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Syllogism: Encyclopedia BETAFree Encyclopedia |
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Of course, the vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises). The table below shows the valid forms of syllogism. The letters standing for the types of proposition (A, E, I, O) have been used since the mediæval Schools to form mnemonic names for the forms:
Barbara:All men are mortal.:Socrates is a man.:Socrates is mortal. Celarent:No reptiles have fur.:All snakes are reptiles.:No snakes have fur. Darii:All kittens are playful.:Some pets are kittens.:Some pets are playful. Ferio:No homework is fun.:Some reading is homework.:Some reading is not fun. Cesare:No healthy food is fattening.:All cakes are fattening.:No cakes are healthy. Camestres:All horses have hooves.:No humans have hooves.:No humans are horses. Festino:No lazy people pass exams.:Some students pass exams.:Some students are not lazy. Baroco:All informative things are useful.:Some websites are not useful.:Some websites are not informative. Darapti:All fruit is nutritious.:All fruit is tasty.:Some tasty things are nutritious. Disamis:Some mugs are beautiful.:All mugs are useful.:Some useful things are beautiful. Datisi:All the industrious boys in this school have red hair.:Some of the industrious boys are boarders.:Some boarders in this school have red hair. Felapton:No jug in this cupboard is new.:All jugs in this cupboard are cracked.:Some of the cracked items in this cupboard are not new. Bocardo:Some cats have no tails.:All cats are mammals.:Some mammals have no tails. Ferison:No tree is edible.:Some trees are green.:Some green things are not edible. Bramantip:All apples in my garden are wholesome.:All wholesome fruit is ripe.:Some ripe fruit is in my garden. Camenes:All coloured flowers are scented.:No scented flowers are grown indoors.:No flowers grown indoors are coloured. Dimaris:Some small birds live on honey.:All birds that live on honey are colourful.:Some colourful birds are small. 'Fesapo:No humans are perfect.:All perfect creatures are mythical.:Some mythical creatures are not human. Fresison:No competent person is always blundering.:Some people who are always blundering work here.:Some people who work here are incompetent. Forms can be converted to other forms, following certain rules, and all forms can be converted into one of the first-figure forms. The syllogism in the history of logicLogic was dominated by syllogistic reasoning until the 19th centuryA prominent example is the Port-Royal Logic, a 1662 logic textbook by Antoine Arnauld and Pierre Nicole. Modifications were incorporated to deal with disjunctive ("A or B") and condititional ("if A then B") statements. Kant infamously claimed that logic was the one completed science, and that Aristotle had more or less discovered everything about it there was to know.Still, it was cumbersome and very limited in its ability to reveal the logical structure of complex sentences. For example, it was unable to express the claim that the real line is a dense orderMichael Friedman emphasizes this in his Kant and the Exact Sciences (1992). In the late 19th century, Frege's discovery of first order logic revolutionized the field and the Aristotilean system has since been left to introductory material and historical study. Everyday syllogistic mistakesPeople often make mistakes when reasoning syllogistically.For instance, given the following parameters: some A are B, some B are C, people tend to come to a definitive conclusion that therefore some A are C. However, this does not follow (for instance, while some cats (A) are black (B), and some black things (B) are televisions (C), it is false that some cats (A) are televisions (C)). In general, a syllogism with two "some"s guarantees no conclusion. Errors of this sort may result from a failure to consider alternative mental models of the situation, aside from the first model to come to mind. This theory, proposed by Philip Johnson-Laird and others, has received wide support. As Johnson-Baird writes: The source of error in a model may be mere ignorance, as in many misconceptions about force in physical systems. Sometimes, however, the error arises from a failure to envisage the situation properly or to hold in mind various possibilities, particularly in difficult deductive inferences. A nice example of the failure to envisage a situation has been described by Hinton (1979). The task is to imagine a cube balanced on one corner with the diametrically opposed corner vertically above it and then to indicate the locations of the other corners of the cube. Correct performance is rare without considerable previous experience with cubes. Many people consider that there are only four other corners that lie on the same horizontal plane.: (from Mental Models: Toward a Cognitive Science of Language, Inference and Consciousness (1983) by Philip Johnson-Laird) References*Aristotle, Prior Analytics. transl. Robin Smith (Hackett, 1989) ISBN 0-87220-064-7.*Blackburn, Simon, Oxford Dictionary of Philosophy (Oxford University Press, 1996) ISBN 0-19-283134-8. *Broadie, Alexander, Introduction to Medieval Logic (Oxford University Press, 1993) ISBN 0-19-824026-0. *Copi, Irving M., Introduction to Logic, Third edition, Macmillan Company, (1969). See also*Venn diagram*Syllogistic fallacy *Forms of syllogism: ** Disjunctive syllogism ** Hypothetical syllogism ** Polysyllogism ** Quasi-syllogism ** Statistical syllogism External links* Abbreviatio Montana article by Prof. R. J. Kilcullen of Macquarie University on the medieval classification of syllogisms.* The Figures of the Syllogism is a brief table listing the forms of the syllogism. * Stanford Encyclopedia of Philosophy entry on Medieval Theories of Syllogisms References
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