Combining Texts

All the ideas for 'Plural Quantification', 'Mathematics is Megethology' and 'The Logic of Infinity'

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22 ideas

2. Reason / D. Definition / 12. Paraphrase
10633 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10807 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
10809 We can accept the null set, but not a null class, a class lacking members [Lewis]
10811 The null set plays the role of last resort, for class abstracts and for existence [Lewis]
10812 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
10813 What on earth is the relationship between a singleton and an element? [Lewis]
10814 Are all singletons exact intrinsic duplicates? [Lewis]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10806 Megethology is the result of adding plural quantification to mereology [Lewis]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10638 A pure logic is wholly general, purely formal, and directly known [Linnebo]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10816 We can use mereology to simulate quantification over relations [Lewis]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10640 Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
10636 Plural plurals are unnatural and need a first-level ontology [Linnebo]
10639 Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
10635 Second-order quantification and plural quantification are different [Linnebo]
10641 Traditionally we eliminate plurals by quantifying over sets [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
10808 Mathematics is generalisations about singleton functions [Lewis]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10815 We don't need 'abstract structures' to have structural truths about successor functions [Lewis]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
18203 Avoid non-predicative classifications and definitions [Poincaré]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
10643 We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
10637 Ordinary speakers posit objects without concern for ontology [Linnebo]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
10810 I say that absolutely any things can have a mereological fusion [Lewis]
19. Language / C. Assigning Meanings / 3. Predicates
10634 Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo]