Logic is reasoning that is used to make valid statements about a conclusion. There are two basic types of reasoning: deductive and inductive.

Deductive reasoning uses facts, or premises, to arrive at a conclusion. A syllogism is an example of deductive reasoning. A syllogism is made up of three premises. The first two premises, which are assumed to be true, each share a term with the third statement. For example:

All mammals have eyes. Humans are mammals. Therefore, humans have eyes.

The third statement shares the term “eyes” with the first statement and it also shares the term “humans” with the second statement.

In research, the conclusion is a new specific fact that is derived from the general theory. Deductive reasoning is considered “top-down” in that it moves from a general premise to specific facts that are derived from the general premise. In the syllogism given above, the major premise describes all mammals; it is the general rule. The next premise states a narrower case from which it can be deduced that humans have eyes.

Sound deductive reasoning always leads to conclusions that are true.

Inductive reasoning works in the opposite direction. Inductive reasoning moves from the specific to the general. It is the process of creating a conclusion based on observations, patterns, and hypotheses. In exploratory data analysis, we are often using inductive reasoning. We sample a population, study the sample, and then make inferences that we believe will be true for the entire population. These inferences can then lead to a hypothesis. That hypothesis would then need to be confirmed by using deductive reasoning.

To avoid making an inference that is not logical, be sure that your sample actually represents the population to which you are applying your conclusions. When asked the question, “What are you touching?” blindfolded people touching different parts of an elephant will report different conclusions.

Inductive arguments should be very clear about the underlying assumptions in the data. For example, in the following series of numbers, what is the next number?

6, 13, 20, 27…

If you said 34, then your underlying assumption is that the data is a simple series of numbers which increases by increments of seven, with no end. However, what if the numbers represent dates? If that is your underlying assumption, then you may not know the next number. Is the month 30 days long, 31 days long, 28 or 29 days long? In this case, there is no month with 34 days, so that cannot be the next number.

Because inductive reasoning tends be exploratory and based in observation, even the most precise inductive reasoning can lead to false conclusions. This is not a flaw of inductive reasoning. Both types of reasoning have their value. Inductive reasoning can lead to the development of hypotheses that require proof through deductive reasoning.

Regardless of whether you are using deductive or inductive reasoning to tell your story, clearly describe the data that is necessary to support your logic. In addition, state any possible caveats or limitations to the truth of your conclusions. This will help your audience to avoid fallacious conclusions and provide them with the information that they require to make decisions.

A fallacy in your reasoning means that your conclusion is not justified by the premise of your argument. This can occur because of several reasons:

• Your argument might not apply a rule of logic.

• Your argument might leave out or misinterpret a crucial premise that would invalidate your conclusion.

• Your conclusion might not follow logically from the premises.

There are two types of logical fallacy:

• Formal fallacy – One or more of the premises can be shown to be false. For example, the following argument is formally fallacious:

If milk is kept in the refrigerator, it will not spoil. The milk is spoiled. Therefore, the milk was not kept in the refrigerator.

The first premise can be shown to be not true. Milk kept in a refrigerator can still spoil.

• Informal fallacy – The premises do not adequately support the conclusion. For example, the following argument is a burden of proof informal fallacy:

Humberto: Some people have psychic powers.

Alexei: Can you prove it?

Humberto: No one has been able to disprove it.

Humberto is obligated to provide evidence for his premise. However, he fallaciously switches the burden of proof to Alexei to disprove Humberto’s claim.

When telling your story, make sure that the evidence of your supporting proposition does not suffer from a logical fallacy. Click here and here for fallacy examples.