Ideas from 'On SecondOrder Logic' by George Boolos [1975], by Theme Structure
[found in 'Logic, Logic and Logic' by Boolos,George [Harvard 1999,067453767x]].
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5. Theory of Logic / A. Overview of Logic / 7. SecondOrder Logic
14249

Boolos reinterprets secondorder logic as plural logic

10830

Secondorder logic metatheory is settheoretic, and secondorder validity has settheoretic problems

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829

A sentence can't be a truth of logic if it asserts the existence of certain sets

5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832

'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed

5. Theory of Logic / K. Features of Logics / 4. Completeness
10834

Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences

5. Theory of Logic / K. Features of Logics / 6. Compactness
13841

Why should compactness be definitive of logic?

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / e. Peano arithmetic 2ndorder
10833

Many concepts can only be expressed by secondorder logic
