# Deductive nomological model

The deductive - nomological model (short- DN model ) is a formal structure of scientific explanation of a causal link via natural language . It serves to explain general laws as well as individual linguistically describable 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 the Hempel-Oppenheim scheme ( HO scheme for short ). It consists of two parts, the sentence to be explained by closing (explanandum) and the explanation (explanans), which is composed of general statements of law and (empirical) boundary conditions (statements of antecedents) as premises.

The basic structure of the scheme has been known since the 19th century at the latest and was taken up by Karl Popper in 1935 in the logic of research . After being worked out by Hempel and Oppenheim in 1948, it was discussed by numerous authors from the late 1950s onwards.

## definition

Quote: The question " Why does the phenomenon occur?" Is understood as the question "According to which general laws and on what preconditions does the phenomenon occur?"

A deductive-nomological explanation of a state of affairs is a logically correct argument that consists of the explanans (the explanatory sentences) - generally applicable (scientific) laws and special conditions - and the explanandum (the sentence to be explained) that can be derived from it . The explanation of the phenomenon consists in the demonstration that the phenomenon obeys the known general laws that apply to the specific circumstances.

Explanans:

L1, ..., Ln (from Latin l ex, laws)
C1, ..., Cr (from Latin c onditio, conditions)

- - - - - - - - - - - - ( implied )
explanandum

The following example comes from Karl Popper (L = law, C = boundary or initial conditions):

Explanans:

(L) Every time a thread of size r is loaded with a weight of at least K, it breaks.
(C1) This is a thread of size r.
(C2) The attached weight is at least K.

Explanandum:

### Explanans

The explanans is the explanatory (present participle active from the Latin explanare "to interpret, explain, interpret"). It is made up of:

• as generally recognized laws (e.g. physical law )
• fulfilled conditions (which allow the application of the laws), the antecedent (the cause)

### Explanandum

The explanandum is the rate of the to be explained (gerundive neuter to explanare) (not the phenomenon itself) describes. It is the event / observation that is to be explained and, if the explanation is successful, it is the result of the conclusion from the explanans.

An explanation can only be correct if the following four necessary conditions are met.

1. The explanandum follows deductively from the explanans (inference condition).
2. The Explanans contains general laws; these must be necessary for explanation (legal requirement).
3. The explanans has an empirical content; i.e. it must be falsifiable (significance condition).

1. All sentences of the explanan are true (truth condition).

## Explanation and prediction

In this model, an explanation is formally identical to a prediction: If the explanandum is given, correctly selected laws and conditions offer its explanation; if the laws and conditions are given, they allow the explanandum to be predicted. An explanation is only adequate if it could have predicted the phenomenon.

If the premises of the DN argument are known first and if the conclusion is derived from it afterwards, one speaks of an ex-ante DN justification (or DN prediction in the epistemic sense). One such argument is DN prediction in the temporal sense if the antecedent event occurs before the explanandum event, and it is retrodiction if it occurs afterwards.

Example: The derivation of a future solar eclipse on the basis of astronomical data (and physical theory) is a prediction, the derivation of a past meteor impact from geological finds is a retrodiction.

## Problem cases for the DN model

• Asymmetry . The DN model does not contain any restrictions on the asymmetry relationship between the explanans and the explanandum.

Example: The derivation of the already known height of a tower from its shadow length is an ex-post DN justification, but not a DN explanation because the shadow length is not the cause of the tower height.

(L) Men who take the pill regularly do not get pregnant.
(C) John Jones is a man who took the pill regularly.
(E) John Jones does not get pregnant.
• Statistical statements . The DN model does not allow reliable conclusions to be drawn from the explanans to the explanandum for statistical statements; rather, the conclusion is only correct with a certain probability. Hempel therefore proposed the inductive statistical model for such statements .

## literature

• Carl Gustav Hempel, Paul Oppenheim: Studies in the Logic of Explanation in Philosophy of Science 15 (1948), 135-175; reproduced in Hempel, Aspects of Scientific Explanation ; pdf .
• Nicholas Rescher : H 2 O: Hempel-Helmer-Oppenheim, an Episode in the History of Scientific Philosophy in the 20th Century in Philosophy of Science, Volume 64, No. 2 (Jun., 1997), pp. 334-360.
• Siegfried Macho: Science and Pseudoscience in Psychology. Hogrefe, Bern 2016 ( ISBN 978-3-456-85616-2 ), pp. 143–156 (critical)

## supporting documents

1. Wesley C. Salmon : The Spirit of Logical Empiricism: Carl G. Hempel's Role in Twentieth-Century Philosophy of Science in Philosophy of Science, Volume 66, No. 3 (Sep., 1999), pp. 333-350; P. 340.
2. ^ Carl Gustav Hempel and Paul Oppenheim (1948). Studies in the Logic of Explanation , p. 136, in the original: ... the question “ Why does the phenomenon happen?” is constructed as meaning "according to what general laws, and by virtue of what antecedent conditions does the phenomenon occur?"
3. ^ Studies , p. 137
4. ^ Studies , p. 138