Combining Texts

All the ideas for 'Remarks on the definition and nature of mathematics', 'Intros to Russell's 'Essays in Analysis'' and 'On the Notion of Cause'

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12 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophers usually learn science from each other, not from science [Russell]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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
Saying mathematics is logic is merely replacing one undefined term by another [Curry]
10. Modality / A. Necessity / 2. Nature of Necessity
'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell]
26. Natural Theory / C. Causation / 7. Eliminating causation
The law of causality is a source of confusion, and should be dropped from philosophy [Russell]
If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Striking a match causes its igniting, even if it sometimes doesn't work [Russell]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
The constancy of scientific laws rests on differential equations, not on cause and effect [Russell]