Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Presupposition' and 'Introduction to 'Self-Knowledge''

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14 ideas

4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Logic would be more natural if negation only referred to predicates [Dummett]
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 / E. Structures of Logic / 2. Logical Connectives / c. not
Natural language 'not' doesn't apply to sentences [Dummett]
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 / 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]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
If we have a pain, we are strongly aware of the bodily self [Cassam]
16. Persons / C. Self-Awareness / 1. Introspection
Knowledge of thoughts covers both their existence and their contents [Cassam]
16. Persons / C. Self-Awareness / 2. Knowing the Self
Outer senses are as important as introspection in the acquisition of self-knowledge [Cassam]
Is there a mode of self-awareness that isn't perception, and could it give self-knowledge? [Cassam]
Neither self-consciousness nor self-reference require self-knowledge [Cassam]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
We can't introspect ourselves as objects, because that would involve possible error [Cassam]