Combining Texts

All the ideas for 'The Concept of a Person', 'First-order Logic, 2nd-order, Completeness' and 'The Sign of Four'

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18 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]
14. Science / C. Induction / 1. Induction
22200 If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
5662 Maybe induction could never prove the existence of something unobservable [Ayer]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
5664 Consciousness must involve a subject, and only bodies identify subjects [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
5668 People own conscious states because they are causally related to the identifying body [Ayer]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
5661 We identify experiences by their owners, so we can't define owners by their experiences [Ayer]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
5665 Memory is the best proposal as what unites bundles of experiences [Ayer]
5666 Not all exerience can be remembered, as this would produce an infinite regress [Ayer]
16. Persons / D. Continuity of the Self / 6. Body sustains Self
5669 Personal identity can't just be relations of experiences, because the body is needed to identify them [Ayer]