Combining Texts

All the ideas for 'fragments/reports', 'Philosophy' and 'First-order Logic, 2nd-order, Completeness'

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23 ideas

3. Truth / A. Truth Problems / 4. Uses of Truth
20320 Truth is what unites, and the profound truths create a community [Jaspers]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
16. Persons / F. Free Will / 2. Sources of Free Will
20323 Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers]
16. Persons / F. Free Will / 4. For Free Will
20322 I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers]
20. Action / C. Motives for Action / 4. Responsibility for Actions
20324 My freedom increases as I broaden my vision of possiblities and motives [Jaspers]
23. Ethics / F. Existentialism / 1. Existentialism
20318 My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers]
20321 The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers]
20325 Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers]
23. Ethics / F. Existentialism / 6. Authentic Self
20315 'Existenz' is the potential being, which I could have, and ought to have [Jaspers]
20317 Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers]
20319 We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers]
23. Ethics / F. Existentialism / 7. Existential Action
20316 Every decision I make moves towards or away from fulfilled Existenz [Jaspers]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]