34 ideas
| 10143 | 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K] |
| 9143 | Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert] |
| 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] |
| 10145 | Abstracts cannot be identified with sets [Fine,K] |
| 10136 | Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K] |
| 10144 | Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 9144 | Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert] |
| 10141 | Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K] |
| 10135 | We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K] |
| 9142 | Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert] |
| 10137 | Abstractionism can be regarded as an alternative to set theory [Fine,K] |
| 10138 | An object is the abstract of a concept with respect to a relation on concepts [Fine,K] |
| 5078 | Kant and Mill both try to explain right and wrong, without a divine lawgiver [Taylor,R] |
| 5067 | Morality based on 'forbid', 'permit' and 'require' implies someone who does these things [Taylor,R] |
| 5079 | Pleasure can have a location, and be momentary, and come and go - but happiness can't [Taylor,R] |
| 5068 | 'Eudaimonia' means 'having a good demon', implying supreme good fortune [Taylor,R] |
| 5076 | To Greeks it seemed obvious that the virtue of anything is the perfection of its function [Taylor,R] |
| 5077 | The modern idea of obligation seems to have lost the idea of an obligation 'to' something [Taylor,R] |
| 5066 | If we are made in God's image, pursuit of excellence is replaced by duty to obey God [Taylor,R] |
| 5065 | The ethics of duty requires a religious framework [Taylor,R] |