Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Events' and 'Essays on Active Powers 1: Active power'

expand these ideas     |    start again     |     specify just one area for these texts

29 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
10170 While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10166 ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10175 Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10165 'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
10174 Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10164 Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10172 Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10167 Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
10169 Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
10179 There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
10181 Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
10182 There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
10168 Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
10178 Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
10176 Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
10177 Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10171 The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
9413 An event is a change in or to an object [Lombard, by Mumford]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
23664 Powers are quite distinct and simple, and so cannot be defined [Reid]
23669 Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
23666 It is obvious that there could not be a power without a subject which possesses it [Reid]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
10173 A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
23665 Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid]
16. Persons / F. Free Will / 4. For Free Will
23668 Our own nature attributes free determinations to our own will [Reid]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
20051 Reid said that agent causation is a unique type of causation [Reid, by Stout,R]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
8383 Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
23667 Regular events don't imply a cause, without an innate conviction of universal causation [Reid]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
23670 Scientists don't know the cause of magnetism, and only discover its regulations [Reid]
23671 Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid]