Combining Texts

All the ideas for 'The Pragmatist Account of Truth', 'The Philosophy of Mathematics' and 'The Analysis of Matter'

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15 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
Man has an intense natural interest in the consistency of his own thinking [James]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
In 1927, Russell analysed force and matter in terms of events [Russell, by Grayling]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
Realities just are, and beliefs are true of them [James]
9. Objects / A. Existence of Objects / 1. Physical Objects
A perceived physical object is events grouped around a centre [Russell]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
An object produces the same percepts with or without a substance, so that is irrelevant to science [Russell]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Russell rejected phenomenalism because it couldn't account for causal relations [Russell, by Grayling]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
We find satisfaction in consistency of all of our beliefs, perceptions and mental connections [James]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
At first matter is basic and known by sense-data; later Russell says matter is constructed [Russell, by Linsky,B]