Combining Texts

All the ideas for 'fragments/reports', 'The Nature of Existence vol.2' and 'First-order Logic, 2nd-order, Completeness'

expand these ideas     |    start again     |     specify just one area for these texts

22 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [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]
7. Existence / B. Change in Existence / 1. Nature of Change
15200 How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin]
14761 Change is not just having two different qualities at different points in some series [McTaggart]
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 / D. Time / 1. Nature of Time / b. Relative time
2608 For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
22936 A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin]
4231 Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
8591 There could be no time if nothing changed [McTaggart]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
22935 The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin]
7802 A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle]
4230 A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe]
15199 The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]