Talk:Abductive reasoning

Example on inductive reasoning actually a case of abductive reasoning

From the current article:

For example, if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. (Indeed, it turns out that some swans are black.)

From https://plato.stanford.edu/entries/abduction/:

The mere fact that an inference is based on statistical data is not enough to classify it as an inductive one. 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.

Which source is correct, and how can the adequate revisions be made, if necessary? 81.2.179.53 (talk) 18:48, 10 April 2024 (UTC)

I don't think the characterisation of induction as inferring a general principle from a body of knowledge is correct (in general) or useful in distinguishing induction from abduction (in fact, it seems to be counterproductive). This claim is found in both the Induction section, and the introduction. Both of these should IMHO be removed from the article.

The example now given for induction (inducing that a specific elephant is gray from a statistical claim on the population of all elephants) doesn't meet this characterisation, while the non-example you mention does.

The article you link is very helpful, particularly this excerpt:

"It suggests that 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. (I emphasize “only,” because in abduction there may also be an appeal to frequencies or statistics, as the example about the elephants exhibits.)"

The second paragraph of the Induction section at least largely agrees with this.

But, note also that the Stanford article makes it clear that it's not universally agreed that inductive and abductive are mutually exclusive ("Harman (1965) conceives induction as a special type of abduction"). This is maybe worth a mention (particularly since the longer quote above does imply inductive logic is often incorporated into an abductive argument in any case).lukeuser (talk) 19:10, 22 September 2024 (UTC)

Reference for Set-cover abduction formalization section

There is a section in the article on the formalization of set-cover abduction. However, there is no reference provided for this. I am searching for the original paper that first proposed the set-cover formalization described in that section. Does anyone know what that paper is? Cerebrality (talk) 05:05, 5 December 2024 (UTC)

We should remove Mastermind, but what to replace it with?

Mastermind is used in this article as a paradigmatic example of abductive reasoning. It seems to me that this is erroneous.

The Mastermind provides information that necessarily closes off parts of the solution space. The player literally deducts solutions from that space. At any given stage, it's not possible to assign relative likelihoods of different possible solutions. There is only enough information to deduce which solutions are possible and which are not, never any information that would permit the player to pick one possible explanation as being best among all those possible. I am no logician, but the article says, "Abduction is then the process that picks out some member of E," and Mastermind just doesn't work that way. Meanwhile, the idea of using a game to illustrate inference to the best explanation was a very good one. Pictures can make the article more engaging, and it would be great to use a paradigmatic example. A game would do very well in this role, but Mastermind does not meet the brief. Are there other games that would do?

Let's brainstorm what kinds of pictures we could use.

Games:

• Sort of pictorial mystery game, something along the lines of, what's happening in this picture?
• Many strategy games ask each player to make some guess about the opponent's strategy, e.g. Stratego.

Non-game examples might be taken from the history of science or criminal investigations.

In any case, unless I'm mistaken and Mastermind is abductive, it cannot remain in the article. So, whether or not I/we find a better picture, I'll remove it. I'll wait a few weeks to provide an opportunity for alternative views to be heard. Flies 1 (talk) 19:59, 6 February 2025 (UTC)

I agree that mastermind may not the best example. However, it formally fits into the explanation of Abductive_reasoning#Logic-based_abduction, with O the observed b/w summaries, T the rules of how to compute a summary in general, and E a set of secret color combinations that would explain O. The simplicity requirement could e.g. include to accept only a singleton set for E. Prior probabilities could be discrete uniform distribution; or, less trivial, take into account some known color preference of the oppenent who chose the secret colors (e.g. it might be known that he likes green, so the bottommost guess in the picture would have a lower prior probability than the one above it). I'd oppose your opinion that mastermind uses deduction: in mastermind, E is not a logical consequence of O, but, vice versa, O is a consequence of E and T, which perfectly matches the 3rd formula line in Abductive_reasoning#Logic-based_abduction ($T\cup E\models O$).

Before adding the mastermind picture, I, too, thought about real-life examples (like yours: scientific experiments, criminology). However, coming up with a formalized theory T is difficult in criminology, while no plausible prior probabilities can be assigned to physics theories (for example, to explain the results of the Michelson-Morley experiment, Einstein considered a first version of his relativity theory - what whould be the numerical value of its prior probability?). In a game, usually all aspects are formalized, and the reader can compare our explanations of T, O, and E to the game description. I'm aware of 2 games about criminology, viz. Scotland Yard (board game) and Sherlock Holmes: Consulting Detective (gamebook), but didn't think in detail about how to use them as an example here (Sherlock Holmes isn't sufficiently formalized, I guess). In your examples, what would be the prior probabilities in Stratego, or/and what would be the background theory T in a pictorial mystery game? - Jochen Burghardt (talk) 11:27, 7 February 2025 (UTC)