Combining Texts

All the ideas for 'Logical Consequence', 'On Platonism in Mathematics' 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 / E. Argument / 1. Argument
Promoting an ontology by its implied good metaphysic is an 'argument-by-display' [Williams,NE]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Very few things in set theory remain valid in intuitionist mathematics [Bernays]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Mathematical abstraction just goes in a different direction from logic [Bernays]
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]
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]