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Single Idea 8071
[filed under theme 4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
]
Full Idea
Aristotle listed a total of nineteen syllogisms involved in logical reasoning, though some of the ones on his list were subsequently shown to be invalid.
Gist of Idea
Aristotle listed nineteen valid syllogisms (though a few of them were wrong)
Source
report of Aristotle (Prior Analytics [c.328 BCE], Ch.1) by Keith Devlin - Goodbye Descartes
Book Ref
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.3
A Reaction
It is quite upsetting to think that the founding genius got some of it wrong, but that just shows how subtle and complex the analysis of rational thought can be.
The
15 ideas
with the same theme
[Aristotle's original account of formal syllogistic logic]:
639
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Socrates developed definitions as the basis of syllogisms, and also inductive arguments
[Socrates, by Aristotle]
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22272
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Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates'
[Potter on Aristotle]
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9405
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Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values
[Aristotle]
|
22271
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Aristotle was the first to use schematic letters in logic
[Aristotle, by Potter]
|
18909
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Aristotelian sentences are made up by one of four 'formative' connectors
[Aristotle, by Engelbretsen]
|
8080
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Aristotelian identified 256 possible syllogisms, saying that 19 are valid
[Aristotle, by Devlin]
|
13912
|
Aristotle replaced Plato's noun-verb form with unions of pairs of terms by one of four 'copulae'
[Aristotle, by Engelbretsen/Sayward]
|
11060
|
Aristotelian syllogisms are three-part, subject-predicate, existentially committed, with laws of thought
[Aristotle, by Hanna]
|
8071
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Aristotle listed nineteen valid syllogisms (though a few of them were wrong)
[Aristotle, by Devlin]
|
18953
|
Modern notation frees us from Aristotle's restriction of only using two class-names in premises
[Putnam]
|
13643
|
Aristotelian logic is complete
[Shapiro]
|
23505
|
Aristotelian logic cannot express 'Everyone loves someone'
[White,RM]
|
13913
|
The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio
[Engelbretsen/Sayward]
|
13914
|
Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts
[Engelbretsen/Sayward]
|
18913
|
Traditional term logic struggled to express relations
[Engelbretsen]
|