How does abduction differ from inductive reasoning?

Consider this statement:

1. Abductive reasoning typically begins with an incomplete set of observations and proceeds to the likeliest possible explanation for the set.
1. But couldn't the same be said about inductive reasoning? Someone finds a penny in a jar. Then they find a second and a third penny, so they conclude that all the coins in the jar are pennies.

Three pennies constitute an incomplete set, so how is that different from abduction?

What example of abduction would complement the following two deduction/induction sets?

DEDUCTION #1: All mammals have vertebrae; llamas are mammals. Therefore, llamas have vertebrae.

INDUCTION #1: The first three bones found in Cave X were vertebrae. Therefore, the other bones may represent mammals.

1. ABDUCTION #1: ???

DEDUCTION #2: All planets orbit stars. Earth is a planet. Therefore, Earth orbits a star.

INDUCTION #2: Astronomers have pronounced Object X a planet. The nearby Object Z is also a planet. Therefore, Object X and Object Z probably orbit the nearest star.

1. ABDUCTION #2: ???

Induction is about the probability of something. Abduction is an assumption as to what is the most likely answer - it's a judgement call.

ABDUCTION #1: The bones of 3 llamas were found in Cave X; therefore the vertebrae found in Cave X are likely from a llama. (since we already found 3 llamas, it's likely that the bones found are also llamas)

ABDUCTION #2: Object A orbits around the Earth. Object A is probably a moon. (it could be a satellite, but judging by the conversation about planets and stars, it makes more sense to assume it's a moon).

Deduction is something that always appears to be so. Induction is something that sometimes appears to be so. Abduction is the best assumption about something.

So for instance:

Deduction: Rain is water. Water makes things wet. Therefore, when it rains, the grass becomes wet.

Induction: It's 90 % chance of showers tomorrow afternoon: therefore, it will probably rain tomorrow afternoon and the grass will be wet.

Abduction: The grass is wet in the afternoon; it probably rained. vs. The grass is wet in the morning, it is probably wet because of dew, not rain. (the best explanation for/an intelligent explanation).

• I would just flag that this answer does not present a standard set of agreed-upon definitions and distinctions, though it sounds like it does and it was accepted. So, have caution. Also, that deductive argument isn’t deductively valid. Feb 21 '18 at 2:27
• @ChristopherE The deductive argument is: if water, then wet; if rain, then water; thus, if rain, then wet. That’s as far as the premises will go. Another premise is needed to add “grass”. Nov 24 '19 at 21:07
• Peirce describes abduction as 'inference to the best explanation' and this seems correct to me. Here 'inference' may include induction but would usually rely on deduction.
– user20253
Nov 25 '19 at 12:18

You are not alone in finding difficulty in distinguishing abductive from inductive reasoning. It doesn't help that 'abductive' inference is a relatively new term in philosophy - historically much more recent than 'deductive' or 'inductive' - or that there is no canonical statement of it.

Will you bear with me a bit while I try out some contrasts ?

In a deductively valid argument the conclusion cannot be false if the premises are true. Well, we know abductive inference is nothing like that.

In an inductively strong argument, the conclusion is merely unlikely to be false if the premises are true.

So what ground is left for abductive inference ? It's really an intelligent guess. It's not just a guess, it's an intelligent guess. Peerhaps this can be illustrated by an example from CS Peirce (wjo some say and others deny originated the notion of abductive inference). He was btw writing long ago :

THE FOUR HORSEMEN EXAMPLE

I once landed at a seaport in a Turkish province; and, as I was walking up to the house which I was to visitr, I met a man upon horseback, surrounded by four horsemen holding a canopy over his head. AS the governor of the province was the only personage I could think of who would be so greatly honored, I inferred that this was he. This was a hypothesis.

Maybe one difference between induction and abduction is that induction often relies on regularities or lawlike correlations. It is an inductive inference that if I smoke 60 cigarettes a day for twenty years, I will get lung cancer. It doesn't deductively follow that I will but there's an uncomfortably high probability.

