Deductive-nomological model
The deductive- nomological model (short DN model) is a formal structure of scientific explanation of a causal link by natural language. It is used both for statement of general laws, as well as of individual linguistic recordable events. The model was proposed by Carl Gustav Hempel and Paul Oppenheim in 1948 in the article " Studies in the Logic of Explanation " and is also known as Hempel - Oppenheim scheme ( short HO- schema ) is known. It consists of two parts, the to be explained by closing sentence ( explanandum ) and the explanation ( explanans ), resulting from general statements of law and ( empirical ) boundary conditions ( antecedent statements ) composed as premises.
The basic structure of the schema is known at least since the 19th century and was taken up by Karl Popper, 1935 in Logic of Scientific Discovery. After the development by Hempel and Oppenheim 1948, was discussed in the late 1950s by numerous authors.
- 2.1 Logical conditions of adequacy
- 2.2 Empirical adequacy condition
Definition
Quote: The question "why the phenomenon occurs " is understood as a question, " What are the general laws and under what preconditions the phenomenon occur? "
A deductive- nomological explanation of a fact is a logically correct argument ( the explanatory sentences ) from the explanans - general ( scientific) laws and special conditions - and the derivable explanandum ( the to -explanatory sentence ) is. The explanation of the phenomenon is to demonstrate that the phenomenon obeys the well-known general laws that apply to the specific situation.
Explanans:
------------ ( Implied) explanandum
The following example comes from Karl Popper ( L = Law, C = boundary or initial conditions ):
Explanans:
Explanandum:
Explanans
The explanatory variable is the explanatory ( present participle active of Latin explanare " interpret, explain, interpret "). It shall be composed of:
- Recognized as universally valid laws (for example Physical Law )
- Satisfied conditions ( which allow the application of the laws), the antecedent ( the cause)
Explanandum
The explanandum is the rate of the ( neuter gerundive to explanare ) describes the thing to be explained (not that phenomenon itself). It is the event / observation to be explained, and is - in a successful explanation - the result of the inference from the explanans.
Conditions of adequacy
One explanation may be correct only if the following four necessary conditions are met.
Logical conditions of adequacy
Empirical adequacy condition
Explanation and prediction
One explanation is formally identical to a prediction in this model: Is the explanandum given, provide incorrect selected laws and conditions his explanation; the laws and conditions are such that they allow the prediction of the explanandum. One explanation is only adequate if they could have predicted the phenomenon.
If the premises of the DN- known argument first and the conclusion is derived from it later, then one speaks of an ex-ante DN- justification ( or DN- prediction in the epistemic sense). Such an argument is a DN- prediction in the temporal sense, if the Antezedensereignis time occurs before the Explanandumereignis, and she is a retrodiction when it occurs afterwards.
Example: The derivation of a future eclipse due to astronomical data ( and physical theory ) is a prediction, the derivation of a recent meteor strike of geological discoveries is a retrodiction.
Problem cases for the DN model
- Asymmetry. The DN model does not contain any restrictions on the asymmetry ratio of explanans and explanandum.
Example: The derivation of the known height of a tower from his shadow length is an ex-post - DN- justification, but not DN- explanation, because the length of the shadow is not the cause of the tower height.
- Irrelevance (example of Wesley Salmon, 1971)
- Statistical statements. The DN model can in statistical statements about any firm conclusions from the explanans to the explanandum, the conclusion is rather properly only with a certain probability. Hempel suggested therefore for such statements before the inductive statistical model.