Combining Texts

All the ideas for 'Letters', 'What is Logic?' and 'Inventing Logical 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]
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 / A. Necessity / 6. Logical Necessity
12189 Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
7320 Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
4581 Virtues and vices are like secondary qualities in perception, found in observers, not objects [Hume]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
4580 All virtues benefit either the public, or the individual who possesses them [Hume]
26. Natural Theory / C. Causation / 3. Final causes
4579 The idea of a final cause is very uncertain and unphilosophical [Hume]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
20705 That events could be uncaused is absurd; I only say intuition and demonstration don't show this [Hume]