Combining Texts

All the ideas for 'fragments/reports', 'First-Order Logic' and 'Logological Fragments I'

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19 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
19579 The history of philosophy is just experiments in how to do philosophy [Novalis]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
19583 Philosophy only begins when it studies itself [Novalis]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
5. Theory of Logic / L. Paradox / 2. Aporiai
19581 A problem is a solid mass, which the mind must break up [Novalis]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
19584 Whoever first counted to two must have seen the possibility of infinite counting [Novalis]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
22025 Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
22067 Poetry is true idealism, and the self-consciousness of the universe [Novalis]
19. Language / F. Communication / 4. Private Language
19585 Every person has his own language [Novalis]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
19582 Morality and philosophy are mutually dependent [Novalis]
23. Ethics / F. Existentialism / 7. Existential Action
22027 Life isn't given to us like a novel - we write the novel [Novalis]
25. Social Practice / E. Policies / 5. Education / c. Teaching
19580 If the pupil really yearns for the truth, they only need a hint [Novalis]