Combining Texts

All the ideas for 'fragments/reports', 'A Universe from Nothing' and 'What is Logic?'

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21 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
13834 Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
13835 Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
7. Existence / C. Structure of Existence / 2. Reduction
21110 An understanding of the most basic physics should explain all of the subject's mysteries [Krauss]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
21105 In 1676 it was discovered that water is teeming with life [Krauss]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
21109 Space itself can expand (and separate its contents) at faster than light speeds [Krauss]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
21104 General Relativity: the density of energy and matter determines curvature and gravity [Krauss]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21107 Uncertainty says that energy can be very high over very short time periods [Krauss]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
21106 Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss]
27. Natural Reality / C. Space / 2. Space
21112 Empty space contains a continual flux of brief virtual particles [Krauss]
27. Natural Reality / E. Cosmology / 3. The Beginning
21108 The universe is precisely 13.72 billion years old [Krauss]
27. Natural Reality / E. Cosmology / 10. Multiverse
21111 It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss]