Is abduction a species of induction? Can we abduce what we could never know by induction?
And has anyone tried to enumerate what we can know by induction?
See Abduction :
The term “abduction” was coined by Charles Sanders Peirce in his work on the logic of science. He introduced it to denote a type of non-deductive inference that was different from the already familiar inductive type.
the best way to distinguish between induction and abduction is this: both are ampliative, meaning that the conclusion goes beyond what is (logically) contained in the premises (which is why they are non-necessary inferences), but in abduction there is an implicit or explicit appeal to explanatory considerations, whereas in induction there is not; in induction, there is only an appeal to observed frequencies or statistics.
This Youtube video distinguished and explained most clearly for me:
For a textual explanation, and the 3 words' etymology and etymological definitions, see https://www.merriam-webster.com/words-at-play/deduction-vs-induction-vs-abduction
If you have trouble differentiating deduction, induction, and abduction, thinking about their roots might help. All three words are based on Latin ducere, meaning "to lead." The prefix de- means "from," and deduction derives from generally accepted statements or facts. The prefix in- means "to" or "toward," and induction leads you to a generalization. The prefix ab- means "away," and you take away the best explanation in abduction.