Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Reals by Abstraction' and 'The Logical Structure of the World (Aufbau)'

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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.
14. Science / B. Scientific Theories / 1. Scientific Theory
18699 Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button]
     Full Idea: Carnap's ultimate ambition in the Aufbau is to provide a constitution-system within which any predicate of any scientific vocabulary can be explicitly defined in terms of primitive relations holding among basic elements, using type theory.
     From: report of Rudolph Carnap (The Logical Structure of the World (Aufbau) [1928]) by Tim Button - The Limits of Reason 05.2
     A reaction: David Chalmers has a modern shot at the same project in 'Constructing the World'. Ramsey sentences seem to be part of the same game.
18. Thought / D. Concepts / 4. Structure of Concepts / g. Conceptual atomism
12131 All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody]
     Full Idea: In the 'Aufbau', Carnap tried to show how all of our concepts can be derived from a few basic concepts. ..Consequently there can be one science which studied all that existed, the science of the objects corresponding to the basic concepts.
     From: report of Rudolph Carnap (The Logical Structure of the World (Aufbau) [1928]) by Baruch Brody - Identity and Essence 2.2
     A reaction: This is Carnap's Constructionist programme.
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').