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Single Idea 13909

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

Full Idea

Just as '(∀x)(...)' is to mean 'take any x: then....', so we write '(∃x)(...)' to mean 'there is an x such that....'

Gist of Idea

Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....'

Source

E.J. Lemmon (Beginning Logic [1965], 3.1)

Book Ref

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.96

A Reaction

[Actually Lemmon gives the universal quantifier symbol as '(x)', but the inverted A ('∀') seems to have replaced it these days]

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]