Skill: Logical Reasoning
Key Skill: The ability to draw logical conclusions based on facts, statements, or arguments and to identify the strengths and weaknesses of those arguments.
Figure 1: Image generated using Copilot from prompt: "Image of Logic".
We just looked at how questions like ‘what, where, when, who, and why’ can help us to evaluate the information sources that we may use. But what if you want to evaluate the strength, or the validity, of the arguments that authors make? What if you want to evaluate the arguments that ‘you’ make?
Some of you may be familiar with the fictional detective Sherlock Holmes, and you may be familiar with his famous catchphrase ‘I deduce’. But what is deduction? Well, deductive reasoning involves drawing valid conclusions from a series of facts (premises) (Hanscomb, 2023, p. 117). This guide is not part of a formal logic course so it will not explore this expansive topic further, but the core message should be clear: draw your conclusions upon facts that you believe to be true. However, in the story entitled The Boscombe Valley Mystery, Sherlock Holmes also said that ‘there is nothing more deceptive than an obvious fact’ (Conan Doyle, 1892, p. 83). You may not be a fan of Sherlock Holmes, but this quotation highlights the importance of verifying the ‘truth’ of facts and their importance for the formation of a valid conclusion.
Develop@Derby’s guidance on academic writing explores how you can formulate your own arguments to reach conclusions that are evidence based. But it is all too easy to make arguments and provide facts in ways that fall short of a high level of critical thinking. Critical thinking requires you to identify when you, or others, have failed to address the real target of investigation and have reached conclusions that are not valid (Brink-Budgen, 2010, p. 44). If you can identify when this happens, you will be well on the way to being a competent critical thinker in your written work and when you interact with others in your career.
Thinking about the ‘truth’ of people’s words
In the study of logic, as you have just seen, the validity of an argument is connected to the truth of an argument’s premises and the conclusions that you draw from them. But this way of thinking about arguments is not confined to logical definitions: it is fundamentally connected to critical thinking (Hadley and Boon, 2023, p. 18). It is important to be able to identify when logical reasoning and arguments fail, either through nefarious deceit or, more commonly, from innocent human error. Unfortunately, this can happen so often—for example in politics (Goffredo et al. (2022), in everyday interactions, and in academic writing (Hadley and Boon, 2023, p. 21)—that the term ‘logical fallacies’ exists to describe how this can happen. Here are some famous logical fallacies, but you can find many resources—and many more examples about the topic—online.
Ad hominem – attacking the character of a person (Pirie, 2015, p. 122)
Figure 2: Image generated using Copilot from prompt: "Image of Ad Hominem".
Argument: John Plato is an academic who writes about the effects of climate change. In his most recent book, he argues that more charging stations for electric cars would improve the environment and protect wildlife.
Ad hominem response: Richard Kant argues that John Plato cannot be taken seriously because he so fanatical about the natural world; therefore, further exploration is needed before reaching a conclusion about the effects of electric cars on the environment.
Explanation: In this example, Richard Kant’s ad hominem response rejects the argument that Plato is presenting because they do not like John Plato’s passion for the natural world. They ignore completely what John Plato has to say about the subject under investigation. When thinking critically, it is very important to ensure that we do not fall into the trap of rejecting someone else’s opinion or position just because we do not like them or some traits of their character.
Red herring – distracting from the argument (Hanscomb, 2023, p. 243)
Figure 3: Image generated using Copilot from prompt: "Image of Red Herring".
Argument: Richard Kant is the head of a major plastic production company. He is in a debate with the environmentalist John Plato. John Plato accuses Richard Kant of not doing enough to stop plastic waste in the world’s oceans.
Red herring response: Richard Kant responds that he has spent millions of pounds on green energy at his production plants.
Explanation: Richard Kant’s response, whilst laudable, completely ignores John Plato’s question. It is designed to distract from the problem of ocean plastic waste—for which one might assume that he has no solution.
Straw man – misrepresenting another’s position (Bassham et al. 2023, p. 132)
Figure 4: Image generated using Copilot from prompt: "Image of simple Straw Man".
Argument: John Plato has written a journal article that explores the link between negative TV news stories and increased depression in viewers. In this article, John Plato does not suggest that TV news should stop showing negative news stories, but he does call for a greater understanding of their effects on the mental health of society.
Straw man response: Richard Kant writes in his own journal article that John Plato is deeply flawed because Plato argues that only positive and happy stories should be reported on TV news.
