Combining Texts

All the ideas for 'New System and Explanation of New System', 'Philosophy of Mathematics' and 'Guidebook to Wittgenstein's Tractatus'

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15 ideas

1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Interpreting a text is representing it as making sense [Morris,M]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Bipolarity adds to Bivalence the capacity for both truth values [Morris,M]
5. Theory of Logic / G. Quantification / 1. Quantification
Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M]
To count, we must distinguish things, and have a series with successors in it [Morris,M]
Discriminating things for counting implies concepts of identity and distinctness [Morris,M]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Reality must be made of basic unities, which will be animated, substantial points [Leibniz]
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]
19. Language / D. Propositions / 1. Propositions
There must exist a general form of propositions, which are predictabe. It is: such and such is the case [Morris,M]
27. Natural Reality / G. Biology / 2. Life
To regard animals as mere machines may be possible, but seems improbable [Leibniz]