16 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] |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| 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] |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| 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] |
| 8119 | Art aims only at beauty, of form, of idea, and (above all) of expression [Winckelmann, by Tolstoy] |