Induction, Deduction, and Abduction

When I first began studying philosophy, one of the most confusing terms floating around (at least for me) was induction and deduction. So the question is, what's the big difference anyway?

Induction
The term induction is widely used for the style of reasoning that takes us from empirical premises to empirical conclusions supported by the premises, but not deductively entailed by them.

Ah! See, this is why philosophy is so hard to get down. Already we have a peculiar new term, "entail."

Entailment is the relationship between a set of premises and conclusion when the conclusion follows from the premises, or may validly be inferred from the premises. (For more on entailment see relevance logics).

Now, before we talk about deduction and the difference from induction, I have to state that there are actually different forms of induction, as it is a formal process of reasoning. For instance, there is eliminative induction, enumerative induction, mathematical induction, and so on.

Induction isn't a perfect process. It can, on occasion  turn out incorrect inferences. One example, called the problem of induction, comes in the form of Goodman's paradox. It comes in the realization that we prefer certain uniformities over others, and will assume a specific uniformity holds true even when it isn't the case. 

For example, suppose that all examined sapphires we have ever discovered are all blue. Uniformity would lead us to expect that future sapphires will be blue as well. But some sapphires are pink. Some are blue. In other words, because our assumption of uniformity is wrong (revealing a probabilistic problem), then our conclusion is, in all probability, not correct even though the premise that sapphires are blue is still true (for a related problem see Hempel's paradox).

Deduction
Likewise, the process of reasoning by which a conclusion is drawn from a set of premises is called a deduction. Deductions are usually confined to cases in which the conclusion is supposed to follow from the premises, i.e. the inference is logically valid. Deduction makes up the bedrock of Classical Logic. 

Now, you all are probably familiar with Sherlock Holmes and his famous claim to utilize the methods of deduction to solve his cases. Actually, Sherlock Holme's methods were an exercise in abduction.

Another funny philosophy word! Abduction, first coined by the famed American Philosopher Charles Sanders Peirce, is a process of using evidence to reach a wider conclusion, as in inference to the best explanation. This is actually what modern forensics investigators do, based in part by the writings of Sir Arthur Conan Doyle. 

So with all these similar terms floating around, how does one keep them organized? Well, I found out the hard way (and still am) is that one simply has to become familiar with the terms, which means reading philosophy, and engaging in philosophical discussions.

Once you gain a general familiarity with the philosophical terminology, it becomes less confusing and things start to make a little more sense.

Summation
So, in summary: Induction is a form of reasoning which takes us from empirical premises to empirical conclusion with the realization that these connection need not be logically sound (they may be intuitive).

Deduction, then, is a type of reasoning which looks at sets of information, usually something written out using predicate calculus, and then derives (or deduces) a conclusion based on the logical process of testing to see if the logic between the premise and conclusion is sound.

Meanwhile, abduction is a process of using evidence to make conclusive predictions that, when all the improbable predictions are excluded, we are left with the inference to the best explanation. Science depends largely on abduction and abductive reasoning in how it tests evidence and uses information to make better (more precise) predictions.