Explanations

Basing explanation on deduction, or "covering laws," within the context of formal logical is misleading in several ways.
 

1. The explanans involves a  universal scientific law.  Not only do explanations extend far beyond science, but it's unlikely that any scientific law is universal.  It is better to say that explanations include a "substantive generalization," what Toulmin called a "warrant," where "substantive" means it is generally true.  It is precisely the truth or falsity of the explanatory generalizations that is obscured by limiting them to universals.
    
2. Explanation is a matter of making the explanandum rationally acceptable.  With an explanation we already know the explanandum is true, so there's no need to justify or prove it.  With a plausible explanation the explanans and explanandum are logically consistent, nothing more.
    
3. The logical consistency of an explanation is a matter of deduction.  The premises of a deduction,  'if x then y' and 'x', are actually equivalent to the conjunction, 'x and y'.  It is this conjunction of the explanans and the explanandum (all of them being true) that creates a plausible explanation.  Thus, narratives, absent any generalizations, can constitute explanations on the same logical ground as deductions using generalizations.