13 ideas
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 3102 | Why don't we experience or remember going to sleep at night? [Magee] |
| Full Idea: As a child it was incomprehensible to me that I did not experience going to sleep, and never remembered it. When my sister said 'Nobody remembers that', I just thought 'How does she know?' | |
| From: Bryan Magee (Confessions of a Philosopher [1997], Ch.I) | |
| A reaction: This is actually evidence for something - that we do not have some sort of personal identity which is separate from consciousness, so that "I am conscious" would literally mean that an item has a property, which it can lose. |
| 23146 | Motives produce intentions, which lead to actions [Driver] |
| Full Idea: Motives will cause persons for form intentions; it is intentions which more directly guide actions. | |
| From: Julia Driver (The Virtues and Human Nature [1996], 3) | |
| A reaction: This is invites the question of whether there is a sharp distinction between the motive and the action. Detectives look for motives, but law courts look for intentions. |
| 23147 | Good intentions are not necessary for virtue [Driver] |
| Full Idea: I deny the claim that good intentions are necessary for virtue. | |
| From: Julia Driver (The Virtues and Human Nature [1996], 3) | |
| A reaction: Presumably one could continually do the right thing, because it was your duty or your job, without actually being well motivated for it. |
| 23144 | Virtue should be defined by consequences, not by states of mind [Driver] |
| Full Idea: The behavioural aspects of virtue are more important than its phenomenology, because virtue is best defined along consequentialist lines. | |
| From: Julia Driver (The Virtues and Human Nature [1996], Intro) | |
| A reaction: This is the thesis of her paper. Quite persuasive. Consequences are, of course, important in all moral theories (even Kant's). She doesn't rely on human nature. The social virtues vary according to the circumstances, such as gossiping in wartime. |
| 23148 | Virtues are character traits or dispositions which produce good consequences for others [Driver] |
| Full Idea: A moral virtue is a character trait (a disposition or cluster of dispositions) which, generally speaking, produces good consequences for others. | |
| From: Julia Driver (The Virtues and Human Nature [1996], 3) | |
| A reaction: There are self-directed virtues, such as keeping fit and healthy. There are virtues for ways to receive the kindness of others. That said, I like this idea. |
| 23150 | Control of pregnancy and knowledge of paternity have downgraded chastity [Driver] |
| Full Idea: Women now have more control over becoming pregnant. Men can now be more certain of paternity, without the constraint of female chastity. Hence chastity is no longer considered a moral virtue. | |
| From: Julia Driver (The Virtues and Human Nature [1996], 5) | |
| A reaction: A persuasive argument that virtues are defined by their consequences (to which I add my example of gossiping in wartime). Different social situations and crises promote or relegate the status of certain virtues (such as food hoarding). |
| 23149 | If generosity systematically turned recipients into parasites, it wouldn't be a virtue [Driver] |
| Full Idea: If generosity towards the needy in the long run produced [social] parasites, and if generosity did this systematically, then it would not be a moral virtue. | |
| From: Julia Driver (The Virtues and Human Nature [1996], 5) | |
| A reaction: A very persuasive example. Hume has similar views - that we encourage those emotions which have good social outcomes. |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |