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All the ideas for 'fragments/reports', 'Russell's Mathematical Logic' and 'The Powers Metaphysics'

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34 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Reductive analysis makes a concept clearer, by giving an alternative simpler set [Williams,NE]
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
2. Reason / E. Argument / 1. Argument
Promoting an ontology by its implied good metaphysic is an 'argument-by-display' [Williams,NE]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / B. Change in Existence / 1. Nature of Change
Change exists, it is causal, and it needs an explanation [Williams,NE]
7. Existence / B. Change in Existence / 2. Processes
Processes don't begin or end; they just change direction unexpectedly [Williams,NE]
Processes are either strings of short unchanging states, or continuous and unreducible events [Williams,NE]
7. Existence / D. Theories of Reality / 1. Ontologies
The status quo is part of what exists, and so needs metaphysical explanation [Williams,NE]
A metaphysic is a set of wider explanations derived from a basic ontology [Williams,NE]
Humeans say properties are passive, possibility is vast, laws are descriptions, causation is weak [Williams,NE]
We shouldn't posit the existence of anything we have a word for [Williams,NE]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Powers are 'multi-track' if they can produce a variety of manifestations [Williams,NE]
Every possible state of affairs is written into its originating powers [Williams,NE]
Naming powers is unwise, because that it usually done by a single manifestation [Williams,NE]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Fundamental physics describes everything in terms of powers [Williams,NE]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
Rather than pure powers or pure categoricals, I favour basics which are both at once [Williams,NE]
Powers are more complicated than properties which are always on display [Williams,NE]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
There are basic powers, which underlie dispositions, potentialities, capacities etc [Williams,NE]
Dispositions are just useful descriptions, which are explained by underlying powers [Williams,NE]
9. Objects / A. Existence of Objects / 1. Physical Objects
If objects are property bundles, the properties need combining powers [Williams,NE]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-Dimensional is Perdurantism (temporal parts), plus Eternalism [Williams,NE]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
Alcmaeon was the first to say the brain is central to thinking [Alcmaeon, by Staden, von]
26. Natural Theory / C. Causation / 1. Causation
Causation needs to explain stasis, as well as change [Williams,NE]
Causation is the exercise of powers [Williams,NE]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
If causes and effects overlap, that makes changes impossible [Williams,NE]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Powers contain lawlike features, pointing to possible future states [Williams,NE]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle]