50 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
20080 | If one action leads to another, does it cause it, or is it part of it? [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] |
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] |
20052 | If you don't mention an agent, you aren't talking about action [Stout,R] |
20050 | Most philosophers see causation as by an event or state in the agent, rather than the whole agent [Stout,R] |
20077 | If you can judge one act as best, then do another, this supports an inward-looking view of agency [Stout,R] |
20049 | Maybe your emotions arise from you motivations, rather than being their cause [Stout,R] |
20046 | For an ascetic a powerful desire for something is a reason not to implement it [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] |
19745 | The nature of people is decided by the government and politics of their society [Rousseau] |
20083 | Aristotelian causation involves potentiality inputs into processes (rather than a pair of events) [Stout,R] |