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All the ideas for 'What is Logic?st1=Ian Hacking', 'What is Justified Belief?' and 'Neutral Relations'

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20 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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
14219 Language imposes a direction on a road which is not really part of the road [Fine,K]
14217 The 'standard' view of relations is that they hold of several objects in a given order [Fine,K]
14216 The 'positionalist' view of relations says the number of places is fixed, but not the order [Fine,K]
14218 A block on top of another contains one relation, not both 'on top of' and 'beneath' [Fine,K]
14220 Explain biased relations as orderings of the unbiased, or the unbiased as permutation classes of the biased? [Fine,K]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
8830 A belief can be justified when the person has forgotten the evidence for it [Goldman]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
8832 If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
8829 Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman]
16. Persons / C. Self-Awareness / 1. Introspection
8831 Introspection is really retrospection; my pain is justified by a brief causal history [Goldman]