Combining Texts

Ideas for 'Metaphysics', 'Truly Understood' and 'The Development of Logic'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

3 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
562 Axioms are the underlying principles of everything, and who but the philosopher can assess their truth? [Aristotle]
     Full Idea: Axioms are more general, and the principles of all things. If this does not belong to the philosopher, who else will have the job of considering truth and falsity in their case?
     From: Aristotle (Metaphysics [c.324 BCE], 0997a09)
573 The axioms of mathematics are part of philosophy [Aristotle]
     Full Idea: A single science, that of the philosopher, also covers the axioms of mathematics.
     From: Aristotle (Metaphysics [c.324 BCE], 1005a15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10051 The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism [Kneale,W and M]
     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.