Combining Texts

All the ideas for 'fragments/reports', 'The Metaphysics of Scientific Realism' and 'Infinity: Quest to Think the Unthinkable'

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47 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
12667 Metaphysics aims at the simplest explanation, without regard to testability [Ellis]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
12666 We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
12688 Mathematics is the formal study of the categorical dimensions of things [Ellis]
7. Existence / B. Change in Existence / 2. Processes
12683 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
12670 A physical event is any change of distribution of energy [Ellis]
8. Modes of Existence / B. Properties / 5. Natural Properties
12673 Physical properties are those relevant to how a physical system might act [Ellis]
8. Modes of Existence / B. Properties / 6. Categorical Properties
12665 I support categorical properties, although most people only want causal powers [Ellis]
12682 Essentialism needs categorical properties (spatiotemporal and numerical relations) and dispositions [Ellis]
12684 Spatial, temporal and numerical relations have causal roles, without being causal [Ellis]
8. Modes of Existence / B. Properties / 11. Properties as Sets
12672 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
12676 Causal powers can't rest on things which lack causal power [Ellis]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
23781 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
12686 Causal powers are a proper subset of the dispositional properties [Ellis]
9. Objects / C. Structure of Objects / 1. Structure of an Object
12685 Categorical properties depend only on the structures they represent [Ellis]
9. Objects / D. Essence of Objects / 5. Essence as Kind
12679 A real essence is a kind's distinctive properties [Ellis]
10. Modality / A. Necessity / 5. Metaphysical Necessity
12668 Metaphysical necessity holds between things in the world and things they make true [Ellis]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
12687 Metaphysical necessities are those depending on the essential nature of things [Ellis]
14. Science / B. Scientific Theories / 2. Aim of Science
12669 Science aims to explain things, not just describe them [Ellis]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
12681 There are natural kinds of processes [Ellis]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
12680 Natural kind structures go right down to the bottom level [Ellis]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
12675 Laws of nature are just descriptions of how things are disposed to behave [Ellis]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
12671 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
12674 Energy is the key multi-valued property, vital to scientific realism [Ellis]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
12689 Simultaneity can be temporal equidistance from the Big Bang [Ellis]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
12690 The present is the collapse of the light wavefront from the Big Bang [Ellis]