Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Rearrangement of Particles' and 'Actualism and Possible Worlds'

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

26 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 / A. Nature of Existence / 3. Being / a. Nature of Being
14664 Necessary beings (numbers, properties, sets, propositions, states of affairs, God) exist in all possible worlds [Plantinga]
7. Existence / B. Change in Existence / 1. Nature of Change
15540 You can't deny temporary intrinsic properties by saying the properties are relations (to times) [Lewis]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
10173 A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / D. Essence of Objects / 1. Essences of Objects
14666 Socrates is a contingent being, but his essence is not; without Socrates, his essence is unexemplified [Plantinga]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
14662 Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc. [Plantinga]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
16472 Plantinga's actualism is nominal, because he fills actuality with possibilia [Stalnaker on Plantinga]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
16469 Plantinga has domains of sets of essences, variables denoting essences, and predicates as functions [Plantinga, by Stalnaker]
16470 Plantinga's essences have their own properties - so will have essences, giving a hierarchy [Stalnaker on Plantinga]
19. Language / D. Propositions / 1. Propositions
14663 Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga]