32 ideas
12780 | We can grasp the wisdom of God a priori [Leibniz] |
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
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] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
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] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
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] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
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] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
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] |
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] |
12775 | Things seem to be unified if we see duration, position, interaction and connection [Leibniz] |
12776 | Every substance is alive [Leibniz] |
12753 | A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz] |
12781 | A composite substance is a mere aggregate if its essence is just its parts [Leibniz] |
12779 | There is a reason why not every possible thing exists [Leibniz] |
12785 | Truth is mutually agreed perception [Leibniz] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
12784 | Allow no more miracles than are necessary [Leibniz] |