Combining Texts

All the ideas for 'On Second-Order Logic', 'Advice to a Young Tradesman' and 'The Ultimate Constituents of Matter'

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18 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes, grouped by a convenient property, are logical constructions [Russell]
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]
7. Existence / D. Theories of Reality / 4. Anti-realism
Visible things are physical and external, but only exist when viewed [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
Sense-data are purely physical [Russell]
If my body literally lost its mind, the object seen when I see a flash would still exist [Russell]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
A man is a succession of momentary men, bound by continuity and causation [Russell]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
We could probably, in principle, infer minds from brains, and brains from minds [Russell]
23. Ethics / B. Contract Ethics / 8. Contract Strategies
Punctuality and justice in dealings are excellent for raising a man in the world [Franklin]
24. Political Theory / D. Ideologies / 11. Capitalism
Time is money, ..credit is money, ..and money breeds more money [Franklin]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
Matter is a logical construction [Russell]
Matter requires a division into time-corpuscles as well as space-corpuscles [Russell]
27. Natural Reality / C. Space / 2. Space
Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell]