Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Answer to 'What is Enlightenment?'' and 'The Logic of Scientific Discovery'

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21 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
22358 Scientific objectivity lies in inter-subjective testing [Popper]
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]
14. Science / A. Basis of Science / 6. Falsification
22188 Give Nobel Prizes for really good refutations? [Gorham on Popper]
7780 Falsification is the criterion of demarcation between science and non-science [Popper, by Magee]
16830 We don't only reject hypotheses because we have falsified them [Lipton on Popper]
6794 If falsification requires logical inconsistency, then probabilistic statements can't be falsified [Bird on Popper]
6795 When Popper gets in difficulties, he quietly uses induction to help out [Bird on Popper]
14. Science / B. Scientific Theories / 2. Aim of Science
3856 Good theories have empirical content, explain a lot, and are not falsified [Popper, by Newton-Smith]
14. Science / C. Induction / 3. Limits of Induction
7779 There is no such thing as induction [Popper, by Magee]
14. Science / C. Induction / 4. Reason in Induction
3860 Science cannot be shown to be rational if induction is rejected [Newton-Smith on Popper]
25. Social Practice / A. Freedoms / 3. Free speech
21058 Enlightenment requires the free use of reason in the public realm [Kant]