Combining Texts

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

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16 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy attains its goal if one person feels perfect accord between their system and experience [Fichte]
2. Reason / A. Nature of Reason / 7. Status of Reason
For Fichte there is no God outside the ego, and 'our religion is reason' [Fichte, by Feuerbach]
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 / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Fichte believed in things-in-themselves [Fichte, by Moore,AW]
We can deduce experience from self-consciousness, without the thing-in-itself [Fichte]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
The absolute I divides into consciousness, and a world which is not-I [Fichte, by Bowie]
Reason arises from freedom, so philosophy starts from the self, and not from the laws of nature [Fichte]
Abandon the thing-in-itself; things only exist in relation to our thinking [Fichte]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]
16. Persons / F. Free Will / 4. For Free Will
Spinoza could not actually believe his determinism, because living requires free will [Fichte]