Combining Texts

All the ideas for 'Leibniz', 'On Second-Order Logic' and 'Causal Structuralism'

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16 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Many concepts can only be expressed by second-order logic [Boolos]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
A categorical basis could hardly explain a disposition if it had no powers of its own [Hawthorne]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
Is the causal profile of a property its essence? [Hawthorne]
If properties are more than their powers, we could have two properties with the same power [Hawthorne]
Could two different properties have the same causal profile? [Hawthorne]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
We can treat the structure/form of the world differently from the nodes/matter of the world [Hawthorne]
9. Objects / D. Essence of Objects / 3. Individual Essences
An individual essence is a necessary and sufficient profile for a thing [Hawthorne]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The Identity of Indiscernibles is really the same as the verification principle [Jolley]
26. Natural Theory / C. Causation / 7. Eliminating causation
Maybe scientific causation is just generalisation about the patterns [Hawthorne]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
We only know the mathematical laws, but not much else [Hawthorne]