Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Models' and 'Logical Atomism'

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27 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]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
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 / E. Structures of Logic / 1. Logical Form
6115 Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell]
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 / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
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 / 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]
14. Science / B. Scientific Theories / 7. Scientific Models
17498 In the 'received view' models are formal; the 'semantic view' emphasises representation [Portides, by PG]
17499 Theoretical models can represent, by mapping onto the data-models [Portides]
17496 'Model' belongs in a family of concepts, with representation, idealisation and abstraction [Portides]
17501 Representational success in models depends on success of their explanations [Portides]
17502 The best model of the atomic nucleus is the one which explains the most results [Portides]
17497 Models are theory-driven, or phenomenological (more empirical and specific) [Portides]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
17500 General theories may be too abstract to actually explain the mechanisms [Portides]
19. Language / A. Nature of Meaning / 1. Meaning
6112 Meaning takes many different forms, depending on different logical types [Russell]