35 ideas
3969 | There are no ultimate standards of rationality, since we only assess others by our own standard [Davidson] |
3972 | Truth and objectivity depend on a community of speakers to interpret what they mean [Davidson] |
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] |
21500 | We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI] |
21501 | If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI] |
6556 | If anything is to be probable, then something must be certain [Lewis,CI] |
21498 | Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI] |
3960 | There are no such things as minds, but people have mental properties [Davidson] |
3964 | If the mind is an anomaly, this makes reduction of the mental to the physical impossible [Davidson] |
3965 | Mental entities do not add to the physical furniture of the world [Davidson] |
3961 | Obviously all mental events are causally related to physical events [Davidson] |
3963 | There are no strict psychophysical laws connecting mental and physical events [Davidson] |
3966 | The correct conclusion is ontological monism combined with conceptual dualism [Davidson] |
3967 | Absence of all rationality would be absence of thought [Davidson] |
3974 | Our meanings are partly fixed by events of which we may be ignorant [Davidson] |
5828 | Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI] |
3968 | Propositions explain nothing without an explanation of how sentences manage to name them [Davidson] |
3970 | Thought is only fully developed if we communicate with others [Davidson] |
3971 | There is simply no alternative to the 'principle of charity' in interpreting what others do [Davidson] |
3973 | Without a teacher, the concept of 'getting things right or wrong' is meaningless [Davidson] |
3962 | Cause and effect relations between events must follow strict laws [Davidson] |