Combining Texts

All the ideas for 'Three Grades of Modal Involvement', 'New System and Explanation of New System' and 'On the Introduction of Transfinite Numbers'

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14 ideas

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Whether a modal claim is true depends on how the object is described [Quine, by Fine,K]
5. Theory of Logic / G. Quantification / 1. Quantification
Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Reality must be made of basic unities, which will be animated, substantial points [Leibniz]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Aristotelian essentialism says a thing has some necessary and some non-necessary properties [Quine]
10. Modality / A. Necessity / 2. Nature of Necessity
Necessity can attach to statement-names, to statements, and to open sentences [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
Necessity is in the way in which we say things, and not things themselves [Quine]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
No machine or mere organised matter could have a unified self [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
The soul does know bodies, although they do not influence one another [Leibniz]
27. Natural Reality / G. Biology / 2. Life
To regard animals as mere machines may be possible, but seems improbable [Leibniz]