Combining Texts

All the ideas for 'Through the Looking Glass', 'Possible Worlds' and 'Principles of Arithmetic, by a new method'

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9 ideas

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 / A. Nature of Existence / 2. Types of Existence
15789 Lewis's distinction of 'existing' from 'being actual' is Meinong's between 'existing' and 'subsisting' [Lycan on Lewis]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
15790 Lewis can't know possible worlds without first knowing what is possible or impossible [Lycan on Lewis]
15791 What are the ontological grounds for grouping possibilia into worlds? [Lycan on Lewis]