Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Reality without Reference' and 'Analogy of Religion'

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16 ideas

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 / 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]
9. Objects / F. Identity among Objects / 9. Sameness
A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
Despite consciousness fluctuating, we are aware that it belongs to one person [Butler]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
If consciousness of events makes our identity, then if we have forgotten them we didn't exist then [Butler]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
Consciousness presupposes personal identity, so it cannot constitute it [Butler]
16. Persons / D. Continuity of the Self / 5. Concerns of the Self
If the self changes, we have no responsibilities, and no interest in past or future [Butler]
19. Language / A. Nature of Meaning / 1. Meaning
A minimum requirement for a theory of meaning is that it include an account of truth [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A theory of truth tells us how communication by language is possible [Davidson]
19. Language / B. Reference / 1. Reference theories
Is reference the key place where language and the world meet? [Davidson]
With a holistic approach, we can give up reference in empirical theories of language [Davidson]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson]