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All the ideas for 'What is Logic?st1=Ian Hacking', 'Rationality' and 'Atomism'

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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
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]
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]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
23304 The ancient Memorists said virtually all types of thinking could be done simply by memory [Sorabji]
23303 Stoics say true memory needs reflection and assent, but animals only have perceptual recognition [Sorabji]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
22809 The social contract sees society as constituted by and for individuals [Taylor,C]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
22811 Assigning a right based on a human capacity implies that the capacity should be developed [Taylor,C]
22815 If freedom depends on society and culture, the greatest freedom is in shaping them [Taylor,C]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
22814 Our reliance on other people close to us does not imply any political obligations [Taylor,C]
25. Social Practice / C. Rights / 1. Basis of Rights
22810 A right is not just a rule, but also asserts certain ideas of moral worth [Taylor,C]
22812 For most people the primacy of rights mainly concerns freedom [Taylor,C]
25. Social Practice / C. Rights / 4. Property rights
22813 Property is not essential for life, but it may be essential for independence [Taylor,C]
25. Social Practice / E. Policies / 3. Welfare provision
23417 If the state is neutral, there won't be sufficient community to support a welfare state [Taylor,C, by Kymlicka]