20 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] |
13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
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] |
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] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |