Logical constant

The expressions selected to indicate the logical form of a sentence. A sentence will play a proper role in inference in virtue of a structure that can be exhibited by means of these expressions. The basic logical constants include expressions for the truth-functions &, ∨, →, — and ¬, the quantifiers (∃) and (∀), and the identity relation =. The parentheses,( ), which indicate the scope of functions, may be counted as logical constants. Richer conceptions of logical form will include other constants: modal logic includes the operators □ and ◊, and tense logic will include operators signifying past, present and future. See Logical symbols

In mathematical logic, a logical constant of a language is a symbol that has the same semantic value under every interpretation of . Two important types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant in many systems of logic.

Some symbols that are commonly treated as logical constants are:

Symbol	Meaning in English
T	"true"
F	"false"
¬	"not"
∧	"and"
∨	"or"
→	"implies", "if...then"
∀	"for all"
∃	"there exists", "for some"
=	"equals"
	"necessary"
	"possible"

For many logical constants also other symbols are commonly used to denote them, such as the symbol "&" for logical and.

One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; that is, what special feature of certain constants that makes them logical in nature?^[1]

See also

• Non-logical symbol
• Logical value
• Logical connective

External links

• Stanford Encyclopedia of Philosophy entry on logical constants

1. ^ Carnap

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