Combining Texts

All the ideas for 'Demonstratives', 'Maths as a Science of Patterns' and 'The Limits of Abstraction'

expand these ideas     |    start again     |     specify just one area for these texts

21 ideas

2. Reason / D. Definition / 3. Types of Definition
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]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
7. Existence / A. Nature of Existence / 4. Abstract Existence
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]
18. Thought / E. Abstraction / 1. Abstract Thought
9144 Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
18. Thought / E. Abstraction / 2. Abstracta by Selection
10141 Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
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]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
14894 Indexicals have a 'character' (the standing meaning), and a 'content' (truth-conditions for one context) [Kaplan, by Macià/Garcia-Carpentiro]
14700 'Content' gives the standard modal profile, and 'character' gives rules for a context [Kaplan, by Schroeter]