Combining Texts

All the ideas for 'The Mental Life of Some Machines', 'First-order Logic, 2nd-order, Completeness' and 'Letters to Jourdain'

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15 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 / F. Referring in Logic / 1. Naming / a. Names

8447	In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege]

5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive

8448	Any object can have many different names, each with a distinct sense [Frege]

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]

17. Mind and Body / C. Functionalism / 2. Machine Functionalism

5495	Instances of pain are physical tokens, but the nature of pain is more abstract [Putnam, by Lycan]

19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning

8446	We understand new propositions by constructing their sense from the words [Frege]

19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference

8449	Senses can't be subjective, because propositions would be private, and disagreement impossible [Frege]