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All the ideas for 'What is Logic?st1=Ian Hacking', 'Apriority and Existence' and 'Law and Causality'

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23 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]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
8859 The main modal logics disagree over three key formulae [Yablo]
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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8865 If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
8863 We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
8862 Platonic objects are really created as existential metaphors [Yablo]
7. Existence / D. Theories of Reality / 7. Fictionalism
8864 We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
8858 Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
10993 Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
14279 Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
6894 Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey]
19. Language / F. Communication / 6. Interpreting Language / d. Metaphor
8861 Hardly a word in the language is devoid of metaphorical potential [Yablo]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
9418 All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey]
9420 Causal laws result from the simplest axioms of a complete deductive system [Ramsey]