Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'An American Indian model of the Universe' and 'On the Source of Necessity'

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17 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
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]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
15102 S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron]
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]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
15103 Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
3916 Hopi consistently prefers verbs and events to nouns and things [Whorf]
14. Science / B. Scientific Theories / 4. Paradigm
3917 Scientific thought is essentially a specialised part of Indo-European languages [Whorf]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
15104 The 'moving spotlight' theory makes one time privileged, while all times are on a par ontologically [Cameron]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
3915 The Hopi have no concept of time as something flowing from past to future [Whorf]