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All the ideas for 'What is Logic?st1=Ian Hacking', 'Review: Meinong 'Untersuchungen zur..'' and 'Equality and Partiality'

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21 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
21546 We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell]
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]
9. Objects / A. Existence of Objects / 4. Impossible objects
21531 Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell]
21545 I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
6479 Noninterference requires justification as much as interference does [Nagel]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics
6450 Morality must be motivating, and not because of pre-moral motives [Nagel]
23. Ethics / B. Contract Ethics / 6. Game Theory
6447 Game theory misses out the motivation arising from the impersonal standpoint [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
6446 In ethics we abstract from our identity, but not from our humanity [Nagel]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
6477 I can only universalise a maxim if everyone else could also universalise it [Nagel]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
6448 A legitimate system is one accepted as both impartial and reasonably partial [Nagel]
25. Social Practice / B. Equalities / 2. Political equality
6478 Democracy is opposed to equality, if the poor are not a majority [Nagel]