Philosophy Dictionary of ArgumentsHome
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| 2nd order Logic: Predicate logic of the 2nd order goes beyond predicate logic of the 1st level allowing quantification over properties and relations, and not just objects. Thus comparisons of the powerfulness of sets become possible. Problems which are expressed in everyday terms with terms such as "greater", "between", etc., and e.g. the specification of all the properties of an object require predicate logic of the 2nd order. Since the 2nd level logic is not complete (because there are, for example, an infinite number of properties of properties), one often tries to get on with the logic of the 1st order._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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Logic Texts on Second Order Logic, HOL - Dictionary of Arguments
Read III 62f "All the characteristics of a great emperor"/compactness/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! >Syntax, >Semantics. The definition area can be arbitrary, provided it is not empty - Russell: Addition: "... and these are all..." ReadVs: that is either superfluous in an 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). III 152f Logic 1st order: individuals, 2nd order: variables for predicates, distribution of predicates by quantifiers. 1st order: allows restricted vocabulary of the 2nd level: existence and universal quantifier. Other properties 2nd level are not definable in the logic of the 1st order: e.g. to be finite, or to be true of most things. >Operator, >Level (Order), >Description level. _____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
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> Counter arguments against Logic Texts
> Counter arguments in relation to Second Order Logic, HOL
Ed. Martin Schulz, access date 2024-04-24