Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Intro to I: Classical Logic' and 'Zettel'

expand these ideas     |    start again     |     specify just one area for these texts

---

15 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy

2626	A philosopher is outside any community of ideas [Wittgenstein]

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 / 6. Classical Logic

9463	Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette]

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]

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

6569	'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin]

13. Knowledge Criteria / C. External Justification / 2. Causal Justification

3790	Causes of beliefs are irrelevant to their contents [Wittgenstein]