Combining Texts

All the ideas for 'fragments/reports', 'Logical Atomism' and 'Remarks on axiomatised set theory'

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19 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Philosophy is logical analysis, followed by synthesis [Russell]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
A logical language would show up the fallacy of inferring reality from ordinary language [Russell]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy should be built on science, to reduce error [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
It is logic, not metaphysics, that is fundamental to philosophy [Russell]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Some axioms may only become accepted when they lead to obvious conclusions [Russell]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Mathematician want performable operations, not propositions about objects [Skolem]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Maths can be deduced from logical axioms and the logic of relations [Russell]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read]
To mean facts we assert them; to mean simples we name them [Russell]
'Simples' are not experienced, but are inferred at the limits of analysis [Russell]
Better to construct from what is known, than to infer what is unknown [Russell]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
19. Language / A. Nature of Meaning / 1. Meaning
Meaning takes many different forms, depending on different logical types [Russell]