Combining Texts

All the ideas for 'fragments/reports', 'What is Logic?' and 'Utilitarianism and the Virtues'

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19 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
3. Truth / A. Truth Problems / 3. Value of Truth
22462 We should speak the truth, but also preserve and pursue it [Foot]
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]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
22458 Consequentialists can hurt the innocent in order to prevent further wickedness [Foot]
22460 Why might we think that a state of affairs can be morally good or bad? [Foot]
22461 Good outcomes are not external guides to morality, but a part of virtuous actions [Foot]
22464 The idea of a good state of affairs has no role in the thought of Aristotle, Rawls or Scanlon [Foot]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
22463 Morality is seen as tacit legislation by the community [Foot]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
22459 For consequentialism, it is irrational to follow a rule which in this instance ends badly [Foot]