Or : what is the likelihood that if I earn more than $100,000 a year I will be audited by the tax authorities ? Regularly about 5% of people on this income scale are audited, so the probability is quite low. (Figures invented.) In the case of Peirce's abductive inference about the governor, nothing like these regularities or lawlike correlations are in play. Yet he made an intelligent guess. On this occasion in the light of Peirce's knowledge of social customs, it was the inference to the best explanation that the person was the governor. There is an academic squabble over whether abductive inference and inference to the best explanation are the same thing. I assume they are. Those who disagree can make their case. References : The Four Horseman example and the phrase, 'intelligent guess', are taken from Douglas Walton, 'Abductive Reasoning', Tuscaloosa : University of Alabama Press, 2004, 5-6. Walton also discusses the abduction/ inference to the best explanation : 6. Fundamental reference : Chance , Love and Logic by C.S. Peirce ( at archive.org). See: Part I, chapter 6 " Deduction, induction and hypothesis"). Peirce is the one who coined this term " abduction". See also : article " reasoning" ( by Peirce) in Baldwin's dictionary of philosophy and psychology. Short answer Both are "ampliative"; but while induction aims at a general rule ( instantiated by previous observations) ; abduction aims at an explanation of a particular observation ( according to known rules). Peirce's idea Deduction, induction and abduction differ by the order in which the elements " rule", " case" and "result" are used and organized. Analytic reasoning The conclusion is contained in the premises: deduction Structure : 1. Rule 2. Case 3. Therefore: Result Non-analytic reasoning , thus synthetic The conclusion "goes further" than the premises, it " adds" something. 2 species : (A) induction : generalization Structure : 1. Case 2. Result 3. Therefore : rule (B) abduction : hypothetical reasoning Structure : 1. Result 2. Rule 3. Therefore: Case Characterization of abduction A given " result" being observed, and a given rule being known ( by induction) , abduction draws the hypothetical conclusion that this result must be explained by the fact that we are in a case falling under this rule. Example : 1. Result : This man has left town immediately after the murder was committed. 2. Rule: Murderers often leave the place where they have committed a crime. 3. Case : This man must be the murderer. I'd agree that these forms of inference overlap in all sorts of ways but they can often be distinguished. I'm no logician (!) but have an opinion. I'd agree with Sarah's answer although am not sure the induction example is quite right. I see abduction (like Peirce) as inference to the best explanation, but not a proof. It is a method much used by Sherlock Holmes. It is a sort of logical 'via negativa'. If out of ten suspect on the list nine have been eliminated, then this is not a proof of the guilt of the tenth, but his guilt would now be the best explanation for the crime. This is a form of deduction, but for me induction is also a form of deduction. 1. Deduction: 2+2=4, thus 2=4-2 2. Induction: I nearly always get my sums wrong so (1) may be a flawed deduction. 3. Ordinary maths becomes impossible unless (1) is a correct deduction and the experts concur with it, so probably it is. (1) allows proof and certainty, the other two do not. Practically this may be the defining difference since the overlap between these methods is so great. It seems to me that abduction is the most important of these methods in philosophy, since we proceed by eliminating bad theories to reveal the best theory, just as Holmes shortens a list of suspects or successively eliminates possible explanations for the crime. But in the end this is not enough and some hard evidence has to be found to turn the result of abduction into a deductive proof. • Nice answer - I have never quite accepted the difference between IBE and abduction though Gil Harman insists on trying to separate them. Certainly neither yields proof if they really are different modes of explanation. Mar 3 '18 at 18:23 I don't see "pattern" or "prediction" in any of the answers so far, and only one instance of "explain". Unlike deduction, which is always at least as correct as the given facts, induction and abduction both rely on probabilities. But those probabilities are used in quite different ways. With inductive reasoning, one takes patterns and by interpolation or extrapolation predicts that some other event was likely to have happened or will happen. • That man was on my bus on Monday, Tuesday, Thursday, and Friday, and even though I didn't take it on Wednesday because I overslept, I'll bet he was on the bus that day too. • All the bones found so far are human. I'll bet the few remaining bones will be too. With abductive reasoning, one takes a single event that has already happened, and explains it by the simplest and most likely reason. • My bus was very late today, and near the back was a large dent that wasn't there yesterday. I'll bet something collided with it and caused the delay. • All the bones found so far are human. I'll bet that this is an old burial site. Abductive reasoning appears in other forms too: There's a medical saying (originating from Zebra (medicine) - Wikipedia): “When you hear hoof beats, think zebras, not horses.” "The simplest explanation is usually the right one." This duplicates https://math.stackexchange.com/a/2126985. This Youtube video distinguished and explained most clearly for me: Understanding these 3 words' etymologies can help:$\color{limegreen}{\text{Retroduction :}}$The prefix "retro," occurs in loanwords from Latin having to do with going backward. Yet, the prefix "retro" provides an implication of deliberateness–of deliberately "choosing" to go backward for a purpose. Thus "retroactive" means choosing to go back to an earlier date and make something operative as of that date. "Retrofit" means choosing to go back and modify an earlier model of something with an improvement of some sort. The combination of the prefix "retro" (as deliberately "going backward") with the suffix "ductive" from the Latin ducere (to lead) places the meaning of retroduction as "deliberately leading backward." This implies that retroduction is intended to be a deliberate and recursive process involving more than the making of an abductive inference. Its Latin roots indicate that "retroduction" refers, not only to the apprehension of a "surprising fact," and an ensuing hunch, but also that the hunch, once formed, is deliberately and recursively taken "backward" for analysis and adjustment (requiring deduction and induction), before it is engendered into a hypothesis worthy of extensive testing.$\color{limegreen}{\text{Abduction :}}$The prefix "ab" appears in loanwords from Latin where it meant "away from." Thus we have words like "abdicate" and "abolition"–going "away from" the throne and from slavery, respectively. Thus, when the prefix "ab" (away from) is combined with the suffix "ductive" (from the Latin ducere, meaning to lead) we have the meaning of abduction as "leading away from." The term "abduction" fits well with the concept of abduction as moving "away from" a particular course or topic, as one would when responding to an anomaly, or a "surprising fact." The Latin root for "abduction" does not fit with the idea of going backward to explicate and evaluate an idea. Rather, this root indicates that the outward movement of an abductive inference allows the result of such an inference to be left as a completion, or used as the sole means for further exploration of possibilities–as in the arts.$\color{limegreen}{\text{Deduction :}}$The prefix "de" from Latin loanwords refers to separation, removal, and negation. When we combine the prefix "de" (to separate) with the suffix "ductive" (to lead), we have the meaning of deduction as "leading to separation, removal, or negation," which are the goals and consequences of deductive reasoning.$\color{limegreen}{\text{Induction :}}\$
The prefix "in," also from the Latin has to do with inclusion. Thus, the prefix "in" (to include) combined with the suffix "ductive" means "leading into" (or including), as one would do when reaching a conclusion by estimating from a sample, or generalizing from a number of instances.

