30 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] |
| 12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 4983 | There are no rules linking thought and behaviour, because endless other thoughts intervene [Davidson] |
| 3529 | Reduction is impossible because mind is holistic and brain isn't [Davidson, by Maslin] |
| 2307 | Anomalous monism says nothing at all about the relationship between mental and physical [Davidson, by Kim] |
| 5497 | Mind is outside science, because it is humanistic and partly normative [Davidson, by Lycan] |
| 4081 | Anomalous monism says causes are events, so the mental and physical are identical, without identical properties [Davidson, by Crane] |
| 2321 | If rule-following and reason are 'anomalies', does that make reductionism impossible? [Davidson, by Kim] |
| 3404 | Davidson claims that mental must be physical, to make mental causation possible [Davidson, by Kim] |
| 3405 | If mental causation is lawless, it is only possible if mental events have physical properties [Davidson, by Kim] |
| 16041 | Supervenience of the mental means physical changes mental, and mental changes physical [Davidson] |
| 6620 | Davidson sees identity as between events, not states, since they are related in causation [Davidson, by Lowe] |
| 3429 | Multiple realisability was worse news for physicalism than anomalous monism was [Davidson, by Kim] |
| 7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
| 3524 | Causation is either between events, or between descriptions of events [Davidson, by Maslin] |
| 3526 | Whether an event is a causal explanation depends on how it is described [Davidson, by Maslin] |