboniferous, over 300 million years ago. Around 6,400 extant species of mammals have been described divided into 29 orders. The largest orders, in terms of number of species, are the rodents, bats, and Eulipotyphla (hedgehogs, moles, shrews, and others). The next three are the Primates (including humans, apes, monkeys, and others), the Artiodactyla ( cetaceans and even-toed ungulates), and the Carnivora (cats, dogs, seals, and others). In terms of cladistics, which reflects evolutionary history, mammals are the only living members of the Synapsida (synapsids); this clade, together with Saur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felidae
Felidae () is the family of mammals in the order Carnivora colloquially referred to as cats, and constitutes a clade. A member of this family is also called a felid (). The term "cat" refers both to felids in general and specifically to the domestic cat (''Felis catus''). Felidae species exhibit the most diverse fur pattern of all terrestrial carnivores. Cats have retractile claws, slender muscular bodies and strong flexible forelimbs. Their teeth and facial muscles allow for a powerful bite. They are all obligate carnivores, and most are solitary predators ambushing or stalking their prey. Wild cats occur in Africa, Europe, Asia and the Americas. Some wild cat species are adapted to forest habitats, some to arid environments, and a few also to wetlands and mountainous terrain. Their activity patterns range from nocturnal and crepuscular to diurnal, depending on their preferred prey species. Reginald Innes Pocock divided the extant Felidae into three subfamilies: the P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Illicit Major
Illicit major is a formal fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion. This fallacy has the following argument form: #''All A are B'' #''No C are A'' #''Therefore, no C are B'' Example: #''All dogs are mammals'' #''No cats are dogs'' #''Therefore, no cats are mammals'' In this argument, the major term is "mammals". This is distributed in the conclusion (the last statement) because we are making a claim about a property of ''all'' mammals: that they are not cats. However, it is not distributed in the major premise (the first statement) where we are only talking about a property of ''some'' mammals: Only some mammals are dogs. The error is in assuming that the converse of the first statement (that all mammals are dogs) is also true. However, an argument in the following form differs from the above, and is valid (Camestres): #''All A are B'' #''No B are C'' #''Therefore, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogistic Fallacy
A syllogism ( grc-gre, συλλογισμός, ''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 BCE book ''Prior Analytics''), a 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 ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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