Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Grounding Concepts' and 'On Sense and Reference'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

17730

Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

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

17887

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

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

17719

Arithmetic concepts are indispensable because they accurately map the world [Jenkins]

17717

Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17724

It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]