Reasoning About Reasoning


Disagreement flourishes in today’s conversations and captions. Whether a lengthy and healthy exchange or a short and summary epitaph, no end to provocative and polarizing rhetoric is in view. Knowledge has never been more abundant or accessible1 – consensus suffers neither of these alliterated accolades. My high school mathematics teacher opined throughout my many classes with him that “the problem with common sense is that it isn’t.” He lamented the lack of shared sensibility and reasoning required for civility and consensus.

While debate and disagreement cannot be claimed as a twenty-first-century phenomenon, the fact that both have proliferated through social media platforms and social gospel priorities is equally undeniable. People around the globe are inspired or offended at the click of a mouse. 
To paraphrase and modernize the words penned by James, the half-brother of Jesus, “Even so the (mouse) is a little member and boasts great things. Behold, how great a matter a little (click) kindles!”2 This short essay introduces a path forward in these contentious times to be productive in disagreement and reach the elusive acquisition of truth and not merely the hoarding of facts. By looking at three classic types of reasoning, the battle lines of conversation can be softened without compromising the firm lines of truth.

Deductive Reasoning – A favorite of every mathematician, this reasoning starts with established evidence and firm facts. While facts can produce emotional responses that should matter to all, the facts themselves are unemotional. At the time of writing this, over 2.7 million cases of COVID-19 are reported worldwide. Sadness and loss are a necessary companion to this fact, and this author extends his condolence to those who have personally been touched by this pandemic. The statistic itself lacks energy or empathy, it is simply a fact. From a fact, or facts, the student relies on laws of logic or rules of reasoning to reach a fresh conclusion from the given information, thereby proving a new fact which is as accurate as the original given information. The argument is deemed valid or invalid based on its review by scholars. Such reasoning is used to prove the Pythagorean (Gougu) Theorem or the value of the sum of the angles of a polygon with n sides. Where the reasoning is sound, the result is certain, and the presenter can confidently declare Quod Erat Demonstradum.3 The Law of the Syllogism4 is one familiar form of deductive reasoning. Every spider has eight legs. Horatio is a spider. Therefore, Horatio has eight legs. Closely related to this is the Law of Detachment.5 To assail the argument requires the antagonist to prove (at least some of) the given information false or to prove the reasoning faulty – false information or faulty reasoning. And while this is a popular method of reasoning among mathematicians, few of today’s hotly debated issues in theology, philosophy or policy lend themselves to this sort of thinking. Nobody debates a mathematics formula that is proven.

Inductive Reasoning – A far more common method to reach a conclusion, inductive reasoning relies on several examples to reach a generalized conclusion. After measuring and recording the three angles of several triangles, the student notices that for each triangle the sum of the three angles is roughly one hundred eighty (180o) degrees. From this observation, the student concludes that for any triangle, the sum of the measures of the three angles must be 180o. If this is based on one or two examples, the antagonist will conclude that this is a weak argument. The more examples that support the conclusion, the stronger the argument. The antagonist can check the results as well. Even one counterexample – one instance where the measurements refute the conclusion – is sufficient to discredit the conclusion. In today’s conversation this sort of reasoning is signaled by sentences which begin with the phrases “Yeah but …” or “What about …” bringing in an anecdote that does not align with the conclusion. In a complex world of opposing experiences, viewpoints, cultures and priorities, such evidence is abundant. Furthermore, “You cannot possibly know what I …” or “Come back when you have walked a mile in my shoes …” can undermine the effectiveness of any inductive argument. For example, when travelling in an unfamiliar city with low fuel and an even emptier stomach, the familiar arches can make a cranky car-full of children so happy. Based on the experience at other similar restaurants, they conclude this to be a suitable and satisfactory place to eat, although none have ever been to this particular restaurant before. And many readers are audibly groaning as they realize the franchise referred to above and remember a personal experience that screams “Run away!” in an audible voice. This reasoning produces lots of debate as it is subject to personal emotion and experiences as well as a well-delivered counterexample.

Abductive Reasoning – Sherlock Holmes (a favorite read of mine when I was younger) said, “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” This illustrates a third type of reasoning with which the reader may be less familiar. A list of all possible known conclusions is reviewed, and the one most likely among them is selected. Note that there is no guarantee that the correct conclusion is included in the list of possible conclusions, a point reinforced by opponents of this sort of reasoning. “A Holmesian fallacy (also Sherlock Holmes fallacy or process of elimination fallacy) is a logical fallacy that occurs when some explanation is believed to be true on the basis that alternate explanations are impossible, yet not all alternate explanations have been ruled out.”6 And while the objection is technically relevant and where absurd examples abound, abductive reasoning is a useful approach to many disputes. To understand an absurd use of abductive reasoning, imagine a teacher asking the students in the class for the value of 2+2. One student says 3, another 6 and still a third says ½. No other options are forthcoming and so the question is asked, “Among 3, 6 and ½, which is the most likely?” One student eliminates 3 since we know that the addition of two even numbers must produce an even result. Another student eliminates the fraction labelling it not possible. A third student confidently concludes, “Given the three possibilities, 6 is the most reasonable.” Abductive reasoning results in a conclusion that is “plausible,” “most likely” or “best available.” Abductive reasoning avoids the hard evaluations of its two predecessors where the argument is valid or invalid (deductive) or strong or weak (inductive) and allows the interlocuters to reach a best available or posited conclusion. Furthermore, it promotes and even requires further research, information, study, and consideration. It lends respect to the person whose opinion is different while insisting on the existence of a correct answer. The harsh rhetoric of right/wrong, informed/ignorant or logical/emotional is replaced by a commitment to pursue knowledge and confirm truth.

Does this solve today’s difficult issues? – hardly. A recognition of the type of reasoning better equips the student to challenge another’s conclusions and to defend their own. Furthermore, the language of confrontation is softened while scholarship and conversation are better served. Do you agree? What is your personal experience with arguments and debates?


1 “Ever learning, and never able to come to the knowledge of the truth.” – 2 Timothy 3:7

2 James 3:5 – sort of!

3 Often abbreviated Q.E.D. this Latin phrase literally means “that which was to be shown.”

4 All A is x. B is an A. Therefore B is x.

5 A B; B C; therefore A C