Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Introducing Persons' and 'A Problem about Substitutional Quantification?'

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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

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 / G. Quantification / 4. Substitutional Quantification

10792

The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)]

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]

16. Persons / B. Nature of the Self / 5. Self as Associations

1394	Can the mental elements of a 'bundle' exist on their own? [Carruthers]

1395	Why would a thought be a member of one bundle rather than another? [Carruthers]

16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity

1396	We identify persons before identifying conscious states [Carruthers]