Combining Texts

All the ideas for 'fragments/reports', 'A Completeness Theorem in Modal Logic' and 'Mathematics is Megethology'

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20 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
1597 Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
10163 Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
10760 With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
16189 The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]
15132 The Barcan formulas fail in models with varying domains [Kripke, by Williamson]
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]
10812 The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis]
10811 The null set plays the role of last resort, for class abstracts and for existence [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 / E. Structures of Logic / 6. Relations in Logic
10816 We can use mereology to simulate quantification over relations [Lewis]
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]
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]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
3013 Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
1494 Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
1713 Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
1742 Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius]