Combining Texts

All the ideas for 'Subjectivist's Guide to Objective Chance', 'First-order Logic, 2nd-order, Completeness' and 'Modal and Anti-Luck Epistemology'

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13 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]

13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues

19729

'Modal epistemology' demands a connection between the belief and facts in possible worlds [Black,T]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem

19728

Gettier and lottery cases seem to involve luck, meaning bad connection of beliefs to facts [Black,T]

26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory

9425	Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis]