Combining Texts

All the ideas for 'Philosophical Fragments', 'Meaning and Reference' and 'First-order Logic, 2nd-order, Completeness'

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19 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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
16007 I assume existence, rather than reasoning towards it [Kierkegaard]
10. Modality / A. Necessity / 2. Nature of Necessity
16013 Nothing necessary can come into existence, since it already 'is' [Kierkegaard]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
9169 A statement can be metaphysically necessary and epistemologically contingent [Putnam]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
5819 Conceivability is no proof of possibility [Putnam]
18. Thought / C. Content / 6. Broad Content
9168 I can't distinguish elm trees, but I mean by 'elm' the same set of trees as everybody else [Putnam]
5820 'Water' has an unnoticed indexical component, referring to stuff around here [Putnam]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
9170 We need to recognise the contribution of society and of the world in determining reference [Putnam]
19. Language / F. Communication / 4. Private Language
5817 Language is more like a cooperative steamship than an individual hammer [Putnam]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
5818 If water is H2O in the actual world, there is no possible world where it isn't H2O [Putnam]