What is the main difference between Inductive and Abductive Reasoning?

A Christian Philosophy

Deductive reasoning (deduction) is clear: logical inference which is as certain as its premises.
My understanding is that both inductive reasoning (induction) and abductive reasoning (abduction) yield uncertain yet reasonable or probable inferences. But what is the main difference between the two? I have done some research and could not find any clear consensus.

Some say that both are Inference to the Best Explanation (IBE), but induction is a general explanation whereas abduction is a specific one. Sources: Lumen Learning, SolvingForPattern. This agrees with the example from Peirce in IEP. If so, then to me the difference is a negligible one.

Wikipedia and SEP are in contradiction on categorizing the following example: "If one observes 100 swans, and all 100 were white, one might infer a universal categorical proposition of the form All swans are white." Wiki calls this induction; SEP calls this abduction (using grey elephants).

Some philosophers say induction is just a specific type of IBE (which is abduction).

In a 1965 paper, Gilbert Harman explained that enumerative induction is not an autonomous phenomenon, but is simply a disguised consequence of Inference to the Best Explanation (IBE). — Wikipedia - Inductive reasoning

SEP says that induction is equivalent to statistics.

the best way to distinguish between induction and abduction is this: [...] 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. — SEP - Abduction

But to me, stats, being a branch of mathematics, is a certain science and would thus be deduction. Of course the stats result in a probability, but (stay with me on this) it's resulting probability is certain. E.g. If 95% of swans are white, then for the next swan picked at random, it is certain that there is a 95% chance it will be white. So this definition of induction is really just deduction.

My position right now is to stick to the first definition: both induction and abduction are Inference to the Best Explanation, and the former is general whereas the latter is specific.

TheMadFool

My personal opinion is that induction differs from abduction. Abduction is what I've come to understand as inference to the best explanation (IBE).

As far as I can remember,

Induction: The argument is probabilistic (the premises are supposed to increase the odds of the conclusion being true)

1. Arguments from analogy

2. Statistical arguments

3. Arguments from authority

Abduction: The best hypothesis for a given set of observations

Suppose we've made 3 observations and come up with two explanatory hypotheses X and Y. X explains two observations but Y explains all three. Choosing hypothesis Y is abduction.

A Christian Philosophy

↪TheMadFool

Hello.
I agree with your view on abduction.
Could you give a specific example of induction? I suspect any instance would fall under either abduction in the sense of IBE, or deduction.

aletheist

↪Samuel Lacrampe

Abduction (or retroduction) is the formulation of an explanatory hypothesis, often prompted by a surprising observation. Deduction is the explication of what would follow necessarily from that hypothesis if it were true. Induction is the evaluation of whether the hypothesis is falsified because those predictions are not borne out by experiments.

A Christian Philosophy

↪aletheist

Hello.
Could you give a specific example of your general description?
I fail to see why the verification of the hypothesis by experiments should not simply fall under deduction.

E.g. we observe 100 swans and all are white; so we hypothesize that all swans that exist are white. Then we test this by looking for more swans, and find one that is black. As "all swans are white" contradicts with "one swan is not white", we reject the original hypothesis. This rejection is based on deduction.

aletheist

↪Samuel Lacrampe

Again, abduction is formulating hypotheses, deduction is making predictions accordingly, and induction is testing those predictions against actual experience.

Abduction: We observe the surprising fact that every swan we have ever seen in the past was white, so we hypothesize (plausibly) that all swans are white.

Deduction: If all swans are white, then (necessarily) every swan that we will ever see in the future will be white.

Induction: We go looking for more swans and see a black one, so our hypothesis is falsified. If we were never to see a black swan, then the hypothesis would not be falsified, but that does not warrant certainty that it is true since we only ever observe a finite sample of swans.

A Christian Philosophy

↪aletheist

I get how each step of the example is categorized in the type of reasoning as you have defined them, but I still don't understand the distinction between induction and deduction in the example, as explained below.

We go looking for more swans and see a black one, so our hypothesis is falsified. — aletheist

Yes. As the original hypothesis is in contradiction with the new data, then it is necessarily false. So this is deduction.

If we were never to see a black swan, then the hypothesis would not be falsified, but that does not warrant certainty that it is true since we only ever observe a finite sample of swans. — aletheist

As the original hypothesis is not in contradiction with the new data, then it is not necessarily false. This is also deduction.

aletheist

As the original hypothesis is in contradiction with the new data, then it is necessarily false. So this is deduction. — Samuel Lacrampe

No, it is not necessarily false, it is contingently false--it is contradicted by experience, not logic. That is what makes it inductive, rather than deductive.

As the original hypothesis is not in contradiction with the new data, then it is not necessarily false. This is also deduction. — Samuel Lacrampe

Again, if the conclusion is not logically necessary, then it is not a deductive inference.

A Christian Philosophy

No, it is not necessarily false, it is contingently false--it is contradicted by experience, not logic. That is what makes it inductive, rather than deductive. — aletheist

Deduction is the explication of what would follow necessarily from that hypothesis if it were true. — aletheist

If some swans are black, the explication that necessarily follows is that the hypothesis "all swans are white" is false. So we falsify the hypothesis with deduction as you've defined it.

Otherwise, in general, all deductions must contain some experience since it checks for possible contradictions between premises that are built from experience.

aletheist

So we falsify the hypothesis with deduction as you've defined it. — Samuel Lacrampe

No, we falsify the hypothesis by observing a black swan. "If some swans are black, then not all swans are white" is deductively valid regardless of whether there actually are any black swans. Induction is the method that tells us to keep checking whether we ever see a non-white swan. Its validity lies in the fact that if there are any, we would eventually find one if we were to keep looking indefinitely.

