Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Lecture on Nominalism' and 'Personal Identity'

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13 ideas

2. Reason / F. Fallacies / 1. Fallacy
The Struthionic Fallacy is that of burying one's head in the sand [Quine]
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 / 6. Relations in Logic
All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
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]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]
16. Persons / B. Nature of the Self / 5. Self as Associations
Personal identity is just causally related mental states [Parfit, by Maslin]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
One of my future selves will not necessarily be me [Parfit]
16. Persons / D. Continuity of the Self / 4. Split Consciousness
If we split like amoeba, we would be two people, neither of them being us [Parfit]
16. Persons / D. Continuity of the Self / 5. Concerns of the Self
Concern for our own lives isn't the source of belief in identity, it is the result of it [Parfit]