Combining Texts

All the ideas for 'Theory of Knowledge (2nd edn)', 'The Gettier Problem' and 'First-order Logic, 2nd-order, Completeness'

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13 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy

2945	Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer]

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis

2946	You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]

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]

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

19699

A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]