I believe that there are four main types of historical exposition.
First, there is analysis, which takes recorded facts and expounds them according to assumed causal or logical connections. Analysis may be given according to the synthetic method, giving first the causes and then the effects, or the analytic method, giving first the effects and moving on to the causes. But this is a difference of style, and both methods are nevertheless historical analysis.
Second, there is conjecture, which proposes facts beyond what is recorded. Conjecture is divided into abductive conjecture, analytic conjecture, and synthetic conjecture.
Abductive conjecture proposes possible causes for a given fact. For instance, a historian may conjecture that a sudden disappearance of a people was due to epidemic disease, although there are no traces of the disease left. Analytic conjecture proposes possible components of a given fact. For instance, a historian may conjecture that a recorded stabbing was done with daggers, although the source does not mention the particular weapons. Synthetic conjecture proposes possible effects of a given fact. For instance, a historian may conjecture that an epidemic caused the afflicted population to save less of their income for the distant future, since their survival was uncertain, although there is no record of the amount of their savings.
All history involves at least some conjecture, since it must be supposed that at least some of the known records are truly records and not fabrications, which is an abductive conjecture, albeit often highly certain.
Legend, myth, and fiction (added 2022-11-30)
In view of the terms just mentioned, I have found it useful to distinguish myths and legends from purely historical narratives, as well as purely fictional narratives.
A narrative exposition may propose facts that have no connection with any given facts; such proposals are not to be called conjectural but arbitrary, and insofar as a narrative does this, it is not historical but legendary.
Insofar as a narrative proposes facts, whether arbitrary or conjectural, that are incomprehensible either by concepts of experience, or by a definite analogy with those concepts, such a narrative is mythical. So, by this division, some myths are legends, and some legends are myths, but not all.
A narrative is purely fictional when it is not intended to be connected with present experience by a chain of efficient causes.
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