Combining Texts

All the ideas for 'Matter and Memory', 'New system of communication of substances' and 'First-order Logic, 2nd-order, Completeness'

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17 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10751 Second-order logic needs the sets, and its consequence has epistemological problems [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 / 3. Being / c. Becoming
21846 Bergson was a rallying point, because he emphasised becomings and multiplicities [Bergson, by Deleuze]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
13169 I call Aristotle's entelechies 'primitive forces', which originate activity [Leibniz]
13168 My formal unifying atoms are substantial forms, which are forces like appetites [Leibniz]
9. Objects / A. Existence of Objects / 5. Simples
13170 The analysis of things leads to atoms of substance, which found both composition and action [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
13171 Substance must necessarily involve progress and change [Leibniz]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
21854 Bergson showed that memory is not after the event, but coexists with it [Bergson, by Deleuze]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
13167 We need the metaphysical notion of force to explain mechanics, and not just extended mass [Leibniz]