Deductive-nomological Model - Formalization

Formalization

The model offers the following account of scientific explanation, where an explanation is set out as a formalized argument:

• Let p be the explanandum - the statement that describes the phenomenon or phenomena to be explained.

• Let s₁. . . s_n be the explanans - the statements that "explain" the statement P.

In the D-N model, at least one of the statements s_i must be a "law-like" statement—a problematic concept, but initially thought to be captured by universal affirmatives, i.e., statements of the form "all X are Y." The explanans must be appropriately testable or observable—they must have "empirical content." If the premises are all true and if the argument is deductively valid, then the following constitutes a correct deductive-nomological explanation of p:

s₁. . . s_n, therefore, p

As a very simple illustration, consider the following: we observe that a piece of chalk falls when released. Why does the chalk fall? A D-N explanation might look like this (without attending to all subtleties in the precisely correct statement of the premises and conclusion):

• Massive objects attract each other with a force proportional to their masses and inversely proportional to the square of their distance apart.

• The chalk and Earth are massive objects.

• Holding the chalk overcomes the force of attraction between it and Earth

• Therefore, the chalk falls when released

The model is influenced by logical positivism in its tone and implication, devised as a prescriptive form for scientific explanations. Due to the way that the model eschews any account of causality, scientific modelling, or simplification—and the general rejection of logical positivism—it is no longer accepted by most current philosophers of science.