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All the ideas for 'What is Logic?st1=Ian Hacking', 'The Ways of Paradox' and 'Theology and Verification'

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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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
21695 The set scheme discredited by paradoxes is actually the most natural one [Quine]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
21693 Russell's antinomy challenged the idea that any condition can produce a set [Quine]
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]
5. Theory of Logic / L. Paradox / 3. Antinomies
21691 Antinomies contradict accepted ways of reasoning, and demand revisions [Quine]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
21690 Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
21689 A barber shaves only those who do not shave themselves. So does he shave himself? [Quine]
21694 Membership conditions which involve membership and non-membership are paradoxical [Quine]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21692 If we write it as '"this sentence is false" is false', there is no paradox [Quine]
29. Religion / D. Religious Issues / 1. Religious Commitment / c. Religious Verification
1470 Belief in an afterlife may be unverifiable in this life, but it will be verifiable after death [Hick, by PG]
1471 It may be hard to verify that we have become immortal, but we could still then verify religious claims [Hick, by PG]
29. Religion / D. Religious Issues / 1. Religious Commitment / d. Religious Falsification
1469 Some things (e.g. a section of the expansion of PI) can be verified but not falsified [Hick, by PG]