In academic writing, deduction, induction and abduction can be read as modes of argumentation:
- deduction: finding data to support an argument.
- induction: finding an argument to explain some data;
- abduction: supplying a warrant that enables us to move from data to argument.
The first is the best in practice: outline an argument based on what you already know about the topic, then research to fill in the gaps (= active reading). This mode cuts down the amount of reading you have to do — and allows your voice to remain strongest in your writing.
The second is the most common — but less effective: research the topic, then come up with an argument based on your research (= reactive writing). This mode is problematic because you can easily get bogged down in over-reading — and your voice can easily be drowned out by others’.
The third deepens your critique: get clear about the assumptions that underlie — or condition — your argument (= active writing). To do so is to problematize — even defamiliarize (or alienate!) — your argument, which will make your voice more distinctive . . . given that these assumptions go unquestioned in most arguments.
The modes in detail . . .
The terms “Fact,” “Rule” and “Case” are medieval nicknames for the propositions that would be called the “conclusion” (C), “major premise” (MP) and “minor premise” (mp) respectively, in the simplest form of deductive syllogism.
- rule, law, major premise (MP)
- case, cause, minor premise (mp)
- fact, effect, conclusion
Thus, we have the following scheme:
Deduction takes a Case, a mp of the form X => Y,
matches it with a Rule, a MP of the form Y => Z,
then adverts to a Fact, a C of the form X => Z.
- All bachelors are unmarried males. Rule/MP
- Hank Moody is a bachelor. Case/mp
- Hank Moody is an unmarried male. Fact/conc.
Deduction allows deriving b as a consequence of a (deriving the consequences of what is assumed).
= applying a law, i.e., finding data to support an argument.
Induction takes a Case of the form X => Y,
matches it with a Fact of the form X => Z,
then adverts to a Rule of the form Y => Z.
- 90% of humans are right-handed.
- Joe is a human.
- Joe is probably right-handed.
Argument from analogy
- Joe is tall, skinny and athletic.
- Hank is tall and skinny.
- Hank is possibly also athletic.
Induction allows inferring a from multiple instantiations of b when a entails b (inferring probable antecedents as a result of observing multiple consequents).
= inferring a law, i.e., finding an argument to explain some data.
Abduction takes a Fact of the form X => Z,
matches it with a Rule of the form Y => Z,
then adverts to a Case of the form X => Y.
- The lawn is wet.
- If it rained last night, then the lawn would be wet.
- It rained last night.
Abduction allows inferring a as an explanation of b (inferring the precondition a from the consequence b).
= assuming a law, i.e., supplying a warrant that enables us to move from our data to our argument (i.e., a hypothesis, a warrant or backing, a condition).
Even more succinctly . . .
N.B. A fourth type is retroduction, which is “reasoning from consequent to [hypothetical] antecedent.” Peirce sometimes calls it “Hypothetic Inference.” It “depends on our hope, sooner or later, to guess at the conditions under which a given kind of phenomenon will present itself.” This is a legitimate use of the fallacy of post hoc ergo propter hoc, a.k.a. affirming the consequent.
 C. S. Peirce, “A Neglected Argument for the Reality of God” , CP 6.469-70.
 C. S. Peirce, Letter to F. A. Woods , CP 8.385-88.