66 ideas
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 20043 | Evolutionary explanations look to the past or the group, not to the individual [Stout,R] |
| 20058 | Not all explanation is causal. We don't explain a painting's beauty, or the irrationality of root-2, that way [Stout,R] |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| 20035 | Philosophy of action studies the nature of agency, and of deliberate actions [Stout,R] |
| 20084 | Agency is causal processes that are sensitive to justification [Stout,R] |
| 20061 | Mental states and actions need to be separate, if one is to cause the other [Stout,R] |
| 20079 | Are actions bodily movements, or a sequence of intention-movement-result? [Stout,R] |
| 20080 | If one action leads to another, does it cause it, or is it part of it? [Stout,R] |
| 20059 | I do actions, but not events, so actions are not events [Stout,R] |
| 20081 | Bicycle riding is not just bodily movement - you also have to be on the bicycle [Stout,R] |
| 20044 | The rationalistic approach says actions are intentional when subject to justification [Stout,R] |
| 20039 | The causal theory says that actions are intentional when intention (or belief-desire) causes the act [Stout,R] |
| 20047 | Deciding what to do usually involves consulting the world, not our own minds [Stout,R] |
| 20065 | Should we study intentions in their own right, or only as part of intentional action? [Stout,R] |
| 20067 | You can have incompatible desires, but your intentions really ought to be consistent [Stout,R] |
| 20078 | The normativity of intentions would be obvious if they were internal promises [Stout,R] |
| 20036 | Intentional agency is seen in internal precursors of action, and in external reasons for the act [Stout,R] |
| 20066 | Speech needs sustained intentions, but not prior intentions [Stout,R] |
| 20073 | Bratman has to treat shared intentions as interrelated individual intentions [Stout,R] |
| 20069 | A request to pass the salt shares an intention that the request be passed on [Stout,R] |
| 20070 | An individual cannot express the intention that a group do something like moving a piano [Stout,R] |
| 20071 | An intention is a goal to which behaviour is adapted, for an individual or for a group [Stout,R] |
| 20038 | If the action of walking is just an act of will, then movement of the legs seems irrelevant [Stout,R] |
| 20050 | Most philosophers see causation as by an event or state in the agent, rather than the whole agent [Stout,R] |
| 20052 | If you don't mention an agent, you aren't talking about action [Stout,R] |
| 20077 | If you can judge one act as best, then do another, this supports an inward-looking view of agency [Stout,R] |
| 20046 | For an ascetic a powerful desire for something is a reason not to implement it [Stout,R] |
| 20049 | Maybe your emotions arise from you motivations, rather than being their cause [Stout,R] |
| 20060 | Beliefs, desires and intentions are not events, so can't figure in causal relations [Stout,R] |
| 20055 | A standard view says that the explanation of an action is showing its rational justification [Stout,R] |
| 20056 | In order to be causal, an agent's reasons must be internalised as psychological states [Stout,R] |
| 20053 | An action is only yours if you produce it, rather than some state or event within you [Stout,R] |
| 20048 | There may be a justification relative to a person's view, and yet no absolute justification [Stout,R] |
| 20068 | Describing a death as a side-effect rather than a goal may just be good public relations [Stout,R] |
| 20083 | Aristotelian causation involves potentiality inputs into processes (rather than a pair of events) [Stout,R] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |