Quantifiers

By Hintikka, Jaakko; Sandu, Gabriel

The quantifiers ‘some’ and ‘every’ were the object of the very first logical theory, Aristotelian syllogistic. An example of a syllogism is ‘Every Spartan is Greek, every Greek ...

Quantifier

Quantifiers, generalized

By Westerstahl, Dag

Generalized quantifiers are logical tools with a wide range of uses. As the term indicates, they generalize the ordinary universal and existential quantifiers from first-order logic, ‘∀x’ and ...

Existential quantifier

Universal quantifier

Objectual interpretation of quantifiers

see Quantifiers, substitutional and objectual.

Substitutional interpretation of quantifiers

see Quantifiers, substitutional and objectual.

Quantifiers, substitutional and objectual

By Richard, Mark

Understood substitutionally, ‘Something is F’ is true provided one of its substitution instances (a sentence of the form ‘a is F’) is true. This contrasts with the objectual ...

Predicate logic

Normal form (prenex)

Normal form (Skolem)

Scope

By Richard, Mark

Scope is a notion used by logicians and linguists in describing artificial and natural languages. It is best introduced in terms of the languages of formal logic. Consider ...

Modal operators

By Schweizer, Paul

Modal logic is principally concerned with the alethic modalities of necessity and possibility, although this branch of logic is applied to a wide range of linguistic and conceptual ...

Leśniewski, Stanisław (1886–1939)

By Wolenski, Jan

Leśniewski was one of the most distinguished members of the Warsaw School of Logic. His scientific development can be divided into two periods. In the first ‘philosophical’ period ...

Logic in the early 20th century

By Moore, Gregory H.

The creation of modern logic is one of the most stunning achievements of mathematics and philosophy in the twentieth century. Modern logic – sometimes called logistic, symbolic logic ...

Second- and higher-order logics

By Lavine, Shaughan

In first-order predicate logic there are symbols for fixed individuals, relations and functions on a given universe of individuals and there are variables ranging over the individuals, with ...

Reference

By Devitt, Michael

It is usual to think that referential relations hold between language and thoughts on one hand, and the world on the other. The most striking example of such ...

Semantics, possible worlds

By Perry, John R.

Possible worlds semantics (PWS) is a family of ideas and methods that have been used to analyse concepts of philosophical interest. PWS was originally focused on the important ...

Existence

By Mackie, Penelope

Philosophical problems concerning existence fall under two main headings: ‘What is existence?’ and ‘What things exist?’. Although these questions cannot be entirely separated, this entry will concentrate on ...

Free logics, philosophical issues in

By Lambert, Karel

The expression ‘free logic’ is a contraction of the more cumbersome ‘logic free of existence assumptions with respect to both its general terms (predicates) and its singular terms’. ...

Logical constants

By McCarthy, Timothy

A fundamental problem in the philosophy of logic is to characterize the concepts of ‘logical consequence’ and ‘logical truth’ in such a way as to explain what is ...

Tense and temporal logic

By Smith, Quentin

A special kind of logic is needed to represent the valid kinds of arguments involving tensed sentences. The first significant presentation of a tense logic appeared in Prior ...

Predicate calculus

By Smiley, Timothy

The predicate calculus is the dominant system of modern logic, having displaced the traditional Aristotelian syllogistic logic that had been the previous paradigm. Like Aristotle’s, it is a ...

Universal instantiation

Non-constructive rules of inference

By Hazen, A.P.

For some theoretical purposes, generalized deductive systems (or, ‘semi-formal’ systems) are considered, having rules with an infinite number of premises. The best-known of these rules is the ‘ω-rule’, ...