In formulating hypotheses and theories, scientists rely on various methods of evidence. Broadly speaking, three different methods can be distinguished, differing in particular in strength (the degree of certainty with which a theory is supported) and the type of explanation. These three methods are deduction, induction and abduction.
Deduction is by far the strongest method; this method of proof, if done correctly, is 100% for sure. If so, why would we use any other methods, you would say. Unfortunately, this method is hardly applicable within different disciplines for the preparation of new theories and explanations because it is based on derivations and not on empirical evidence.
Deduction is a method that comes from Logic, and is mainly used in Logic, Mathematics and Physics. It uses reasoning like it syllogism, whereby a conclusion is derived from a number of premises (or assumptions). Arguably the most famous example of a syllogism is the following:
All humans are mortal (premise 1)
Socrates is human (premise 2)
So: Socrates is mortal (conclusion)
For such arguments, if the premises are true, the conclusion must necessarily be true. So the reasoning is only as strong as its premises. Once we have general laws, we can deduce anything from them. The problem is, where do we derive these generally applicable laws? The answer is: from other generally applicable laws. We call the so-called 'most general laws', which can no longer be deduced from anything and are 'at the top' of the hierarchy, axioms or postulates. To be an example of axioms the postulates of Euclid which underlie Euclidean geometry.
Where deduction often goes from general statements to more specific statements, induction is the exact opposite. One tries to deduce general laws from various individual empirical observations. This method is by far the most common in the various scientific disciplines. Undoubtedly the most famous example of inductive reasoning is that of the white swans. Seventeenth-century biologists were convinced that all swans are white. After all, they reasoned:
The first swan is white;
the second swan is white;
... the nth swan is white;
So: all swans will be white.
This conclusion does not necessarily follow (as with deduction) from the foregoing, because it is conceivable that not all swans have actually been observed. This was ultimately the case: it turned out that there were indeed swans that were not white. So it is difficult to derive a general law from all previous observations. Yet this is done in most scientific disciplines, because otherwise it is virtually impossible to conduct science. It is important to always keep in mind that an observation can be made that rejects the generally applicable law obtained by induction. A nice example to illustrate this induction problem, the impossibility to derive a generally applicable law from a finite number of observations, is the Russell's chicken.
On a farm, a farmer had a number of chickens. These chickens agreed: their farmer was very benevolent. After all: every morning she heard the farmer coming and they got enough food from him to live on. The chickens knew no better than that this would continue every day. Until one day the farmer showed up again and the chickens were expecting their food again. But, you can already feel it coming, the farmer himself wanted a snack this time and decided to slaughter the chickens.
What we can learn from this example is that past performance is no guarantee for the future. The generally applicable laws that we have drawn up in various scientific disciplines have been extensively tested and verified, but nonetheless are still fallible. Within the philosophy of science there is therefore much discussion about the justification of the use of the inductive method. Because: although fallible, it does seem to work. Anyway, that too is of course an inductive reasoning ...
Abduction (inference to the best explanation)
Abduction or inference to the best explanation is not such a strong method, but is used in situations where the empirical evidence is limited. The best possible explanation is maintained as long as no evidence is found that rejects the explanation (theory). If evidence is found that conflicts with the statement, an alternative explanation will be devised that better matches the (new) evidence. Rejection is no shame with this method.
Abduction mainly occurs in scientific disciplines where empirical evidence is scarce, such as Archeology and Paleontology. An example from paleoanthropology are the various theories of Homo sapiens migration; There are several explanations as to how man has spread around the world, but there is too little evidence to give a definitive answer.