14 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 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. |
| 8439 | Maybe each event has only one possible causal history [Bennett] |
| Full Idea: Perhaps it is impossible that an event should have had a causal history different from the one that it actually had. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.220) | |
| A reaction: [He cites van Inwagen for this] The idea is analagous to baptismal accounts of reference. Individuate an event by its history. It might depend (as Davidson implies) on how you describe the event. |
| 8440 | Maybe an event's time of occurrence is essential to it [Bennett] |
| Full Idea: It has been argued that an event's time of occurrence is essential to it. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.221) | |
| A reaction: [He cites Lawrence Lombard] This sound initially implausible, particularly if a rival event happened, say, .1 of a second later than the actual event. It might depend on one's view about determinism. Interesting. |
| 8441 | Delaying a fire doesn't cause it, but hastening it might [Bennett] |
| Full Idea: Although you cannot cause a fire by delaying something's burning, you can cause a fire by hastening something's burning. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.223) | |
| A reaction: A very nice observation which brings out all sorts of problems about identifying causes. Bennett is criticising the counterfactual account. It is part of the problem of pre-emption, where causes are queueing up to produce a given effect. |
| 8436 | Either cause and effect are subsumed under a conditional because of properties, or it is counterfactual [Bennett] |
| Full Idea: We must choose between subsumption and counterfactual analyses of causal statements. The former means that cause and effect have some properties that enables them to be subsumed under a conditional. The latter is just 'if no-c then no-e'. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.217) | |
| A reaction: I have an immediate preference for the former account, which seems to potentially connect it with physics and features of the world which make one thing lead to another. The counterfactual account seems very thin, and is more like mere semantics. |
| 8435 | Causes are between events ('the explosion') or between facts/states of affairs ('a bomb dropped') [Bennett] |
| Full Idea: Theories of causation are split between event and fact/state of affairs theories. The first have the form 'the explosion caused the fire' (perfect nominals) and the second have the form 'the fire started because a bomb dropped' (sentential clauses). | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987]) | |
| A reaction: Surely events must have priority? The form which uses facts is drifting off into explanation, and is much more likely to involve subjective human elements and interpretations. Events are closer to the physics, and the mechanics of what happens. |
| 8437 | The full counterfactual story asserts a series of events, because counterfactuals are not transitive [Bennett] |
| Full Idea: The refinement of a simple counterfactual analysis is to say that cause and effect depend on a series of events. This must be asserted because counterfactual conditionals are well known not to be transitive. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987]) | |
| A reaction: This fills out the theory, but offers another target for critics. If the glue that binds the series is not in the counterfactuals, is it just in the mind of the speaker? How do you decide what's in the series? Cf. deciding offside in football (soccer!). |
| 8438 | A counterfactual about an event implies something about the event's essence [Bennett] |
| Full Idea: Any counterfactual about a particular event implies or presupposes something about the event's essence. | |
| From: Jonathan Bennett (Event Causation: counterfactual analysis [1987], p.219) | |
| A reaction: This is where the counterfactual theory suddenly becomes more interesting, instead of just being a rather bare account of the logical structure of causation. (Bennett offers some discussion of possible essential implications). |
| 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. |