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Inductive reasoning moves from the specific to the general. Beginning with the evidence of specific facts, observations, or experiences, it moves to a general conclusion. Inductive conclusions are considered either reliable or unreliable instead of true or false. An inductive conclusion indicates probability, the degree to which the conclusion is likely to be true. Inductive reasoning is based on a sampling of facts. An inductive concluson is held to be reliable or unreliable in relation to the quantity and the quality of the evidence supporting it. Induction leads to new truths and can support statements about the unknown on the basis of what is known." (Wilson, Forensic Procedures for Boundary and Title Investigation, p. 51.)

Slothful induction" probably isn't the best phrase to describe what is the failure to see or concede the most likely inference from the evidence. The failure to infer is rarely due to laziness. It demonstrates an unwillingness to follow the evidence wherever it may lead due to stupidity, dogma, or vested interests. Usually it is a red flag that someone is not principally interested in the truth of a matter. And, because inductive arguments are at best probabilistic, not definitive, someone can always hold out against the preponderance of evidence. Nevertheless, there are times when it is appropriate to resist the inference of even a good inductive argument, namely, when there are countervailing reasons that support the contrary conclusion. For example, when new evidence appears against a well-established scientific theory, it can be appropriate to retain it until the evidence to the contrary is sufficiently strong. In such cases an ad hoc hypothesis may be introduced to explain how the established thesis may still be true in spite of the implications of this new inductive evidence.

An explanation is a form of reasoning which attempts to answer the question "why?" For example, it is with an explanation that we answer questions such as, "Why is the sky blue?" Explanation can be based on a scientific theory, on agency, or purpose (teleology). In this case, the explanation of why the sky is blue might begin in terms of the composition of the sky and theories of reflection. Of course, blue, as we commonly refer to it, does not refer to a wavelength of light but to that color we see in our mind's eye (qualia) when we look at the sky, a blueberry, or iodine. And the phenomenelogical answer to why the sky appears blue to our minds will be of a different sort. If one is open to the idea that the universe was created or designed for a purpose or with intentionality, one might also venture an answer in terms of teological or aesthetics.

An explanation is intended to explain why some phenomenon happens. In this case, there is evidence that the phenomenon occurred, but it is trumped up, biased or ad hoc evidence.

An explanation is intended to explain who some phenomenon happens. The explanation is fallacious if the phenomenon does not actually happen or if there is no evidence that it does happen.

The theory advanced to explain why some phenomen occurs cannot be tested. We test a theory by means of its predictions. For example, a theory may predict that light bends under certain conditions, or that a liquid will change colour if sprayed with acid, or that a psychotic person will respond badly to particular stimuli. If the predicted event fails to occur, then this is evidence against the theory. A thoery cannot be tested when it makes no predictions. It is also untestable when it predicts events which would occur whether or not the theory were true.

The theory doesn't explain anything other than the phenomenon it explains.

Theories explain phenomena by appealing to some underlying cause or phenomena. Theories which do not appeal to an underlying cause, and instead simply appeal to membership in a category, commit the fallacy of limited depth.

Propositions and their truth values are two elemental ingredients of logical reasoning.

A proposition is an assertion that something is the case. We use sentences to express propositions. A sentence may be made of black ink, be on a page, and be four inches long. But the content of the sentence cannot be found on the page. The proposition it expresses appears to be a non-physical entity which can be in the mind.

A proposition can have the following truth values: true or false. "P" is true if and only if P. "P" is false if and only if not P. In other words, a proposition is true if and only if what it says about the world is in fact the way the world is. Though this correspondence view of truth has long been questioned, and especially so in these postmodern times, it remains our common sense, everyday understanding of truth.

A logical operator joins two propositions to form a new, complex, proposition. (If you have not read about propositions, you should do so now. Follow the Next links until you return to this page.) The truth value of the new proposition is determined by the truth values of the two propositions being joined and by the operator that joins them.

Any two propositions P and Q can be conjoined, producing the new, complex, proposition:

P and Q

The proposition P and Q is true if and only if both P and Q are true. It is false otherwise.

Any two propositions P and Q can be disjoined, producing the new, complex, proposition:

P or Q

The proposition P and Q is true if and only if either P or Q are true. It is false only if both P and Q are false.

Any two propositions P and Q can be joined by a conditional operator, producing the new, complex, proposition:

If P then Q

The proposition If P then Q is true if and only if either P is false or Q is true. It is false only when P is true and Q is false.

Any proposition P can be converted into its negation with a negation operator, producing the new, complex, proposition:

Not P

The proposition Not P is true if and only if P is false. It is false only if P is true. The truth table for Not P is as follows:

Any two propositions P and Q can be joined with the biconditional operator, producing the new, complex, proposition:

P if and only if Q

The proposition P if and only if Q is true if and only if both P and Q are true, or if both P and Q are false. It is false only when one of them is true and the other false.

Each of these fallacies is characterized by the illegitimate use of a logical operator in order to distract the reader from the apparent falsity of a certain proposition. The following fallacies are fallacies of distraction:

A limited number of options (usually two) is given, while in reality there are more options. A false dilemma is an illegitimate use of the "or" operator. Putting issues or opinions into "black or white" terms is a common instance of this fallacy. "The fallacy of false dilemma is committed when an argument limits consideration of positions on an issue to two mutally exclusive ones, thereby setting up an apparent dilemma, when there are other positions that could be offered." (Bowell & Kemp, Critical Thinking, p. 164)

Also called argumentum ad ignorantiam, arguments of this form assume that since something has not been proven false, it is therefore true. Conversely, such an argument may assume that since something has not been proven true, it is therefore false. (This is a special case of a false dilemma, since it assumes that all propositions must either be known to be true or known to be false.) Other phrases often employed here, are "lack of proof is not proof"; "absence of evidence is not evidence of absence"; "the lack-of-knowledge inference"; and, "negative proof" or "negative evidence".