Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'In Praed.' and 'Prolegomena to Any Future Metaphysic'
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11 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
16918
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Mathematics cannot proceed just by the analysis of concepts [Kant]
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6. Mathematics / A. Nature of Mathematics / 2. Geometry
16930
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Geometry is not analytic, because a line's being 'straight' is a quality [Kant]
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16919
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Geometry rests on our intuition of space [Kant]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
16920
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Numbers are formed by addition of units in time [Kant]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
16929
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7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890
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There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
16910
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Mathematics can only start from an a priori intuition which is not empirical but pure [Kant]
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16917
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All necessary mathematical judgements are based on intuitions of space and time [Kant]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
16928
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Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant]
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