8 ideas
| 22642 | Man has an intense natural interest in the consistency of his own thinking [James] |
| Full Idea: After man's interest in breathing freely, the greatest of all his interests (because it never fluctuates or remits….) is his interest in consistency, in feeling that what he now thinks goes with what he thinks on other occasions. | |
| From: William James (The Pragmatist Account of Truth [1908], 'Seventh') | |
| A reaction: People notoriously contradict themselves all the time, but I suspect that it is when they get out of their depth in complexities such as politics. They probably achieve great consistency within their own expertise, and in common knowledge. |
| 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 Michčle 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. |
| 22641 | Realities just are, and beliefs are true of them [James] |
| Full Idea: Realities are not true, they are; and beliefs are true of them. | |
| From: William James (The Pragmatist Account of Truth [1908], 'Fourth') | |
| A reaction: At last, a remark by James about truth which I really like. For 'realities' I would use the word 'facts'. |
| 22640 | We find satisfaction in consistency of all of our beliefs, perceptions and mental connections [James] |
| Full Idea: We find satisfaction in consistency between the present idea and the entire rest of our mental equipment, including the whole order of our sensations, and that of our intuitions of likeness and difference, and our whole stock previously acquired truths. | |
| From: William James (The Pragmatist Account of Truth [1908], 'Fourth') | |
| A reaction: I like this, apart from the idea that the criterion of good coherence seems to be subjective 'satisfaction'. We should ask why some large set of beliefs is coherent. I assume nature is coherent, and truth is the best explanation of our coherence about it. |
| 7482 | Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson] |
| Full Idea: The idea of resurrection in Judaism seems to have first developed around 160 BCE, during the time of religious martyrdom, and as a response to it (the martyrs were surely not dying forever?). It is first mentioned in the book of Daniel. | |
| From: report of Anon (Dan) (27: Book of Daniel [c.165 BCE], Ch.7) by Peter Watson - Ideas | |
| A reaction: Idea 7473 suggests that Zoroaster beat them to it by 800 years. |