10 ideas
| 14767 | The demonstrations of the metaphysicians are all moonshine [Peirce] |
| Full Idea: The demonstrations of the metaphysicians are all moonshine. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 14764 | I am saturated with the spirit of physical science [Peirce] |
| Full Idea: I am saturated, through and through, with the spirit of the physical sciences. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.1) |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 14768 | Infallibility in science is just a joke [Peirce] |
| Full Idea: Infallibility in scientific matters seems to me irresistibly comical. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.3) |
| 14765 | Association of ideas is the best philosophical idea of the prescientific age [Peirce] |
| Full Idea: The doctrine of the association of ideas is, to my thinking, the finest piece of philosophical work of the prescientific ages. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 14766 | Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce] |
| Full Idea: The works of Duns Scotus have strongly influenced me. …His logic and metaphysics, torn away from its medievalism, …will go far toward supplying the philosophy which is best to harmonize with physical science. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 20698 | Irenaeus says evil is necessary for perfect human development [Irenaeus, by Davies,B] |
| Full Idea: Echoing Irenaeus, John Hick argues that the existence of evil is necessary for the perfect development of human beings. Hick understands evil in the light of God's desire not to coerce people into accepting him. | |
| From: report of Irenaeus (works [c.190]) by Brian Davies - Introduction to the Philosophy of Religion 3 'Notable' | |
| A reaction: I don't suppose I could opt out of perfect development? If I endure the evil, can I be guaranteed that my development will be 'perfect'. Oh, and could I just check what is meant by 'development'? |