Combining Texts

All the ideas for 'The Case against Closure (and reply)', 'Remarks on the definition and nature of mathematics' and 'A New Kind of Science'

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12 ideas

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
17807 To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
20660 At one level maths and nature are very similar, suggesting some deeper origin [Wolfram]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17806 It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17808 Saying mathematics is logic is merely replacing one undefined term by another [Curry]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
19544 Closure says if you know P, and also know P implies Q, then you must know Q [Dretske]
19545 We needn't regret the implications of our regrets; regretting drinking too much implies the past is real [Dretske]
19546 Knowing by visual perception is not the same as knowing by implication [Dretske]
19547 Reasons for believing P may not transmit to its implication, Q [Dretske]
19548 The only way to preserve our homely truths is to abandon closure [Dretske]
19549 P may imply Q, but evidence for P doesn't imply evidence for Q, so closure fails [Dretske]
19550 We know past events by memory, but we don't know the past is real (an implication) by memory [Dretske]
27. Natural Reality / C. Space / 4. Substantival Space
20659 Space and its contents seem to be one stuff - so space is the only existing thing [Wolfram]