Combining Texts

All the ideas for 'fragments/reports', 'The Philosophy of Mathematics' and 'The Extended Mind'

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13 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
A notebook counts as memory, if is available to consciousness and guides our actions [Clark/Chalmers]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
A mechanism can count as 'cognitive' whether it is in the brain or outside it [Clark/Chalmers, by Rowlands]
If something in the world could equally have been a mental process, it is part of our cognition [Clark/Chalmers]
Consciousness may not extend beyond the head, but cognition need not be conscious [Clark/Chalmers]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
If a person relies on their notes, those notes are parted of the extended system which is the person [Clark/Chalmers]