6 ideas
| 6294 | In the beginning was the Word, and the Word was with God, and the word was God [John] |
| Full Idea: In the beginning was the Word, and the Word was with God, and the word was God. | |
| From: St John (04: Gospel of St John [c.95], 01.01) | |
| A reaction: 'Word' translates the Greek word 'logos', which has come a long way since Heraclitus. The interesting contrast is with the later Platonist view that the essence of God is the Good. So is the source of everything to be found in reason, or in value? |
| 8821 | Jesus said he bore witness to the truth. Pilate asked, What is truth? [John] |
| Full Idea: Jesus: I came into the world, that I should bear witness unto the truth. Everyone that is of the truth heareth my voice. Pilate saith unto him, What is truth? | |
| From: St John (04: Gospel of St John [c.95], 18:37-8) | |
| A reaction: There is very little explicit discussion of truth in philosophy before this exchange (apart from Ideas 251 and 586), and there isn't any real debate prior to Russell and the pragmatists. What was Pilate's tone? Did he spit at the end of his question? |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| Full Idea: Zermelo's paper sets out to show that the standard set-theoretic axioms (what he calls the 'constitutive axioms', thus the ZF axioms minus the axiom of infinity) have an unending sequence of different models, thus that they are non-categorical. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1209 | |
| A reaction: Hallett says later that Zermelo is working with second-order set theory. The addition of an Axiom of Infinity seems to have aimed at addressing the problem, and the complexities of that were pursued by Gödel. |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| Full Idea: Zermelo included Replacement in 1930, after it was noticed that the sequence of power sets was needed, and Replacement gave the ordinal form of the well-ordering theorem, and justification for transfinite recursion. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Penelope Maddy - Believing the Axioms I §1.8 | |
| A reaction: Maddy says that this axiom suits the 'limitation of size' theorists very well, but is not so good for the 'iterative conception'. |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| Full Idea: Two opposite tendencies of thought, the idea of creative advance and of collection and completion (underlying the Kantian 'antinomies') find their symbolic representation and their symbolic reconciliation in the transfinite numbers based on well-ordering. | |
| From: Ernst Zermelo (On boundary numbers and domains of sets [1930], §5) | |
| A reaction: [a bit compressed] It is this sort of idea, from one of the greatest set-theorists, that leads philosophers to think that the philosophy of mathematics may offer solutions to metaphysical problems. As an outsider, I am sceptical. |
| 6011 | There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara] |
| Full Idea: Numenius argues that material reality depends on intelligible being, which depends on a first god - the Good - which is difficult to grasp, but which inspires a second god to imitate it, turning to matter and organizing it as the world. | |
| From: report of Numenius (fragments/reports [c.160]) by Dominic J. O'Meara - Numenius | |
| A reaction: The interaction problem comes either between the two gods, or between the second god and the world. The argument may have failed to catch on for long when people scented an infinite regress lurking in the middle of it. |