Combining Texts

All the ideas for 'De Natura Corporis', 'Introduction to the Theory of Logic' and 'Letters to Des Bosses'

expand these ideas     |    start again     |     specify just one area for these texts

32 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
12780 We can grasp the wisdom of God a priori [Leibniz]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10888 Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10889 The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
10890 A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10886 Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10887 Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10897 A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10893 Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
10899 Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10896 Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
10900 Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10903 A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
10891 If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
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]
12782 Monads control nothing outside of themselves [Leibniz]
12777 Monads do not make a unity unless a substantial chain is added to them [Leibniz]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
12710 As well as extension, bodies contain powers [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]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
12784 Allow no more miracles than are necessary [Leibniz]