Combining Texts

All the ideas for 'fragments/reports', 'Can there be Vague Objects?' and 'First-order Logic, 2nd-order, Completeness'

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

18 ideas

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]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
16129 Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe]
16459 Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans]
16457 There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis]
16460 Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
14484 If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson]
9. Objects / F. Identity among Objects / 6. Identity between Objects
16224 There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG]
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]