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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 from 'Philosophy of Logic'

18949 The universal syllogism is now expressed as the transitivity of subclasses [Putnam]
18951 For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam]
18950 Physics is full of non-physical entities, such as space-vectors [Putnam]
18955 Having a valid form doesn't ensure truth, as it may be meaningless [Putnam]
18952 '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]
18953 Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
18954 Before the late 19th century logic was trivialised by not dealing with relations [Putnam]
18956 Asserting first-order validity implicitly involves second-order reference to classes [Putnam]
18957 Nominalism only makes sense if it is materialist [Putnam]
18958 In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
18959 Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam]
18960 Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam]
18962 Unfashionably, I think logic has an empirical foundation [Putnam]
18961 We can identify functions with certain sets - or identify sets with certain functions [Putnam]