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All the ideas for 'The Metaontology of Abstraction', 'works' and 'Philosophy of Mathematics'

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28 ideas

2. Reason / F. Fallacies / 1. Fallacy
12223 It is a fallacy to explain the obscure with the even more obscure [Hale/Wright]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23445 Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
12230 Singular terms refer if they make certain atomic statements true [Hale/Wright]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
23447 In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
23443 The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
23444 To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
23446 You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
23448 Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12224 Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
23441 Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
23442 Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
12226 The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright]
8. Modes of Existence / B. Properties / 3. Types of Properties
12229 Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
18443 A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright]
14. Science / B. Scientific Theories / 3. Instrumentalism
7621 Special relativity, unlike general relativity, was operationalist in spirit [Putnam on Einstein]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
12227 Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright]
12228 Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
12231 Reference needs truth as well as sense [Hale/Wright]
26. Natural Theory / C. Causation / 1. Causation
22955 Einstein took causation to be the bedrock of physics [Einstein, by Coveney/Highfield]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
20638 General relativity assumes laws of nature are the same in all frames of reference [Einstein, by Close]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
20636 Newton is a special case of Einstein's general theory, with an infinite speed of light [Einstein, by Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
21230 The theory is 'special' because it sticks to observers moving straight, at constant speeds [Einstein, by Farmelo]
21231 Assume the speed of light is constant for all observers, and the laws of physics are the same [Einstein, by Farmelo]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
20634 General Relativity says there is no absolute force or acceleration [Einstein, by Close]
27. Natural Reality / B. Modern Physics / 4. Standard Model / d. Mass
20648 Mass is a measure of energy content [Einstein]
27. Natural Reality / C. Space / 6. Space-Time
21232 Space-time arises from the connection between measurements of space and of time [Einstein, by Farmelo]
28. God / C. Attitudes to God / 5. Atheism
7626 I do not believe in a personal God [Einstein]