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An opaque context is a linguistic context in which it is not possible to substitute co-referential terms while guaranteeing the preservation of semantic values.

The term is used in philosophical
Philosophy

Philosophy is the study of general problems concerning matters such as existence, knowledge, truth, beauty, justice, validity, mind, and language....
 theories of reference, and is to be contrasted with "transparent context". For example:





Similar usage of the term applies for artificial languages such as programming languages
Programming language

A programming language is a machine-readable artificial language designed to express computations that can be performed by a machine, particularly a computer....
 and logics
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
. The Cicero-Tully example above can be easily adapted.






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An opaque context is a linguistic context in which it is not possible to substitute co-referential terms while guaranteeing the preservation of semantic values.

The term is used in philosophical
Philosophy

Philosophy is the study of general problems concerning matters such as existence, knowledge, truth, beauty, justice, validity, mind, and language....
 theories of reference, and is to be contrasted with "transparent context". For example:

  • Opacity: "Mary knows that Cicero
    Cicero

    Marcus Tullius Cicero was a Ancient Rome philosopher, statesman, lawyer, political theorist, and Constitution of the Roman Republic. Cicero is widely considered one of Rome's greatest rhetoric and prose stylists....
     is a great orator" is referentially opaque; although Cicero was also called Tully, we can't simply substitute "Tully" for "Cicero" in this context ("Mary knows that Tully is a great orator"), for Mary might not know that the names 'Tully' and 'Cicero' refer to one and the same thing. Of course, if Mary does know that Cicero is a great orator, then there is a sense in which Mary knows that Tully is a great orator, even if she does not know that 'Tully' and 'Cicero' corefer. It is the sense forced on us by direct theories of reference of proper names, i.e., those that maintain that the meaning of proper names just are their referents. This is also called Referential opacity.


  • Transparency: "Cicero was a Roman orator" is referentially transparent; there is no problem substituting "Tully" here: "Tully was a Roman orator". Well, this is an oversimplified account as it may not hold in all circumstances, e.g., when, even though 'Tully' and 'Cicero' are grammatically proper names, their meanings are in part dependent on something other than their referents. This occurs, e.g., when someone has two separate personae that are referred to separately by two distinct proper names, and that, although referring to the same person, do so in significantly different ways that their substitutions into what are usually taken to be transparent contexts results in sentences with different truth values. For example, 'Clark Kent wooed the ladies', or 'Clark Kent was a great hero' are generally taken to be false even though they are true when 'Superman' is substituted for 'Clark Kent' in each.


Similar usage of the term applies for artificial languages such as programming languages
Programming language

A programming language is a machine-readable artificial language designed to express computations that can be performed by a machine, particularly a computer....
 and logics
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
. The Cicero-Tully example above can be easily adapted. Let be interpreted as a function symbol returning a "name" of the value of the variable
Variable

A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e....
  on a language with domain . Define a predicate
Predicate

Predicate or predication may refer to:*Predicate , the rest of a sentence apart from the subject in traditional grammar and in many Phrase structure grammar approaches...
 with the property that is true if and only if has characters. Then induces an opaque context, or is referentially opaque because is true while is false. Programming languages often have richer semantics than logics' semantics of truth and falsity, and so an operator
Operator

In mathematics, an operator is a function which operates on another function. Often, an "operator" is a function which acts on functions to produce other functions ; or it may be a generalization of such a function, as in linear algebra, where some of the terminology reflects the origin of the subject in operations on the functions which ar...
 such as may fail to be referentially transparent for other reasons if it is not a pure function
Pure function

In computer programming, a function may be described as pure if both these statements about the function hold:# The function always evaluates the same result value given the same argument value....
.

See also

  • Masked man fallacy
    Masked man fallacy

    The masked man fallacy is a fallacy of formal logic in which substitution of identical designators in a true statement can lead to a false one. The name comes from the example "I do not know who the masked man is", which can be true even though the masked man is Jones, and I know who Jones is....
  • Transitivity of identity
  • W.V.O. Quine
  • Pure functions
    Pure function

    In computer programming, a function may be described as pure if both these statements about the function hold:# The function always evaluates the same result value given the same argument value....