I had not heard the term abductive reasoning before, but recognised it as my own the moment it was explained. It is inferring the most likely answer or solution, rather than relying on deductive, mathematical-style proofs for everything. Some things do not have clear answers, or more exactly, whatever absolute answer they might have is not accessible to us. God either exists or he doesn't, but we are unable to prove this either way. People make their choice based on observing reality, thinking about it, and deciding which is the most likely.
Much interpretation of Scripture is like this, and it is an approach CS Lewis uses often. When a formal proof is available, it should win the day, and sometimes one should be attempted just to see how far one can go. We don't know what Jesus meant by the Beatitudes, but the words have meanings and taken as a batch they seem to point in a direction. Also, we can see some things that we can solidly conclude he did not mean. We at a much more distant point in both the first and last books of the Bible. People who try to reduce either book to proofs are the most likely to lead us astray.
In the wiki entry diagnosis is mentioned, another good instance of a problem that might have a right answer, but we do not have perfect knowledge about the body nor of all possible conditions. Clinicians therefore look at the data and choose what they believe is the most likely explanation for the data.
This comes up regularly at the Hall, where I usually frame it in terms of Aristotle's discussion of appropriate reasoning from the beginning of the Nicomachean Ethics (specifically EN 1.3).
"Our discussion will be adequate if it has as much clearness as the subject-matter admits of, for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts. Now fine and just actions, which political science investigates, admit of much variety and fluctuation of opinion, so that they may be thought to exist only by convention, and not by nature. And goods also give rise to a similar fluctuation because they bring harm to many people; for before now men have been undone by reason of their wealth, and others by reason of their courage. We must be content, then, in speaking of such subjects and with such premisses to indicate the truth roughly and in outline, and in speaking about things which are only for the most part true and with premisses of the same kind to reach conclusions that are no better. In the same spirit, therefore, should each type of statement be received; for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs."
That's what Aristotle says about it. Note that here the argument isn't that we do what you're calling 'abductive reasoning' because it's an inferior sort of reasoning, but we don't always have access to deductive proofs. Rather, the argument is that you would be foolish to look for deductive proofs in fields where they are not possible. It would be just as unwise to accept a deductive proof on a political question as it would be to accept a rhetorical argument as a solution to a mathematical question.
I have a whole talk I give about why this might be true. The short version is that I think that logical objects don't exist in the physical world (see the recent discussion of the Parmenides for example), and as such logical reasoning can't apply to the physical world. Rather, what we have instead is analogies: two things that are different are treated by us as more-or-less the same, so that we can reason about them as if in fact they were the same.
However, all analogies always break, because in fact the two different things are not the same. At some point, every analogy runs into that problem and breaks. So, the kind of reasoning we have to do in physical reality is analogical and probabilistic, as Aristotle says. We can do good work in deciding if the breaking point in our analogy is going to come before or after the conclusion we're hanging on the analogy, for example; we can try to construct better analogies by finding more-similar objects. What we can't do is reason from the Forms, as Plato had hoped to do, because the Forms (which are logical objects) don't exist as themselves in the physical world. Neither do other logical objects (e.g., mathematical objects like circles are only approximated; thus, handling an object as if it were a circle or a sphere is another kind of analogy).
God may be able to do better, but not us. Thus, for us, part of 'good thinking' is recognizing when we shouldn't even be aiming for deductive proofs or other sorts of strict logic. When we find someone claiming to engage in those things in spaces where those things are inappropriate, we should reject their arguments.
Grim: brilliant (because I’ve persuaded myself that what you’ve expressed so well reflects my own inchoate thoughts, which didn’t exist in actuality.)
Cardinal John Henry Newman had a word for the assertion of belief based on probability.....
It's in the Grammar of Assent. Not Twitter.
Why thank you, Galen.
The illative sense
Grim: What we can't do is reason from the Forms, as Plato had hoped to do, because the Forms (which are logical objects) don't exist as themselves in the physical world.
Perhaps we are misunderstanding your argument, but reasoning with abstractions is pervasive in the natural sciences.
grok, to understand intuitively; derived from the Martian.
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