Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Guidebook to Wittgenstein's Tractatus' and 'Preface to 'Principles of Philosophy''

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17 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics is the roots of the tree of science [Descartes]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Interpreting a text is representing it as making sense [Morris,M]
2. Reason / F. Fallacies / 4. Circularity
I know the truth that God exists and is the author of truth [Descartes]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
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 / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
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 / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Understanding, not the senses, gives certainty [Descartes]
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]
28. God / C. Attitudes to God / 5. Atheism
Atheism arises from empiricism, because God is intangible [Descartes]