Combining Texts

All the ideas for 'fragments/reports', 'Isolation and Non-arbitrary Division' and 'First-order Logic, 2nd-order, Completeness'

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

17 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]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
17435 Objects do not naturally form countable units [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17433 We can still count squares, even if they overlap [Koslicki]
17439 There is no deep reason why we count carrots but not asparagus [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17434 We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
17436 We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
541 Virtue comes more from habit than character [Critias]
28. God / C. Attitudes to God / 5. Atheism
542 Fear of the gods was invented to discourage secret sin [Critias]