Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Ontological Categories' and 'Principles of Arithmetic, by a new method'

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20 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
13134 We negate predicates but do not negate names [Westerhoff]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
18113 PA concerns any entities which satisfy the axioms [Peano, by Bostock]
17634 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
15653 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
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
7. Existence / E. Categories / 1. Categories
13117 How far down before we are too specialised to have a category? [Westerhoff]
13116 Maybe objects in the same category have the same criteria of identity [Westerhoff]
13118 Categories are base-sets which are used to construct states of affairs [Westerhoff]
13125 Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff]
13126 Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff]
13130 Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff]
13124 Categories can be ordered by both containment and generality [Westerhoff]
7. Existence / E. Categories / 2. Categorisation
13131 The aim is that everything should belong in some ontological category or other [Westerhoff]
7. Existence / E. Categories / 3. Proposed Categories
13123 All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff]
7. Existence / E. Categories / 5. Category Anti-Realism
13115 Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff]
13119 Categories merely systematise, and are not intrinsic to objects [Westerhoff]
13135 A thing's ontological category depends on what else exists, so it is contingent [Westerhoff]
9. Objects / D. Essence of Objects / 5. Essence as Kind
13129 Essential kinds may be too specific to provide ontological categories [Westerhoff]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]