Logical constant

Inlogic,alogical constantorconstant symbolof alanguage${\mathcal {L}}$is asymbolthat has the samesemantic valueunder everyinterpretationof${\mathcal {L}}$.Two important types of logical constants arelogical connectivesandquantifiers.Theequalitypredicate (usually written '=') is also treated as a logical constant in manysystems of logic.

One of the fundamental questions in thephilosophy of logicis "What is a logical constant?";that is, what special feature of certain constants makes themlogicalin nature?

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"
$\Box$	"necessarily"
$\Diamond$	"possibly"

Many of these logical constants are sometimes denoted by alternate symbols (for instance, the use of the symbol "&" rather than "∧" to denote thelogical and).

Defining logical constants is a major part of the work ofGottlob FregeandBertrand Russell.Russell returned to the subject of logical constants in the preface to the second edition (1937) ofThe Principles of Mathematicsnoting that logic becomes linguistic: "If we are to say anything definite about them, [they] must be treated as part of the language, not as part of what the language speaks about."The text of this book usesrelationsR,theirconversesandcomplementsasprimitive notions,also taken as logical constants in the formaRb.

See also

• Logical connective
• Logical value
• Non-logical symbol

External links

• Stanford Encyclopedia of Philosophy entry on logical constants