Reasoning

There are three basic ways of gaining information about the world: inductive reasoning, deductive reasoning, and abductive reasoning.


 * 1) Inductive reasoning starts by looking at information and trying to figure out the causes.
 * 2) Deductive reasoning takes starting assumptions and derives things from them.
 * 3) Abductive reasoning occurs when someone attempts to find which explanation is the right one for a known fact. Abduction is usually based on showing "concomitance", i.e. any type of similarity or co-occurrence, in space and time.

Abductive reasoning
Abductive reasoning involves Occam's razor where observations are made, and one tries to find the simplest — and therefore most likely cause. Hence, it is often referred to as Inference to the best explanation. It is more similar to induction than deduction.

Examples

 * Two friends frequently go jogging together. They have a major argument, and therefore a falling out. However, the next week, you see them jogging together again, and assume they made up.
 * Observing a billiard game and seeing the 'eight' ball moving towards us, and abducing that the cue struck the ball.

Usefulness
Abductive reasoning pervades our thinking and everyday reasoning. Often, we are given information that is incomplete, yet want to form quick conclusions about possible causes or courses of action. Abductive reasoning allows us to take this incomplete information and determine the most likely cause. Without it, we would be unable to act based on the information provided unless it were absolute, which isn't possible much of the time (since we are not omnipresent or omniscient, unlike someone we know).

The problem? It's logically fallacious. Indeed. Technically it is affirming the consequent, or, if you want a fancy Latin phrase, post hoc ergo propter hoc. Here's the logical form for the second example given:

"If the cue strikes the eight ball, it will move towards us." (this is reasonable) "The eight ball is moving towards us..." (okay, nothing wrong yet) "...therefore the cue struck the eight ball." (yikes!)

By abducing that the cue struck the ball, and thus caused its movement towards us, we are able to make sense of the incomplete information (we only saw the ball rolling in our direction, not what first moved it), but affirm the consequent in doing so because there are multiple inputs (or causes of movement) or the single output (the eight ball moving). For example, someone could have flicked it with their finger.

Abduction can be useful. Just be careful with it when working with more complex scenarios.

Inductive reasoning
Inductive reasoning is a means of gaining information about reality by starting with results, outcomes, or effects, and then inferring the causes.

Examples

 * Experimental science obtains data and evaluates competing hypotheses or explanations for how the data came about.
 * Medicine uses symptoms presented by patients to diagnose disease.
 * Any logical process of the form "If outcome Y, then possible cause(s) X".

Medicine is a good example of how induction differs from deduction. In diagnostic medicine, patients generally do not walk into hospitals and say, "I have disease X. Please tell me what symptoms Y I should have." If they did, doctors could always reason deductively to find the symptoms Y for disease X. (Recall that "if X, then Y" is deduction.) Instead, patients say "I have symptoms Y.  What disease X do I have?"

Usefulness
Inductive reasoning has the advantage of being flexible, and has the ability to evaluate competing hypotheses even when information incompatible with the known causes or hypotheses is observed.

The disadvantage of induction is that absolute truth and objectivity are compromised. Outcomes Y could have several different causes X. For instance, a patient may exhibit a sore throat, a runny nose, a rash, and splenomegaly. There may be several different diseases that cause those symptoms (e.g., acute retroviral syndrome or mononucleosis); the hard task of figuring out which one to diagnose is the reason doctors make big bucks. Furthermore, the diagnosis of one doctor may not be the same as another (although only one of them may be correct); hence, there is a subjective component to induction and the need for the use of evidence.

David Hume argued that inductive reasoning cannot be rationally justified at all, and that whenever we make inductive inferences, we rely on the 'uniformity of nature', the assumption that the Universe is uniform and does not change. Though it can be argued that while conclusions through induction aren't certain, they are probable and can measure likelihood.

Deductive reasoning
Deductive reasoning occurs when you are inferring an observable fact from general principles. Scientists usually do this in order to test whether the general principles are true.

Before the advent of inductive reasoning in science, knowledge was mainly gained in the more abstract deductive reasoning, which begins with assumptions, axioms, or hypotheses, and then makes derivations from them. This is still used in mathematics, logic, and philosophy, and up to around the 17th century, in the sciences (hence things like "natural philosophy", i.e., physical sciences).

Usefulness
Deductive reasoning has the advantages of certainty and objectivity. The statement "If X, then Y" guarantees that Y is true when X is true, regardless of belief. The question then becomes "Is X true?", which is likely to be challenged for near anything.

As mentioned above, deduction depends on X being true or false, or more generally speaking, making assumptions. Those assumptions can be challenged and found to be biased or even incorrect, which causes the deductive argument to return a false conclusion. In addition, deduction is not as flexible as abduction or induction due to its reliance on a priori reasoning.