Combining Texts

All the ideas for 'fragments/reports', 'What is Logic?' and 'Intro to Principles of Morals and Legislation'

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22 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 / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
5901 Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
5934 Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
3777 Pleasure and pain control all human desires and duties [Bentham]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
3554 Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham]
3781 The value of pleasures and pains is their force [Bentham]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
3778 The community's interest is a sum of individual interests [Bentham]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
25. Social Practice / F. Life Issues / 6. Animal Rights
20280 Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham]
26. Natural Theory / A. Speculations on Nature / 1. Nature
3779 Unnatural, when it means anything, means infrequent [Bentham]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
3780 We must judge a thing morally to know if it conforms to God's will [Bentham]