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Syllogism: Deducing True Conclusions

Introduction

Little Jane really wants a puppy. More specifically, she wants a yellow puppy. Her parents agree to adopt a golden retriever puppy named Rusty. When she hears the good news, Jane asks her dad Carson, “Is Rusty yellow?” Carson answers, “Of course. All golden retrievers are yellow, and Rusty is a golden retriever.”

Explanation

Carson is using a form of reasoning called syllogism to explain to Jane why her new puppy is yellow. He starts with a general piece of information: the fact that all golden retrievers are yellow. Next, he makes a claim about Rusty the puppy: Rusty is a golden retriever. These two facts reveal something important about Rusty’s nature. As long as it is true that all golden retrievers are yellow and Rusty is a golden retriever, then it necessarily follows that Rusty is yellow.

Definition of Syllogism

Syllogisms are a form of deductive reasoning that typically starts with a major premise about a general topic. Next, it adds a minor premise about a particular thing. These two premises work to conclude a property of the particular thing. 

How It Works

An argument is valid when the conclusion must be true if both the premises are true. Since all golden retrievers are yellow and Rusty is a golden retriever, Rusty must be yellow. However, a syllogism can be valid and still have a false conclusion. This happens when the premises are not true. Consider a slightly different example. Imagine that Rusty is not a golden retriever but a poodle. Again, Jane asks Carson, “Is Rusty yellow?” Carson answers, “Of course. All poodles are yellow, and Rusty is a poodle.” Jane and Carson are in for a surprise. Rusty is actually black. Although Carson’s syllogism is a valid argument, it is not sound. A sound argument is a valid argument with all true premises. In this case, the premise that all poodles are yellow is false, making Carson’s argument unsound.

Note that Carson still had a valid syllogism. An argument can be valid without all its premises being factually true. If all poodles were yellow, he would have reached an accurate conclusion. However, even factual premises do not guarantee a correct final assertion. Consider this argument: All strawberries are red. This apple is red. Therefore, this apple is a strawberry. This argument looks like a valid syllogism. It has a major and minor premise with recurring terms. However, it is an invalid argument, meaning it is possible for the premises to be true and the conclusion false. Here, both the premises are factual, but the conclusion is evidently wrong. This type of argument where both the major and minor premises have matching predicates is called a syllogistic fallacy.

Syllogistic fallacies are harder to spot when they happen to have true conclusions. Consider this: All US presidents have been men. Obama is a man, so he was a US president. This syllogism is invalid. Although the premises and conclusion are individually true, the premises do not logically lead to the conclusion. Obama being a man does not prove that he was a US president. For a syllogism to be valid, the truth of its premises must necessitate the truth of its conclusion.

Applying It

Syllogisms are common in both logic and literature. It is a familiar argument and can be useful for persuasion and explanation. However, be on the lookout for syllogistic fallacies in both your arguments and others’. If you are ever confused about whether a syllogism is valid, it is helpful to formalize the premises and conclusion in order to analyze the logic. It may be useful to switch some of the subjects to clarify a syllogism’s invalidity, being careful to retain the same form. Many syllogistic fallacies are easy to spot, but others can be more difficult when you know less about the topic being discussed. When this is the case, it is important to do extra research to make sure the facts are correct.

Think Further

  1. Can you think of an example from literature or philosophy that uses syllogism?
  2. Why would you want to use a syllogism in your writing?
  3. Why might you be persuaded by an invalid syllogism?

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Learn More

  1. Nordquist, Richard. “Definition and Examples of Syllogisms.” Thought Co., 23 June 2019. https://www.thoughtco.com/syllogism-logic-and-rhetoric-1692167.
  2. PhilHelper. “A Crash Course in Formal Logic Pt 6a: Categorical Syllogisms, Terms, Mood and Figure.” Youtube, 14 July 2013. https://www.youtube.com/watch?v=KcNESCrkIiQ.
  3. Stangroom, Jeremy. “Valid or Invalid? – Six Rules for the Validity of Syllogisms.” Philosophy Experiments, 2020. https://www.philosophyexperiments.com/validorinvalid/Default5.aspx.