Combining Texts

All the ideas for 'fragments/reports', 'First-order Logic, 2nd-order, Completeness' and 'Letters to Des Bosses'

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25 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
12780 We can grasp the wisdom of God a priori [Leibniz]
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 / C. Structure of Existence / 6. Fundamentals / c. Monads
12774 Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz]
12777 Monads do not make a unity unless a substantial chain is added to them [Leibniz]
12782 Monads control nothing outside of themselves [Leibniz]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
12778 There is active and passive power in the substantial chain and in the essence of a composite [Leibniz]
12783 Primitive force is what gives a composite its reality [Leibniz]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
12775 Things seem to be unified if we see duration, position, interaction and connection [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
12776 Every substance is alive [Leibniz]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
12753 A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz]
9. Objects / D. Essence of Objects / 12. Essential Parts
12781 A composite substance is a mere aggregate if its essence is just its parts [Leibniz]
10. Modality / B. Possibility / 1. Possibility
12779 There is a reason why not every possible thing exists [Leibniz]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
12785 Truth is mutually agreed perception [Leibniz]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
12784 Allow no more miracles than are necessary [Leibniz]