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Inductive explanations have an explanandum and an explanans.

One of the most important goals of the nature of scientific studies is to find explanations of natural phenomena. In this case, scientists accept an explanation is a form of an argument. We know that an argument is a group of statements, which are designed to explain the truth of an idea. However, explanations have two main components: the explanandum and the explanans. Ergo, an explanation can be considered as an argument where its conclusion should include an explanation to a fact (i.e. explanandum), which is supposed to be explained. The explanans, on the other hand,  is the group of statements (i.e. premises), which is aimed to perform an actual explaining.

The explanandum is the fact that is to be explained.

The explanandum is actually a problem, or a phenomenon, something, or some-event to be explained and it is the conclusion of an inductive argument.

An appropriate logical relation must exist between the explanandum and the explanans. Therefore, ‘the explanans entails the explanandum‘.

The “explanatory facts” adduced are irrelevant to the explanandum event despite the fact that the explanandum follows ( deductively or inductively) from the explanans.

According to encyclopedia of philosophy of science: The Covering-Law Model of Explanation

Hempel reports three different forms of covering-law explanation:

  • Deductive-nomological (D-N): These are deductive arguments whose premises include universal (deterministic) laws along with statements of particular conditions.
  • Inductive-statistical (I-S): These are inductive arguments whose premises include statistical laws.
  • Deductive-statistical (D-S): These are deductive arguments in which statistical laws are entailed by more comprehensive statistical laws.

“Explanations may be further subdivided according to the logical character of the explanandum statement. The explanandum statement may be either a singular statement, a universal statement, or a statistical generalization.”

To sum up, explanandum should have a (logical) consequence of the explanans, which shall have some empirical content, i.e. some of its statements should be empirically testable.