Structural fallacies result in invalid and therefore unsound deductive arguments.

Structural fallacies are arguments that are not valid even if the premises are true. There are many structural fallacies that can result in invalid deductive arguments (Cederblom and Paulsen, 2011). However, three fallacies that are particularly common or important are:

1) Irrelevant Premise(s) ("non sequitur"): Premises not related to conclusions, leading to an invalid argument. For example:

PREMISE: Prominent climate scientists tried to suppress evidence contradicting the theory of anthropogenic climate change.

CONCLUSION: Climate change is not occurring.

EXPLANATION: In 2009, a controversy (later termed "Climategate") ensued after hackers stole emails from the Climatic Research Unit at the University of East Anglia (for more explanation, see Skeptical Science). The emails were selectively released to create the appearance that climate researchers were manipulating data and suppressing evidence. However, a full review of the emails showed that there was no fraud or scientific misconduct. Therefore, the premise of the argument was untrue.

However, even if the premise HAD BEEN true, the argument would still NOT be sound. Why?

The reason why the truth of the premise that scientists falsified data has no bearing on the soundness of the conclusion that climate change is occurring is because the argument is a non sequitur. Although the premises may seem to be related, the behavior of climate scientists has no influence whatsoever on whether anthropogenic climate change is occurring or not. The climate is changing whether or not scientists act ethically. Therefore, arguments about climate change based on the behavior of individual scientists are not valid.

APPLICATION: Many logical fallacies are, in a general sense, non sequiturs if the fallacies involve premises that do not relate to conclusions (Cederblom and Paulsen, 2011). Therefore, it is important to make sure that premises strongly relate to conclusions.

2) Circular Reasoning ("begging the question"): The conclusion is defined in the premises. For example,

PREMISE: X implies Y: If successful people all achieved high S.A.T. scores, then the S.A.T. test predicts success .

PREMISE: Assume X Success is going to a top university that only selects students with high S.A.T. scores.

CONCLUSION: Conclude Y The S.A.T. test predicts success.

EXPLANATION: Circular reasoning can take many forms. However, circular arguments often involve the conclusion being a re-statement of one of the premises, or one of the premises defining the conclusion to be true. In the previous argument, success is defined as having high S.A.T. scores. Therefore, the conclusion that S.A.T. scores predict success is a meaningless re-statement of the premise. Circular arguments are not valid.

APPLICATION: We often know the conclusion before we begin to formally present an argument. However, we must be careful to prevent the conclusion from influencing our premises.

3) Affirming the Consequent. Affirming the Consequent involves arguments of the form:

PREMISE: If P then C If people smoke, they get lung cancer.

PREMISE: We observe C My grandfather died of lung cancer.

CONCLUSION: We conclude P My grandfather smoked.

(Layman, 2005). What is "Affirming the Consequent?" Why is the argument about smoking and cancer a fallacy?

EXPLANATION: In science, affirming the Consequent is often a fallacy because many causes can result in the same effects. In the example of smoking, there are many risk factors for lung cancer (e.g. asbestos, pollution, genetics, etc.) in addition to smoking (Akhtar and Bansal, 2017). Therefore, getting lung cancer does NOT prove that someone smoked. Arguments that "Affirm the Consequent" are not valid.

Affirming the Consequent is arguably the most important deductive fallacy for science.

Affirming the Consequent seems very similar to the most important valid argument for science: modus tollens. However, Affirming the Consequent and modus tollens differ in one key respect: whether the argument seeks to "prove" or reject the prediction made in the first premise. Rejecting a prediction can be valid, whereas "proving" a prediction is a deductive fallacy.

Affirming the Consequent is therefore important for at least three important reasons:

A) Impossibility of "proving" hypotheses. Affirming the Consequent is one reason that we cannot "prove" hypotheses. Hypotheses are explanations of natural phenomena that lead to testable predictions. We test hypotheses empirically by comparing the predictions of the hypotheses to data that we experimentally measure. We could construct the following syllogism:

PREMISE: Hypothesis H1 leads logically to prediction P1.

PREMISE: Experimental data match prediction P1.

CONCLUSION: We have proven hypothesis H1.

However, the syllogism is a deductive fallacy because it Affirms the Consequent! Even if the data match the predictions of a hypothesis exactly, there could still be some other phenomenon that actually explains the data. It could simply be a coincidence that hypothesis H1 makes a prediction that matches the data. Therefore, we can never experimentally "prove" hypotheses.

B) Affirming the consequent also prevents us from using inductive reasoning to "prove" hypotheses. Please refer to the inductive reasoning section for additional explanation.

C) Correlation does not imply causation. People are inclined to engage in "narrative fallacy," consistently seeking to connect even unrelated events with meaning or causality (Taleb, 2010). However, even when two events are actually correlated with each other, the correlation does NOT mean that one event causes the other to happen. There are an infinite number of spurious correlations that happen to be true by chance. For example, any variable that steadily increases with time will be correlated to the expansion of the universe. However, to our knowledge, the expansion of the universe does not cause most phenomena that steadily increase with time.

"Correlation does not imply correlation" is an example of Affirming the Consequent! We could consider the syllogism:

PREMISE: If phenomenon C1 causes event E1, then C1 and E1 will be correlated.

PREMISE: C1 and E1 are correlated.

CONCLUSION: Therefore, C1 causes E1.

The syllogism has the form of Affirming the Consequent. Therefore, correlation does not imply causation.

APPLICATION: Many logical fallacies can make deductive arguments invalid. Importantly, the logical fallacy of Affirming the Consequent prevents experimental research from "proving" hypotheses or inferring causation simply from correlation. Therefore, to test hypotheses using deductive reasoning, scientists must reject hypotheses using modus tollens.