Combining Texts

All the ideas for 'Events and Their Names', 'Logical Atomism' and 'First-order Logic, 2nd-order, Completeness'

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26 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
6118 Philosophy is logical analysis, followed by synthesis [Russell]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
6116 A logical language would show up the fallacy of inferring reality from ordinary language [Russell]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
6117 Philosophy should be built on science, to reduce error [Russell]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
6110 Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
6107 It is logic, not metaphysics, that is fundamental to philosophy [Russell]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10751 Second-order logic needs the sets, and its consequence has epistemological problems [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
6115 Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell]
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 / 1. Axiomatisation
6109 Some axioms may only become accepted when they lead to obvious conclusions [Russell]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
6108 Maths can be deduced from logical axioms and the logic of relations [Russell]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
8978 Events are made of other things, and are not fundamental to ontology [Bennett]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
10968 Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read]
6113 To mean facts we assert them; to mean simples we name them [Russell]
6114 'Simples' are not experienced, but are inferred at the limits of analysis [Russell]
21722 Better to construct from what is known, than to infer what is unknown [Russell]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
6111 As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell]
19. Language / A. Nature of Meaning / 1. Meaning
6112 Meaning takes many different forms, depending on different logical types [Russell]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
10364 Facts are about the world, not in it, so they can't cause anything [Bennett]