Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Criterion of Validity in Reasoning' and 'Inexpressible Properties and Propositions'

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14 ideas

2. Reason / A. Nature of Reason / 4. Aims of Reason
I reason in order to avoid disappointment and surprise [Peirce]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
That a judgement is true and that we judge it true are quite different things [Peirce]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Instances of minimal truth miss out propositions inexpressible in current English [Hofweber]
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 / A. Overview of Logic / 3. Value of Logic
Only study logic if you think your own reasoning is deficient [Peirce]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]
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]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
Facts are hard unmoved things, unaffected by what people may think of them [Peirce]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Since properties have properties, there can be a typed or a type-free theory of them [Hofweber]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber]