Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Reals by Abstraction' and 'A Theory of Conditionals'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10632 The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright]
     Full Idea: The real numbers may be introduced by abstraction as ratios of quantities. ..They are not defined by Dedekind cuts; rather, the cuts constitute a domain with the properties that are a necessary precondition.
     From: report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3
     A reaction: This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle.
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
14286 In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker]
     Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world.
     From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
     A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14285 A possible world is the ontological analogue of hypothetical beliefs [Stalnaker]
     Full Idea: A possible world is the ontological analogue of a stock of hypothetical beliefs.
     From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
     A reaction: Sounds neat and persuasive. What is the ontological analogue of a stock of hopes? Heaven!
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').