Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'Relations' and 'What Metaphors Mean'

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17 ideas

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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
We want the ontology of relations, not just a formal way of specifying them [Heil]
Two people are indirectly related by height; the direct relation is internal, between properties [Heil]
Maybe all the other features of the world can be reduced to relations [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
In the case of 5 and 6, their relational truthmaker is just the numbers [Heil]
Truthmaking is a clear example of an internal relation [Heil]
If R internally relates a and b, and you have a and b, you thereby have R [Heil]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
If properties are powers, then causal relations are internal relations [Heil]
19. Language / F. Communication / 6. Interpreting Language / d. Metaphor
Understanding a metaphor is a creative act, with no rules [Davidson]
We accept a metaphor when we see the sentence is false [Davidson]
Metaphors just mean what their words literally mean [Davidson]