Sir Karl Popper presents us with a somewhat unsystematic list of six types of cases in which we should be inclined to say of a THEORY 1 (T1),that it is superseded by THEORY 2 (T2) ,i.e. as far as we know, T2 corresponds better to the facts than T1, in some sense or the other.
(1) T2 makes more precise assertions than T1, and these more precise assertions stand up to more precise tests.
(2) T2 takes account of, and explains, more facts than T1. If we apply this to our criteria in (1), it would mean, other things being equal, T2‘s assertions are more precise).
(3) T2 describes or explains, the facts in more detail than T1.
(4) T2 has passed tests which T1 has failed to pass.
(5) T2 has suggested new experimental tests, not considered before T2 was designed (and not suggested by T1, and perhaps not even applicable to T1); and T2 has passed these tests.
(6) T2 has unified or connected various hitherto unrelated problems. — The list above combines the ideas of truth and of content into one–the ideas of a degree of better (or worse) correspondence to truth, likeness to truth, approximation to truth aka Verisimilitude.
In dealing with history research, issues of interpolation but also transliteration, transposition and translation errors do pop up. Justificatory approach (also a positivist approach.. don’t let the name fool you) aka inductive logic jumps to the blunder of ignoring everything that does not support its own theory.
To protect oneself from such blunders, one must do the following…
Assuming that the truth-content and the falsity-content of two theories T1 and T2 are comparable, we can say that T2 is more closely similar to the truth, or corresponds better to the facts, than T1,
IF AND ONLY IF EITHER…
(1) The truth-content but not the falsity-content of T2 exceeds that of T1, or
(2) The falsity-content of T1, but not its truth-content, exceeds that of T2.