Combining Texts

All the ideas for 'Events and Their Names', 'Principles of Arithmetic, by a new method' and 'The Prince'

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14 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Events are made of other things, and are not fundamental to ontology [Bennett]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
If men are good you should keep promises, but they aren't, so you needn't [Machiavelli]
24. Political Theory / B. Nature of a State / 3. Constitutions
The principle foundations of all states are good laws and good armies [Machiavelli]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
People are vengeful, so be generous to them, or destroy them [Machiavelli]
To retain a conquered state, wipe out the ruling family, and preserve everything else [Machiavelli]
A sensible conqueror does all his harmful deeds immediately, because people soon forget [Machiavelli]
25. Social Practice / E. Policies / 1. War / a. Just wars
A desire to conquer, and men who do it, are always praised, or not blamed [Machiavelli]
25. Social Practice / E. Policies / 2. Religion in Society
Machiavelli emancipated politics from religion [Machiavelli, by Watson]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Facts are about the world, not in it, so they can't cause anything [Bennett]