Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Introduction to the Theory of Logic' and 'The Analysis of Matter'

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24 ideas

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
10900 Logically true sentences are true in all structures [Zalabardo]
10895 'Logically true' (|= φ) is true for every truth-assignment [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 / B. Change in Existence / 4. Events / b. Events as primitive
6402 In 1927, Russell analysed force and matter in terms of events [Russell, by Grayling]
9. Objects / A. Existence of Objects / 1. Physical Objects
14732 A perceived physical object is events grouped around a centre [Russell]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
14733 An object produces the same percepts with or without a substance, so that is irrelevant to science [Russell]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
6418 Russell rejected phenomenalism because it couldn't account for causal relations [Russell, by Grayling]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
21706 At first matter is basic and known by sense-data; later Russell says matter is constructed [Russell, by Linsky,B]