Combining Texts

All the ideas for 'Non-Monotonic Logic', 'Metaphysics: a very short introduction' and 'What Numbers Are'

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16 ideas

2. Reason / E. Argument / 1. Argument
You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli]
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli]
4. Formal Logic / E. Nonclassical Logics / 12. Non-Monotonic Logic
Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli]
Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli]
Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli]
Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli]
We can rank a formula by the level of surprise if it were to hold [Antonelli]
People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
In classical logic the relation |= has Monotony built into its definition [Antonelli]
Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Substances, unlike aggregates, can survive a change of parts [Mumford]
10. Modality / B. Possibility / 3. Combinatorial possibility
Maybe possibilities are recombinations of the existing elements of reality [Mumford]
Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford]
Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford]