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Single Idea 18952

[filed under theme 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC ]

Full Idea

The symbol '⊃' (read 'if...then') is used with the definition 'Px ⊃ Qx' ('if Px then Qx') is short for '¬(Px & ¬Qx)'.

Gist of Idea

'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)'

Source

Hilary Putnam (Philosophy of Logic [1971], Ch.3)

Book Ref

Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.26

A Reaction

So ⊃ and → are just abbreviations, and not really a proper part of the language. Notoriously, though, this is quite a long way from what 'if...then' means in ordinary English, and it leads to paradoxical oddities.

The 4 ideas with the same theme [meanings of the symbols used in predicate logic]:

13909 Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon]
13902 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon]
13911 The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon]
18952 '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]