Explanation: The straw man response misrepresents John Plato’s argument to prevent any discussion about what John Plato believes. John Plato does not suggest that TV news should stop reporting stories that are negative (see also Pirie, 2015, p. 193). The straw man response is clever because it does refer to John Plato—giving the appearance of critical engagement—but it has deliberately misrepresented what John Plato says.
Time for some mathematics
Logical reasoning is not just confined to some clever word play. Critical thinking can sometimes involve questioning mathematical information. Let’s look at these fictitious headlines and TV adverts, which reveal just some of the ways that you will see statistics presented to you.
76% of people agreed that the product whitened their teeth
Percentages are useful, but unless you know the values that underlie them, you cannot see the full picture. The claim of this advert sounds impressive, but it means very little unless we know the size of the group of people (the sample).
If there are 50 people in the group, then some mathematics reveals that 38 people think the product whitens their teeth. Crucially, 12 people think that the product does not whiten their teeth. The claim is not that convincing simply because so few people constitute those who have actually used the product.
But if the sample size is 4000, then some mathematics reveals that 3000 people think the product whitens their teeth. 1000 people continue to believe that the product does not whiten their teeth, but 3000 people is perhaps more persuasive than 38 (see also Cottrell, 2013, p. 193).
Horror! The number of aggressive pet hamsters has doubled since last year
Figure 5: Image generated using Copilot from prompt: "Image of Aggressive Hamster".
This newspaper headline seems shocking, but we have no idea about how many aggressive pet hamsters there are. In 2024 there were apparently 600,000 pet hamsters in the UK (UK Pet Food, 2024). Let’s imagine that 2 hamsters were aggressive in 2024, which is 0.0003%. This fictitious headline—let’s imagine that it appears in 2025—claims that the number of aggressive hamsters has doubled, which sounds worrying. But only 4 hamsters are now aggressive. Let’s further imagine that 600,000 hamsters continue to exist, that would still mean only 0.0006% of hamsters are aggressive this year. The headline could also say Horror! The number of aggressive hamsters has risen. Again, this is true, but there is very little to worry about at this point—except maybe your fingers!
Alert! 100% increase in aggressive hamsters
Again, this headline sounds terrifying, but we know that the 100% increase only refers to an increase from 2 aggressive hamsters to 4 aggressive hamsters—and this is out of a population of 600,000. This example relates to much broader topics called absolute risk and relative risk—both of which are very common in healthcare. The following publication provides a good summary, and it will be of interest to those who want to dig a little deeper into statistics.
References
Bassham, G. et al. (2023) Critical Thinking: A Student’s Introduction. 7th edn. New York: McGraw Hill.
Brink-Budgen, R. van den (2010) Critical Thinking for Students: Learn the Skills of Analysing, Evaluating and Producing Arguments. 4th ed. Oxford: How To Books.
Conan Doyle, A. (1892) The Adventures of Sherlock Holmes. London: George Newnes.
Copilot (2025) Image of logic [Digital Art], response to Steven Bembridge, 4 February 2025.
Copilot (2025) Image of ad hominem [Digital Art], response to Steven Bembridge, 24 February 2025.
Copilot (2025) Image of red herring [Digital Art], response to Steven Bembridge, 24 February 2025.
Copilot (2025) Image of simple straw man [Digital Art], response to Naomi Bowers-Joseph, 3 April 2025.
Copilot (2025) Image of aggressive hamster [Digital Art], response to Steven Bembridge, 3 March 2025.
Goffredo, P., Haddadan, S., Vorakitphan, V., Cabrio, E. and Villata, S. (2022) ‘Fallacious Argument Classification in Political Debates,’ Thirty-First International Joint Conference on Artificial Intelligence, IJCAI-22. Vienna (Austria), Jul 2022, pp.4143-4149. Available at: http://dx.doi.org/10.4995/HEAD20.2020.11787
Hadley, G. and Boon, A. (2023) Critical Thinking. Abingdon, Oxon: Routledge.
Hanscomb, S. (2023) Critical Thinking: the Basics. Second edition. Abingdon, Oxon: Routledge.
Pirie, M. (2015) How to Win Every Argument: The Use and Abuse of Logic. 2nd edn. London: Bloomsbury.
UK Pet Food. (2024). Number of pet hamsters in the United Kingdom (UK) from 2011 to 2024 (in millions)*. Statista. Statista Inc.. Accessed: March 05, 2025. https://www-statista-com.derby.idm.oclc.org/statistics/515403/hamsters-population-in-the-united-kingdom-uk/