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All the ideas for 'What is Logic?st1=Ian Hacking', 'Introduction to Zermelo's 1930 paper' and 'Causal Explanation'

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27 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
3. Truth / A. Truth Problems / 6. Verisimilitude
15557 Verisimilitude has proved hard to analyse, and seems to have several components [Lewis]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
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]
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17833 The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
17834 Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17837 Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
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 / 5. The Infinite / g. Continuum Hypothesis
17836 The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
15554 A disposition needs a causal basis, a property in a certain causal role. Could the disposition be the property? [Lewis]
10. Modality / B. Possibility / 7. Chance
15560 We can explain a chance event, but can never show why some other outcome did not occur [Lewis]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
15559 Does a good explanation produce understanding? That claim is just empty [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
15556 Science may well pursue generalised explanation, rather than laws [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
15558 A good explanation is supposed to show that the event had to happen [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
4809 Lewis endorses the thesis that all explanation of singular events is causal explanation [Lewis, by Psillos]
14321 To explain an event is to provide some information about its causal history [Lewis]
26. Natural Theory / C. Causation / 2. Types of cause
15555 Explaining match lighting in general is like explaining one lighting of a match [Lewis]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
15552 We only pick 'the' cause for the purposes of some particular enquiry. [Lewis]
15551 Ways of carving causes may be natural, but never 'right' [Lewis]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
15553 Causal dependence is counterfactual dependence between events [Lewis]