@misc{Lexicon of Arguments,
title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 20 May 2018},
author = {Logic Texts},
subject = {Second Order Logic, HOL},
note = {Re III 62f
"All the characteristics of a great commander"/compact/1st Level/2nd level/Read: a categorical set of axioms for arithmetic must be a 2nd level logic - logical form: "for every quality f, if for every person x, if x was a great general, then x had f, then Napoleon had f - but: purely syntactically you cannot decide whether this is 1st or 2nd level - what distinguishes the two is their semantics!
The definition area can be arbitrary, provided it is not empty - Russell: Addition: "... and these are all..." - ReadVs: either superfluous in explicitly specified conjunction or wrong - Omega rule: needs the addition, however it cannot be expressed in the 1st level logic - to exclude non-standard models, but it should be formulated in the 1st level (i.e. in logical terms).
---
Re III 152f
Logic 1st level: individuals, 2nd level variables for predicates, distribution of predicates by quantifiers - 1st level allows restricted vocabulary of the 2nd level: existence and universal quantifier - other properties 2nd level are not definable in the logic of the 1st stage: e.g. to be finite, or to be true of most things.},