Ideas from 'The Development of Logic' by W Kneale / M Kneale [1962], by Theme Structure

[found in 'The Development of Logic' by Kneale,William and Martha [OUP 1984,0-19-824773-7]].

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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism
                        Full Idea: There is something profoundly unsatisfactory about the axiom of infinity. It cannot be described as a truth of logic in any reasonable use of that phrase, and so the introduction of it as a primitive proposition amounts to the abandonment of logicism.
                        From: W Kneale / M Kneale (The Development of Logic [1962], XI.2)
                        A reaction: It seems that the axiom is essentially empirical, and it certainly makes an existential claim which seems to me (intuitively) to have nothing to do with logic at all.