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All the ideas for 'Natural Science (lost)', 'Trees, Terms and Truth' and 'Russell's Metaphysical Logic'

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26 ideas

2. Reason / D. Definition / 8. Impredicative Definition
21704 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18915 If facts are the truthmakers, they are not in the world [Engelbretsen]
18919 There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
18913 Traditional term logic struggled to express relations [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
18907 Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21705 Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
18912 Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18922 Logical syntax is actually close to surface linguistic form [Engelbretsen]
18905 Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18908 Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
21727 Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
21719 Extensionalism means what is true of a function is true of coextensive functions [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
21723 The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21721 Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
21703 Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
21714 The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
21713 Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
21715 For those who abandon logicism, standard set theory is a rival option [Linsky,B]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
527 Everything exists which anyone perceives [Metrodorus of Chios]
18917 Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
18916 Facts are not in the world - they are properties of the world [Engelbretsen]
7. Existence / E. Categories / 4. Category Realism
18921 Individuals are arranged in inclusion categories that match our semantics [Engelbretsen]
8. Modes of Existence / B. Properties / 11. Properties as Sets
21729 Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B]
19. Language / B. Reference / 2. Denoting
18918 Terms denote objects with properties, and statements denote the world with that property [Engelbretsen]
19. Language / D. Propositions / 1. Propositions
18920 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen]
19. Language / F. Communication / 3. Denial
18906 Negating a predicate term and denying its unnegated version are quite different [Engelbretsen]