Combining Texts

All the ideas for 'works', 'fragments/reports' and 'Higher-Order Logic'

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21 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
21970 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
6912 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 / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
21973 Fichte believed in things-in-themselves [Fichte, by Moore,AW]
21914 We can deduce experience from self-consciousness, without the thing-in-itself [Fichte]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
20951 The absolute I divides into consciousness, and a world which is not-I [Fichte, by Bowie]
21964 Reason arises from freedom, so philosophy starts from the self, and not from the laws of nature [Fichte]
21968 Abandon the thing-in-itself; things only exist in relation to our thinking [Fichte]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
20769 Sphaerus he was not assenting to the presence of pomegranates, but that it was 'reasonable' [Sphaerus, by Diog. Laertius]
16. Persons / F. Free Will / 4. For Free Will
21965 Spinoza could not actually believe his determinism, because living requires free will [Fichte]