Opaque context

As an opaque context (Latin opacus, shaded ',' opaque ') is in the philosophy of language refers to a linguistic context in which with the same scope of meaning of the truth value of the statement expressed may change by replacing part of expressions. In ordinary non- opaque contexts, the replacement of the same meaningless expressions is always truth preserving, salva veritate. The representation of opaque contexts is one of the main challenges for each model of a formal semantics, as evidenced by them that neither the ordinary objects in the world still private shows the meaning of linguistic expressions can be immediate. Gottlob Frege identified among other playback foreign expressions in indirect speech as an opaque context ( of him as " odd speech " means ). The investigation of opaque contexts plays a role in the philosophical theory of proper names, the theory of modal logic and labeling and for epistemic logic.

Explanation

Co- extensionality

Koextensionalität is a semantic property of expressions: proper names or labels are co - extensional if they refer to the same thing. Co- extensional are thus, for example, the terms " the highest mountain in the world " and " Mount Everest " a marking and a proper name, which both refer to the same object.

A classic and now historically outdated example is from Willard van Orman Quine. The terms " the number 9 " and " the number of planets ( in our solar system ) " could apply to Quine's time as co- extensional, since the common list of planets at the time Pluto nor included (see Planet # assignments).

From co- extensional names for concepts or predicates is when everything that is playing a phrase, and the other term plays and vice versa. The terms have the same extent, that is, the amounts of the things that meet the predicates are identical. Co- extensional terms would be for an example of Rudolf Carnap " () is a living creature with a heart" and " () is a creature with kidneys " since Carnap assumes that all living beings, who have a heart, have also kidney and vice versa.

Substitutability salva veritate

Under normal circumstances, the truth or falsity of a statement does not change when an expression is replaced in her by a co- extensional, therefore we also speak of substitutability salva veritate. The importance of complex linguistic expressions is directly dependent in this case about the importance of simple linguistic expressions occurring in them. If we replace, for example, in " Frank climbed Mount Everest. " The term " Mount Everest " by " the highest mountain in the world ", we get " Frank climbed the highest mountain in the world ".

These two sentences have the same truth value now, since the meaning should not have changed. That if the first sentence is true and the second sentence must be true, and vice versa. Analogously with it: " All living beings with heart are mammals " and " All living beings are mammals with kidneys ", even these rates are either both true or both false.

Opaque context

Opaque contexts are now specific linguistic constructions in which the substitution principle, that is, usually applicable substitutability co- extensional expressions salva veritate is overridden. For ". Peter believes that Frank has climbed Mount Everest " and ". Peter believes that Frank has climbed the highest mountain in the world " it may actually be that the first sentence true and the second is false; as if Peter does not know that Mount Everest is the highest mountain in the world. Similarly, it is with the words: " Peter believes that all animals are mammals with a heart. " And " Peter believes that all animals with kidney are mammals. ".

Is a part of a complex sentence in which an attitude or intention of a person at that rate is reported, so it is as well as in indirect speech to an opaque context. These cases of opaque contexts, for example by words such as " believes ," " looking forward to that", "reported that " displayed etc.. In special cases, such as " erroneously assumes that " is a superposition of opaque and non-opaque context instead, since in a sentence of the form "It is false that p" the truth value already from which the proposition p depends on a set of the form " assumes that P" is not.

Another class of expressions that create opaque contexts, Modalausdrücke such as " necessary" and "possible". Thus, from the two sets " The number eight is necessarily straight. " And "The number of planets in our solar system is necessarily straight. " The first sentence true since it expresses a mathematical truth (there are no circumstances conceivable, under which the number eight is not straight); however, the second sentence is false, the number of planets is precisely, but this is not necessarily the case, since it is a simple empirical fact. It would be consistent to imagine that there could be a planet, more or less. This shows that even in modal contexts the substitutability co- extensional expressions is not generally guaranteed that there is to say on opaque contexts.

Applications

The theory of opaque contexts is relevant for epistemic logic, so that sub-discipline of logic, " believes that" with the analysis of expressions like, or " know " deals. In formulating the applicable here regularities must be considered that the end of a statement like " Peter believes that Frank Mount Everest has climbed " "believes Peter that Frank has climbed the highest mountain in the world " on is not universally valid, but under the assumption is that Peter believes that Mount Everest is the highest mountain in the world. Quite the same applies to the modal logic, ie the sub-discipline of logic, with the terms " necessary" and " possible " deals.