How to learn the truth with statistics 

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Despite the bad faith use of these fallacies by politicians and companies, practicing and studying statistics and logic can aid in analyzing arguments.  Photo by Carlos Muza on Unsplash

Despite the bad faith use of these fallacies by politicians and companies, practicing and studying statistics and logic can aid in analyzing arguments. Photo by Carlos Muza on Unsplash

Arguments are sets of statements called premises followed by a conclusion. Arguments are used as a means of rationalizing decision making. It is incumbent upon the populace to evaluate arguments in such a manner as to prevent flawed reasoning from resulting in flawed decision making.  

In the west, logical analysis is often considered as the best method of determining the propriety of the conclusion of an argument, given true premises. Unfortunately, there are many intuitively compelling argument forms and rhetorical stratagems that fail to properly support the conclusion upon rigorous analysis. If these compelling but faulty forms are commonly encountered, they are collectively called fallacies and given specific names to create shortcuts in analysis through recognition of these fallacies. Despite the bad faith use of these fallacies by politicians and companies, practicing and studying statistics and logic can aid in analyzing arguments. 

Before the tricks that exploit intuition can be studied, a discussion of the acceptable methods of argumentation is required. Formal deductive logic is the study of how the form of an argument enables or fails to enable the conclusion to follow from the premises.  

Critically, formal logic is split into logical analysis and truth value analysis. Logical analysis attempts to determine if the arguments form requires the entailment of the conclusion from the premises. If the form fails to withstand the logical analysis, we call the argument invalid. The politician’s syllogism is a formal fallacy, popularly used for arguments regarding emotionally charged subject matter as it proposes action without evaluating whether the proposal actually solves the problem addressed.

Other formal fallacies include denying the antecedent, affirming the consequent and the fallacy of the four terms (also an informal fallacy). 


Probabilistic fallacies arise out of statistical innumeracy leading to faulty conclusions.  Photo by Stephen Dawson on Unsplash.

Probabilistic fallacies arise out of statistical innumeracy leading to faulty conclusions. Photo by Stephen Dawson on Unsplash.

Fallacies need not be restricted to deductive arguments but can also apply to inductive and abductive arguments. Inductive logic and abductive arguments both consist of an argument where the conclusion is more general than the premises but lacks the certainty of a deductive conclusion which does not engage in such generalizations. Induction is the logic of generalizing from observations to reasonable consequences of a generalized form of the observations. Abduction attempts to ascertain the explanation for the observations that requires the least unqualified assumptions. Due to the means in which humans experience the world, most arguments tend to be inductive or abductive. 

Famous inductive and abductive fallacies include probabilistic fallacies and abuse of induction when induction fails, such as assuming all swans are white from a single white swan or that the police must restore stolen items even if it is contraband.   

Probabilistic fallacies arise out of statistical innumeracy leading to faulty conclusions. Darell Huff, an American journalist, discusses common statistical tricks utilized to fool the public in his book “How to Lie with Statistics.”   

The best guard against such deceptions is an evaluation of the original data which produced the conclusion. An introductory logic or statistics course would hopefully impart the knowledge of the tricks utilized to deceive or mislead the statistically innumerate. However, knowledge of these tricks does not inculcate a reasoner from these fallacies, unless that knowledge is applied. However, without knowledge, it is impossible to defend against these fallacies. As such, to provide the requisite knowledge, I recommend making an introductory logic or statistics course mandatory for students in high school. 


As demonstrated by the Wason selection task, most people are unaware of proper logical forms.  Photo by Ruthson Zimmerman on Unsplash.

As demonstrated by the Wason selection task, most people are unaware of proper logical forms. Photo by Ruthson Zimmerman on Unsplash.

Furthermore, there are informal fallacies which distract from the analysis through irrelevant objections or personal attacks. These include the infamous slippery slope fallacy, nirvana fallacy, ad hominem, genetic fallacy, red herring, Gish gallop, argumentum ad populum and begging the question. Another extremely pernicious fallacy is the fallacy fallacy, where one argues that a conclusion is false due to the invalid argument used to support it. These all rely on specious claims and often involve attacking reputation or soundness rather than validity. All informal fallacies disregard the analysis and potential alternative arguments that could support the conclusion. 

Why do we commit such errors in reasoning? Firstly, as demonstrated by the Wason selection task, most people are unaware of proper logical forms. This test asks participants to select which “cards” would enable them to determine the truth of a given conditional rule. 75 to 80% of people fail to apply the valid form of material implication and instead follow intuitions about how to falsify the conditional.  

Psychologists Leda Cosmides and John Tooby argue that an overreliance on heuristics and specific problems explains these failures of logical reasoning. These heuristics may not generalize to other contexts, especially as natural languages have significant extra-logical components  that reasoners may have difficulty in decoupling from the arguments. Secondly, for many politicians, their proposals may not stand up to truth and logical analysis; therefore it is useful for such politicians to prevent such analysis from occurring . Even those with law degrees, which should inculcate a politician from these fallacies, does not ensure that a politician will not exploit the public’s lack of knowledge for political or commercial gain. If well-reasoned policy is not the goal of a politician, but rather personal or ideological success in enacting bills, the compelling nature of these faulty arguments would convince all but the most scrupulous politicians from indulging in these forms in order to persuade those who lack awareness of these fallacies. 

As one can see, fallacious arguments are common in political discourse. This can arise out of a lack of knowledge of these fallacies or a lack of will to apply such knowledge. The lack of knowledge is most likely rectified by requiring introductory logic and statistics courses for students. These courses may not succeed in preventing the use of such fallacies, but will resign such fallacies to a failure to apply knowledge of the fallacies or bad faith arguments.  

Disclaimer: The views and opinions expressed by individual writers in the opinion section do not reflect the views and opinions of The Daily Campus or other staff members. Only articles labeled “Editorial” are the official opinions of The Daily Campus.


 Jacob Ningen is a contributor for The Daily Campus. He can be reached via email at jacob.ningen@uconn.edu.

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