There's logic behind that inference

Deductive reasoning: conclusion guaranteed

Deductive reasoning starts with the assertion of a general rule and proceeds from there to a guaranteed specific conclusion. Deductive reasoning moves from the general rule to the specific application: In deductive reasoning, if the original assertions are true, then the conclusion must also be true. For example, math is deductive:

• If x = 4
• And if y = 1
• Then 2x + y = 9

In this example, it is a logical necessity that 2x + y equals 9; 2x + y must equal 9. As a matter of fact, formal, symbolic logic uses a language that looks rather like the math equality above, complete with its own operators and syntax. But a deductive syllogism (think of it as a plain-English version of a math equality) can be expressed in ordinary language:

In the syllogism above, the first two statements, the propositions or premises, lead logically to the third statement, the conclusion. Here is another example:

• A video streaming technology ought to be funded if it has been used successfully to educate adults.

• Hybrid open classrooms are being used to educate adults successfully in more than 70 new educational environments.

• Hybrid (sunchronous and asynchronous) classrooms and video streaming technology should be funded.

The conclusion to fund both classrooms and technology follows the truth of the success of both treatments to educate adults successfully.

Here is an example of a false conclusion reached through a correct deductive process.

• There is no such thing as drought in the midwest.

• North Dakota is in the mid-West.

• North Dakota does not have to plan for a drought.

In the example above, though the inferential process itself is valid, the conclusion is false because the premise is questionable, thus this deduction cannot guarantee a necessary true conclusion,

Some might argue that there is no new knowledge through logical deduction. Their idea is that if conclusions contain the terms of the premise, then there is nothing new in the conclusion. This is a view held for example by John Stuart Mill

Assuming the propositions are sound, the rather stern logic of deductive reasoning can give you absolutely certain conclusions. However, deductive reasoning cannot really increase human knowledge (it is nonampliative) because the conclusions yielded by deductive reasoning are tautologies-statements that are contained within the premises and virtually self-evident. Therefore, while with deductive reasoning we can make observations and expand implications, we cannot make predictions about future or otherwise non-observed phenomena.

Inductive reasoning: conclusion merely likely

Inductive reasoning begins with observations that are specific and limited in scope, and proceeds to a generalized conclusion that is likely, but not certain, in light of accumulated evidence. You could say that inductive reasoning moves from the specific to the general. Much scientific research is carried out by the inductive method: gathering evidence, seeking patterns, and forming a hypothesis or theory to explain what is seen.

Conclusions reached by the inductive method are not logical necessities: no amount of inductive evidence guarantees the conclusion. This is because there is no way to know that all the possible evidence has been gathered, and that there exists no further bit of unobserved evidence that might invalidate the hypothesis. Thus, while the newspapers might report the conclusions of scientific research as absolutes, scientific literature itself uses more cautious language, the language of inductively reached, probable conclusions.

Because inductive conclusions are not logical necessities, inductive arguments are not simply true. Rather, they are cogent: that is, the evidence seems complete, relevant, and generally convincing, and the conclusion is therefore probably true. Nor are inductive arguments simply false; rather, they are not cogent.

It is an important difference from deductive reasoning that, while inductive reasoning cannot yield an absolutely certain conclusion, it can actually increase human knowledge (it is ampliative). It can make predictions about future events or as-yet unobserved phenomena.

For example, Albert Einstein observed the movement of a pocket compass when he was five years old and became fascinated with the idea that something invisible in the space around the compass needle was causing it to move. This observation, combined with additional observations (of moving trains, for example) and the results of logical and mathematical tools (deduction), resulted in a rule that fit his observations and could predict events that were as yet unobserved.

Abductive reasoning: taking your best shot

Abductive reasoning begins with whatever information you have on hand. When you reason this way you take that information and abduce (from the Latin aducere to lead from) a probable explanation. The problem is that our information is nearly always incomplete. It might be not only incomplete but also not very credible.

Example of abduction reasoning include medical diagnoses, identification of assailants, the success of a never before seen product in a completely new and unknown market, the validity of any test results when test reported are bribed.

• Given a result (I have a high fever, focus groups would buy the product, test results are better than ever), and

• set of symptoms, observations from a focus group, test results

• is an application of abductive reasoning: given this set of symptoms, what is the diagnosis that would best explain most of them? Likewise, when jurors hear evidence in a criminal case, they must consider whether the prosecution or the defense has the best explanation to cover all the points of evidence. While there may be no certainty about their verdict, since there may exist additional evidence that was not admitted in the case, they make their best guess based on what they know.

While cogent inductive reasoning requires that the evidence that might shed light on the subject be fairly complete, whether positive or negative, abductive reasoning is characterized by lack of completeness, either in the evidence, or in the explanation, or both. A patient may be unconscious or fail to report every symptom, for example, resulting in incomplete evidence, or a doctor may arrive at a diagnosis that fails to explain several of the symptoms. Still, he must reach the best diagnosis he can.

The abductive process can be creative, intuitive, even revolutionary. Einstein’s work, for example, was not just inductive and deductive, but involved a creative leap of imagination and visualization that scarcely seemed warranted by the mere observation of moving trains and falling elevators. In fact, so much of Einstein’s work was done as a “thought experiment” (for he never experimentally dropped elevators), that some of his peers discredited it as too fanciful. Nevertheless, he appears to have been right. For example, his remarkable conclusions about space-time continue to be verified.