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Single Idea 18949
[filed under theme 4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
]
Full Idea
On its modern interpretation, the validity of the inference 'All S are M; All M are P; so All S are P' just expresses the transitivity of the relation 'subclass of'.
Gist of Idea
The universal syllogism is now expressed as the transitivity of subclasses
Source
Hilary Putnam (Philosophy of Logic [1971], Ch.1)
Book Ref
Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.5
A Reaction
A simple point I've never quite grasped. Since lots of syllogisms can be expressed as Venn Diagrams, in which the circles are just sets, it's kind of obvious really. So why does Sommers go back to 'terms'? See 'Term Logic'.
The
14 ideas
with the same theme
[general ideas about formal arguments in syllogism form]:
13819
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Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs
[Bostock on Aristotle]
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20778
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Stoics like syllogisms, for showing what is demonstrative, which corrects opinions
[Stoic school, by Diog. Laertius]
|
8084
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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]
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14453
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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]
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13439
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Venn Diagrams map three predicates into eight compartments, then look for the conclusion
[Bostock]
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19006
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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]
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10688
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'Equivocation' is when terms do not mean the same thing in premises and conclusion
[Beall/Restall]
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13915
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Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences
[Engelbretsen/Sayward]
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