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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: ???
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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).

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    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. – ChristopherE Feb 21 '18 at 2:27
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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.

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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. – Geoffrey Thomas Mar 3 '18 at 18:23
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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.

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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.

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