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Full Idea
Some moods of the syllogism are fallacious, e.g. 'Darapti': 'All M is S, all M is P, therefore some S is P', which fails if there is no M.
Gist of Idea
The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M?
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], XV)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.164
A Reaction
This critique rests on the fact that the existential quantifier entails some existence, but the universal quantifier does not.
Related Idea
Idea 13819 Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs [Bostock on Aristotle]
| 13819 | Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs [Bostock on Aristotle] |
| 20778 | Stoics like syllogisms, for showing what is demonstrative, which corrects opinions [Stoic school, by Diog. Laertius] |
| 8084 | Syllogisms are verbal fencing, not discovery [Locke] |
| 12572 | Many people can reason well, yet can't make a syllogism [Locke] |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| 14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
| 5401 | The mortality of Socrates is more certain from induction than it is from deduction [Russell] |
| 18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
| 15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
| 13439 | Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock] |
| 19006 | An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo] |
| 8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| 13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |