Combining Texts

All the ideas for 'Logical Necessity: Some Issues', 'First-order Logic, 2nd-order, Completeness' and 'The Doctrine of Necessity Examined'

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24 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]
10. Modality / A. Necessity / 6. Logical Necessity
12184 Logical necessity overrules all other necessities [McFetridge]
15083 The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale]
15084 In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale]
12180 Logical necessity requires that a valid argument be necessary [McFetridge]
12181 Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge]
12183 It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge]
12192 The mark of logical necessity is deduction from any suppositions whatever [McFetridge]
10. Modality / B. Possibility / 2. Epistemic possibility
12182 We assert epistemic possibility without commitment to logical possibility [McFetridge]
10. Modality / B. Possibility / 7. Chance
14804 Is chance just unknown laws? But the laws operate the same, whatever chance occurs [Peirce]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
12187 Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
12186 Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge]
22. Metaethics / B. Value / 2. Values / e. Death
14805 Is there any such thing as death among the lower organisms? [Peirce]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
14806 If the world is just mechanical, its whole specification has no more explanation than mere chance [Peirce]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
14803 The more precise the observations, the less reliable appear to be the laws of nature [Peirce]