The term "abduction" was coined by CS Peirce to describe the process that puts hypotheses on the docket to be tried by induction and deduction. Sometimes folks use it to mean something like "inference to best explanation", but that's not how Peirce meant it.

> Proposals for hypotheses inundate us in an overwhelming flood, while the process of verification to which each one must be subjected before it can count as at all an item, even of likely knowledge, is so very costly in time, energy, and money -- and consequently in ideas which might have been had for that time, energy, and money, that Economy would override every other consideration even if there were any other serious considerations. In fact there are no others. For abduction commits us to nothing. It merely causes a hypothesis to be set down upon our docket of cases to be tried.

— CS Peirce (Collected Papers §5.602)

> abduction commits us to nothing. It merely causes a hypothesis to be set down upon our docket of cases to be tried.

This is the perfect phrasing. Consider the contrast with deduction: if I have a premise, P, there are many deductive inferential rules I could apply to that premise to produce a new truth.

E.g. Given P, we can infer "not not P", and if we're also given "P implies Q" we can infer Q

Abduction flips this on its head: we have Q. And Q could be just the double negation of a P we weren't given. Or it could be the consequence of "P implies Q". There's really no way to know with certainty.

This is forensics. It's exactly the reasoning used in courtrooms: from the evidence (or "consequences"), we need to use science and logic to figure out how we got there (i.e. what were the antecedents).

This is why the most famous fictional user of "abduction" is Sherlock Holmes. But really it's what every forensic investigator (including a detective) is doing. Abduction is most common in judicial settings (i.e. when we are trying to assign blame).

Ah,

That is actually an illuminating perspective cutting through verbiage.

Abduction is the first "step", that the produces the ideas that can be considered ... by induction or deduction. It is the principle that we have to start somewhere.

Basically, an abductive step is something like "I can think of only ten hypotheses that explain X and only one of them works. I could consider an infinity of possibilities but it's not worth it. I will stick with my working hypothesis".

That's wrong. Induction is the process of empirically producing natural laws.

Our givens are the observed state of the experiment before (i.e. the antecedent, or "premise"), and after (i.e. the consequent, or "conclusion" of) an event. These givens are the only observations.

Induction is the process of creating an inferential rule (e.g. a causal hypothesis) that allows us to deduce the given consequent from the given antecedent (e.g. by applying a formula).

Abduction has different givens. In that case, we have observed consequences, and are given a set of inferential rules (e.g. natural laws) that could have produced the observed consequence. We then try to acquire evidence to support theories about which (unobserved) antecedent led to the (observed) consequent, by using one of our given inferential rules.

Your usage of "premise" and "conclusion" as shorthands for "the state of the world at a time t" is somewhat confusing to me, when I hear those words I think of propositions that have truth value, not events/states. You can sort of encode the state of the world at any instant as a proposition which is the conjunction of all possible true propositions describing the world at that instant ("The sky is blue", "Water is wet", "Temperature is 40C",...), but it's not obvious that this is a useful way to think in.

For example, suppose you're a mathematician with a conclusion (conjecture) C and a premise P (axioms), you search for a proof to get C from P, and you find it. That fits your definition of induction. Now suppose you're a pre-copernicus astronomer who have a "conclusion" and a "premise", which are actually just the state of the world recorded at different times, and you want to find a law that gets you the conclusion from the premise, and you find it in a system of epicycles. This too fits your definition of induction.

But those 2 situations are radically different. The mathematician's proof is much more correct and permanent than the astronomer's "proof". If I find another proof of the mathematician's claim, even a very different proof, that doesn't render the first proof obsolete, and it doesn't mean my proof is wrong either. But if I find another law that explains the states of the world the astronomer explained, then unless one of the laws is a special case of the other, either me or the astronomer is wrong, or the world is crazy and somehow obeys 2 sets of laws that aren't reducible to each other at the same time.

In other words, if logical propositions are imagined as a DAG where the edges represent valid rules of inference, then it doesn't matter which path (proof) got you to a node as long as you got there. But if you imagine the states of the world like this, then it actually matters what specific laws got you to a particular node. Maybe actual reality doesn't care and there are infinite systems of physics that all perfectly well explain the universe, but we very much care about path uniqueness, much more than we do in math, chess or other such systems. That's why I think the encoding of world states as propositions is lossy. A state\event is more than the propositions describing it.

> Your usage of "premise" and "conclusion" as shorthands for "the state of the world at a time t" is somewhat confusing to me

I agree, and the correct terms are "antecedent" and "consequent"; a premise is a type of antecedent, and a conclusion a type of consequent. But using those terms right away makes it harder to relate to formal arguments.