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All the ideas for 'Thinking About Mathematics', 'works' and 'The Metaphysics of Scientific Realism'

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51 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics aims at the simplest explanation, without regard to testability [Ellis]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Mathematics is the formal study of the categorical dimensions of things [Ellis]
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / B. Change in Existence / 2. Processes
Objects and substances are a subcategory of the natural kinds of processes [Ellis]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
A physical event is any change of distribution of energy [Ellis]
8. Modes of Existence / B. Properties / 5. Natural Properties
Physical properties are those relevant to how a physical system might act [Ellis]
8. Modes of Existence / B. Properties / 6. Categorical Properties
I support categorical properties, although most people only want causal powers [Ellis]
Essentialism needs categorical properties (spatiotemporal and numerical relations) and dispositions [Ellis]
Spatial, temporal and numerical relations have causal roles, without being causal [Ellis]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Properties and relations are discovered, so they can't be mere sets of individuals [Ellis]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Causal powers can't rest on things which lack causal power [Ellis]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
Categoricals exist to influence powers. Such as structures, orientations and magnitudes [Ellis, by Williams,NE]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
Causal powers are a proper subset of the dispositional properties [Ellis]
9. Objects / C. Structure of Objects / 1. Structure of an Object
Categorical properties depend only on the structures they represent [Ellis]
9. Objects / D. Essence of Objects / 5. Essence as Kind
A real essence is a kind's distinctive properties [Ellis]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical necessity holds between things in the world and things they make true [Ellis]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Metaphysical necessities are those depending on the essential nature of things [Ellis]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
14. Science / B. Scientific Theories / 2. Aim of Science
Science aims to explain things, not just describe them [Ellis]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Armies and businesses create moralities in which their activity can do no wrong [Marx, by Weil]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Liberal freedom is the right to be separate, and ignores the union of man with man [Marx]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
Liberals want the right to be separate, rather than for people to be united [Marx]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Early Marx anticipates communitarian objections to liberalism [Marx, by Oksala]
24. Political Theory / D. Ideologies / 9. Communism
By saying the material dialectic of history aspires to the best, Marx agreed with capitalism [Weil on Marx]
False consciousness results from concealment by the superstructure [Marx, by Singer]
Marx says force is everything, and that the weak will become strong, while remaining the weak [Weil on Marx]
Marx rejected equal rights because they never actually treat people as equals [Marx, by Kymlicka]
24. Political Theory / D. Ideologies / 11. Capitalism
Capitalism changes the world, by socialising the idea of a commodity [Marx, by Bowie]
The essence of capitalism is the subordination of people to things [Marx, by Weil]
Marx thought capitalism was partly liberating, and could make labour and ownership more humane [Marx, by Bowie]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
There are natural kinds of processes [Ellis]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
Natural kind structures go right down to the bottom level [Ellis]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Laws of nature are just descriptions of how things are disposed to behave [Ellis]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
I deny forces as entities that intervene in causation, but are not themselves causal [Ellis]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
Energy is the key multi-valued property, vital to scientific realism [Ellis]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Simultaneity can be temporal equidistance from the Big Bang [Ellis]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
The present is the collapse of the light wavefront from the Big Bang [Ellis]