55 ideas
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
19347 | Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins] |
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] |
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] |