Concepts as Involving Laws and Inconceivable Without Them

Formal implication is usually represented by symbolization such as ‘(x) φ x ⊃ Ψx,’ which may be read, “for all values of ‘x’, φ x (materially) implies Ψx.” If the values of the variable ‘x’, in ‘φ x’ and ‘Ψx’ be ‘x 1 ’ ‘x 2 ’ ‘x 3 ’, etc., then … ‘ φ x’ formally implies ‘Ψx’ if and only if, whatever values of ‘x’, ‘x n ’, be chosen, ‘ φ x n ’ materially implies ‘Ψx n ’ … However, this still leaves it doubtful which of two possible interpretations of expressions having the form ‘(x) φ x ⊃ Ψx’ is to be taken as correct. … It means one thing to say, “Every existent having the property φ … has also the property Ψ,” and it means quite a different thing to say, “Every thinkable thing which should have the property φ must also have the property Ψ.” The second of these holds only when having the properly φ logically entails having the property Ψ; when ‘ Ψ x’ is deductible from ‘φx’ . … The first of them, however, holds not only in such cases … but also in every case where among existent things, one property is universally accompanied by another. (C. I. Lewis, An Analysis of Knowledge and Evaluation , pp. 217–8. I am responsible for the italicizing of the sentence, otherwise the italics follow Lewis.)