### Ideas from 'What is Logic?' by Ian Hacking , by Theme Structure

#### [found in 'A Philosophical Companion to First-Order Logic' (ed/tr Hughes,R.I.G.) [Hackett 1993,0-87220-181-3]].

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###### 2. Reason / D. Definition / 3. Types of Definition
 13838 A decent modern definition should always imply a semantics
###### 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
 13834 Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C'
 13835 Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with
###### 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
###### 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
 13844 A limitation of first-order logic is that it cannot handle branching quantifiers
###### 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
 13842 Second-order completeness seems to need intensional entities and possible worlds
###### 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
###### 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
###### 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