Therefore, based upon their Latin derivations (to which Peirce was partial, as he was for Greek roots) our four terms have the following meanings:

Deduction = leading to separation, removal, or negation.
Induction = "leading into" (or including) .

Abduction = inference to the best explanation and even may be wildly wrong.

Induction = basing "knowledge" of the future on past experience and may still be wrong but we are biologically "programmed" to do so.

As I understand it, abduction is how most people make most decisions. You make the best call you can with the information that you have at the time when the decision must be made. The process can include both deduction and induction, but it accepts data from a wider variety of sources, such as personal experience and second-hand information, than a formal proof would require.

As far as I understand it, an inductive inference is any inference that is non deductive, essentially meaning an argument in which the premisses can be true whilst the conclusion is false as the premisses do not necessarily entail the conclusion, whereas in a deductive inference the premises must always entail the conclusion. An abductive inference is simply one type of inductive inference, in which we infer the most likely possibility as the conclusion. e.g.

1.The weather forecast says there will be an 80% chance of rain at 1200 tomorrow

C. It will rain tomorrow

A different type of inductive inference might be

1.I hear a sound akin to a car engine outside

2.The only thing I know to cause that sound is a car

3.If so, then there must be a car outside

C.There is a car outside

The premisses do not necessarily entail the conclusion as there could be other things thats make that sound, and it is not necessarily the most likely case that there is a car outside (perhaps where I live there is a strange animal I am unaware of, capable of making the same sound, which does so very frequently whilst cars actually come by very rarely). As such it is a non-abductive type of inductive inference