Combining Texts

All the ideas for 'Content Preservation', 'Properties' and 'Mathematics is Megethology'

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29 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
We can accept the null set, but not a null class, a class lacking members [Lewis]
The null set plays the role of last resort, for class abstracts and for existence [Lewis]
The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What on earth is the relationship between a singleton and an element? [Lewis]
Are all singletons exact intrinsic duplicates? [Lewis]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Megethology is the result of adding plural quantification to mereology [Lewis]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
We can use mereology to simulate quantification over relations [Lewis]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mathematics is generalisations about singleton functions [Lewis]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
We don't need 'abstract structures' to have structural truths about successor functions [Lewis]
8. Modes of Existence / B. Properties / 2. Need for Properties
Without properties we would be unable to express the laws of nature [Armstrong]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong]
To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong]
8. Modes of Existence / D. Universals / 2. Need for Universals
Universals are required to give a satisfactory account of the laws of nature [Armstrong]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
Deniers of properties and relations rely on either predicates or on classes [Armstrong]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong]
We want to know what constituents of objects are grounds for the application of predicates [Armstrong]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
In most sets there is no property common to all the members [Armstrong]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
I say that absolutely any things can have a mereological fusion [Lewis]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge]
19. Language / C. Assigning Meanings / 3. Predicates
Predicates need ontological correlates to ensure that they apply [Armstrong]
There must be some explanation of why certain predicates are applicable to certain objects [Armstrong]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong]
The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong]