Combining Texts

All the ideas for 'Subjectivist's Guide to Objective Chance', 'works' and 'First-order Logic, 2nd-order, Completeness'

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19 ideas

4. Formal Logic / G. Formal Mereology / 1. Mereology
10397 Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P]
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]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
10396 If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P]
10395 Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
15384 Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio]
10. Modality / A. Necessity / 4. De re / De dicto modality
8481 The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein]
18. Thought / E. Abstraction / 8. Abstractionism Critique
15385 Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard]
19. Language / C. Assigning Meanings / 3. Predicates
15383 Nothing external can truly be predicated of an object [Abelard, by Panaccio]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
10398 Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
9425 Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis]