Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Introduction to 'Modality'' and 'There Are No Abstract Objects'

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15 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]
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 / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
14596 Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
14597 Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]
10. Modality / A. Necessity / 1. Types of Modality
14528 Maybe modal thought is unavoidable, as a priori recognition of necessary truth-preservation in reasoning [Hale/Hoffmann,A]
10. Modality / A. Necessity / 11. Denial of Necessity
14598 Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]