Combining Texts

All the ideas for 'Elements of Mathematical Logic', 'The Limits of Abstraction' and 'Thought: a very short introduction'

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


18 ideas

2. Reason / D. Definition / 3. Types of Definition
Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
'Creative definitions' do not presuppose the existence of the objects defined [Fine,K]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher]
7. Existence / A. Nature of Existence / 4. Abstract Existence
Abstracts cannot be identified with sets [Fine,K]
Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K]
Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
How we evaluate evidence depends on our background beliefs [Bayne]
Clifford's dictum seems to block our beliefs in morality, politics and philosophy [Bayne]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Physicalism correlates brain and mind, explains causation by thought, and makes nature continuous [Bayne]
18. Thought / A. Modes of Thought / 8. Human Thought
Perception reveals what animals think, but humans can disengage thought from perception [Bayne]
Some people centre space on themselves; others centre space on the earth [Bayne]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
The alternative to a language of thought is map-like or diagram-like thought [Bayne]
18. Thought / E. Abstraction / 1. Abstract Thought
Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
Abstractionism can be regarded as an alternative to set theory [Fine,K]
An object is the abstract of a concept with respect to a relation on concepts [Fine,K]