Combining Texts

All the ideas for 'Introduction to Russell's Theory of Types', 'The Mengzi (Mencius)' and 'Logical Consequence'

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19 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
If the King likes music then there is hope for the state [Mengzi (Mencius)]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Human nature is naturally compassionate and good (as a 'sprout'), but people may not be good [Mengzi (Mencius), by Norden]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Righteousness is extending the unthinkable, to reveal what must be done [Mengzi (Mencius)]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Each correct feeling relies on an underlying virtue [Mengzi (Mencius)]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
Should a coward who ran fifty paces from a battle laugh at another who ran a hundred? [Mengzi (Mencius)]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
A true king shares his pleasure with the people [Mengzi (Mencius)]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Extend the treatment of the old and young in your family to the rest of society [Mengzi (Mencius)]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Only put someone to death if the whole population believes it is deserved [Mengzi (Mencius)]
25. Social Practice / E. Policies / 1. War / e. Peace
Seeking peace through war is like looking for fish up a tree [Mengzi (Mencius)]
25. Social Practice / F. Life Issues / 6. Animal Rights
Avoid the animals you are going to eat, as it is hard once you have got to know them [Mengzi (Mencius)]