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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 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]