Otherwise, in general, all deductions must contain some experience since it checks for possible contradictions between premises that are built from experience. — Samuel Lacrampe

Indeed, experience only contributes to the premisses, not the conclusion. Deduction derives necessary conclusions based strictly on formal considerations. It takes no experience at all, just competence in the English language, to deduce that there are no married bachelors. Induction is not required, since looking for a counterexample would be pointless.

A Christian Philosophy

Deduction derives necessary conclusions based strictly on formal considerations. — aletheist

I accept that claim. Thanks.

But now, how is induction different from abduction? Upon observing a black swan, the only reasoning needed at that point is: "I observe a black swan, therefore some swans are black". But that's just abduction; is it not?

Another way to say the same thing: arguments are composed only of premises and conclusion. Premises are built from abduction, and conclusions are built from deduction. There seems to be no need for a third type of reasoning.

aletheist

But now, how is induction different from abduction? — Samuel Lacrampe

Abduction is formulating a hypothesis, while induction is testing a hypothesis. Abduction offers a plausible explanation of a previously observed phenomenon, while induction evaluates whether that explanation is actually borne out by additional experience.

Premises are built from abduction, and conclusions are built from deduction. — Samuel Lacrampe

No, all three types of reasoning can be illustrated with syllogisms having two premisses and a conclusion. The key difference is how the conclusion follows from the premisses in accordance with what Charles Sanders Peirce called the "logical leading principle." He helpfully characterized the three propositions as rule, case, and result.

Deduction: The result (conclusion) is a necessary inference from the rule and the case (premisses).

Rule: All the beans in this bag are white.
Case: This bean is from this bag.
Result: This bean is white.

Induction: The rule (conclusion) is a probable inference from the case and the result (premisses).

Case: This bean is from this bag.
Result: This bean is white.
Rule: All the beans in this bag are white.

Abduction: The case (conclusion) is a plausible inference from the rule and the result (premisses).

Rule: All the beans in this bag are white.
Result: This bean is white.
Case: This bean is from this bag.

A Christian Philosophy

Abduction is formulating a hypothesis, while induction is testing a hypothesis. — aletheist

This distinction is in the function but not in the act. It seems to me that both are IBE, which is used both to build the hypothesis and to test it against new data.

[...] He helpfully characterized the three propositions as rule, case, and result. — aletheist

Yes I'm familiar with how Peirce described it (I gave the link to this example in the OP). In which case, it seems to me that both abduction and induction are IBE, and the distinction is that induction is a general explanation whereas abduction is a specific one.

I notice as well that your definition of induction as "testing a hypothesis" does not seem to fit Peirce's example of induction. The concluding rule "All the beans in this bag are white" does not serve to test either the case: "This bean is from this bag" or the result: "This bean is white". It's just a general IBE.

aletheist

↪Samuel Lacrampe

Conceiving a hypothesis to explain past experience is not the same as testing that hypothesis against subsequent experience. Inferring that a white bean of unknown origin (plausibly) came from a bag known to contain only white beans is not the same as inferring that all the beans in a given bag are (probably) white because one bean known to have come from that bag is white. More to the point, induction calls for taking additional random samples of beans from the bag to see whether those always consist entirely of white beans. Pursued indefinitely, if in fact there are some non-white beans in the bag (or even just one), then this method would eventually reveal it.

A Christian Philosophy

↪aletheist

So it seems the distinction is merely in the chronological order of experience. Abduction is an explanation based on past experience, whereas induction is a revised explanation based on subsequent experience. And had the subsequent experience actually happened before the original explanation, then it would be called abduction instead of induction; right? If this is true, then I find the distinction to be negligible.

As a side question, what is the difference between 'probable' and 'plausible'?

aletheist

↪Samuel Lacrampe

No, but I have explained it as well as I can at this point, and a dictionary will tell you the difference between "probable" and "plausible." Cheers!

Michael

Deduction, induction, abduction

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.

The two examples it offers for inductive and abductive reasoning are:

Induction

96 per cent of the Flemish college students speak both Dutch and French.
Louise is a Flemish college student.
Hence, Louise speaks both Dutch and French.

Abduction

You may have observed many gray elephants and no non-gray ones, and infer from this that all elephants are gray, because that would provide the best explanation for why you have observed so many gray elephants and no non-gray ones.

In the case of abduction the conclusion is inferred as the best explanation for the premise, whereas this isn't the case for induction (you wouldn't say that Louise speaking both Dutch and French is the best explanation for why 96 percent of Flemish college students speak both Dutch and French).

A Christian Philosophy

↪aletheist

Thanks anyways!

aletheist

↪Michael

:up:

↪Samuel Lacrampe

Note that in @Michael's examples, it is probable (96% chance based on available data about a random sample of Flemish college students) that Louise speaks both Dutch and French, while it is merely plausible (no known counterexamples yet) that all elephants are grey.

A Christian Philosophy

↪Michael

Hello.
That is indeed one of the descriptions I found, as described in the OP. But 2 things to notice.

(1) This description of induction is not compatible with other descriptions above such as here and here. (Not a criticism; just an observation).

(2) It seems like induction is very much deduction, but with a small extra leap. In your example, the reasoning would be deduction if the conclusion was written as "Hence, Louise probably (96%) speaks both Dutch and French". The small extra leap is to assume it is the case if we really had to choose.

So could we generalize and say induction is just choosing the outcome that has been deduced as most probable? It would seem odd to rank such as statement as a type of reasoning.

A Christian Philosophy

↪aletheist

So 'probable' is 'plausible' but with numbers involved.

Note that, as described previously, it seems that Michael's description of induction is not compatible with yours, because it is not evaluating a hypothesis.

What is the main difference between Inductive and Abductive Reasoning?

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