====== Vacuous truth ======

Refers to a logical or mathematical statement which is formally //true// but has no expressive power.

Example:
> <u questionable "Vacuous truth">If //Paris// is in //Italy//, then //Madrid// is the capital of //Sweden//.</u>

Regardless of in which country Madrid is located, the overall statement is //true//, paradoxically precisely //because// the [[glossary:antecedent|antecedent]] ("Paris is in Italy") is //false//. 

===== Description =====

By applying the rules of logic, one can also come to findings which are //formally true// but do not lead to further knowledge.

For example, in the case of a [[glossary:subjunction|subjunction]], a //false// (counterfactual) //antecedent// (in the above example: "Paris is in Italy") always leads to a //true// overall statement - regardless of the truth value of the //consequent//.

This is not limited to //subjunctions//. Such "empty" statements are possible with (almost) all inferential forms. Similarly, [[glossary:tautology|tautologies]] are //empty truths// and one could call [[glossary:contradiction|contradictions]] "empty falsehoods" (since they are always //false//).

With certain forms of inferences, it is also true that statements that refer to empty extensions are always true and thus also represent //vacuous truths//.

For example:

> //All unicorns are immortal.//

This is true, because no unicorn exists that could ever die.

===== Colloquial use =====

In colloquial language, a form of //vacuous truth// is sometimes used to point out the absurdity of a statement:

> //If// Oslo is the capital of Sweden, //then// I am the emperor of China.

Although this is formally also only //vacuously true//, there is actually an information conveyed here, namely that the speaker considers the statement "Oslo is the capital of Sweden" to be counterfactual (read: false!).

===== See also =====

  * [[glossary:contradiction|Contradiction]]
  * [[logic:formal_fallacies:existential|Existential Fallacy]]
  * [[glossary:tautology|Tautology]]

===== More information =====

  * [[wp>Vacuous truth]] on //Wikipedia//