The basic definition of induction is to use the past to predict the future. For instance:
Premise A: Many Asians have small eyes
Premise B: I am Asian
Conclusion: I probably have small eyes
As it is a prediction, the conclusions of inductive argument are subjected to the ambiguity of probabilities – which is its core weakness.
Nonetheless, for both convenience and the scarcity of decisive premises, we often resort to inductive argument. This is often so when we are making small decisions everyday like what to eat and what movie to watch; in which you would simply just recall your experience with that sushi you ate from Sakae Sushi or the previous movie you watched which was directed by Steven Spielberg in order to make your decision.
This is also the case in court when there are no conclusive evidence, only circumstantial ones; which leads the court to consider inductive arguments and decide, based on the balance of probabilities, the result.
“When you have eliminated the impossible, whatever remains, however improbable, must be the truth.” -Sherlock Holmes
This species of argument runs counter-intuitively to both deductive and inductive argument because it draws its conclusion not straight from its premises; but rather from the premises that aren’t there – mathematically, (AUB)’
Abductive argument is a tedious process of ruling out possible explanations until you are left with the most plausible one given the evidence. For instance, as I might point out that this example is taken from CrashCourse video:
You and your roommate ate sushi last night.
You both wake up with violent stomach aches
Therefore you and your roommates probably ate some bad sushi
As you might have already noticed, abductive arguments are also subjected to the ambiguity of probability. As much as Holmes may say that the conclusion must be true, we do not often possess so much evidence to conclude that the resulting conclusion is absolute. We must always account for the omission of evidence that lies outside our knowledge. Such as when we want to conclude that sushi is the culprit, we would do well to find more evidence that suggests other causes of stomachache to reduce the margin of error; such that it becomes negligible. Or else the correlation does not equate to causation rebuttal is going to find you trouble some day.
It is here that I shall share a wisdom from Sherlock Holmes, in which by extension is from Sir Arthur Conan Doyle:
“It is a capital mistake to theorize before you have all the evidence. It biases the judgement.”