Syllogism

The Basic Idea

Syllogisms are a type of logical reasoning often used in philosophical arguments. Logical reasoning involves abstract thinking: you approach a problem by organizing a series of steps (called premises) into a particular order

Syllogisms are the most common way of arranging premises into a good argument. A syllogism is a form of deductive argument where the conclusion follows from the truth of two (or more) premises. A deductive argument moves from the general to the specific and opposes inductive arguments that move from the specific to the general:1

  1. All mammals are animals.
  2. Camels are mammals.
  3. Therefore, camels are animals.

As long as premise one and premise two are true, then the conclusion must also be true. If mammals are animals, and camels are mammals; there is no way camels aren’t animals!

Usually, syllogisms have three-parts – two premises and a conclusion – although “syllogism” is sometimes used to refer to any deductive argument.

The first premise is called the “major premise;” the second premise is called the “minor premise.” Universal syllogisms, like the one above, use all-encompassing words, such as ‘all’, or ‘only’. Particular syllogisms, on the other hand, are only about some things: 2

  1. No humans are immortal.
  2. Some organisms are immortal.
  3. Therefore, some organisms aren’t humans.

However, we must remember that only when both premises are true can the argument be sound. A syllogism may state that all birds can fly, penguins are birds, and therefore, penguins can fly. Though the argument is logically valid, it includes a false premise (all birds can fly), making the argument unsound.

A syllogism is valid (or logical) when its conclusion follows from its premises. A syllogism is true when it makes accurate claims – that is, when the information it contains is consistent with the facts. To be sound, a syllogism must be both valid and true. However, a syllogism may be valid without being true or true without being valid.

– Professors of English Laurie J. Kirszner and Stephen R. Mandell in their grammar and composition exercise textbook, The Concise Wadsworth Handbook3

Key Terms

Logic: an abstract form of thinking that uses step-by-step inferences to arrive at a conclusion.

Deductive Reasoning: reasoning where the truth of the premises guarantees the truth of the conclusion:1

  1. All humans are mortal.
  2. Socrates is a human.
  3. Therefore, Socrates is mortal.

These kinds of arguments are justified based on how they’re arranged, rather than from any particular experiences. They are most commonly used in philosophy.

Inductive Reasoning: reasoning where the conclusion is not guaranteed by the truth of the premises:

  1. In the past, eating peanuts did not cause me to have an allergic reaction.
  2. Therefore, in the future, I will not have an allergic reaction to peanuts.

Unlike deductive arguments, the conclusion can be false even if the premises are true. (You could develop a peanut allergy later in life.) Inductive reasoning usually relies on experience and is most commonly used in science.1

Major Premise: a premise that is general or universal.4

Minor Premise: a premise that is about a particular instance of the major premise4

Syllogistic Fallacy: a fallacy is a mistake in logic. A syllogistic fallacy is a fallacy in a deductive argument, where the conclusion does not follow from the premises:

  1. No behavioral scientists are sharks.
  2. Sharks are not mammals.
  3. Therefore, no behavioral scientists are mammals.

The premises (as far as we know) are true; but the conclusion is clearly false. Since this is a deductive argument, it suffers from a syllogistic fallacy.

Enthymemes: arguments that function in a similar way to syllogisms, but at least one premise is implicit. It is assumed that the audience knows that the implicit premise is true.2 For example:

  1. All humans are mortal.
  2. Therefore, Aristotle is mortal.

The implicit premise is that Aristotle is a human.

Valid: A deductive argument is said to be valid if it is impossible for the conclusion to be false if the premises are true. If the conclusion logically follows the premises, the syllogism is valid. A syllogism can be valid but not sound:

  1. All birds can fly.
  2. Penguins are birds.
  3. Therefore, penguins can fly.

If the premises were true, the conclusion would be true. But since premise 1 is false, the argument is not sound.

Sound: A deductive argument is sound when it is valid and its premises are true:

  1. All humans are mortal.
  2. Socrates is a human.
  3. Socrates is mortal.

The conclusion follows from the premises, and each of the premises is true, so the argument is sound.

Reductio ad impossibile: A way to check an argument’s validity. If denying the conclusion but accepting the premises would be contradictory, then the argument is valid.

History

Aristotle, an ancient Greek philosopher, was one of the first to discuss syllogisms. In Prior Analytics, published around 350 BCE, Aristotle outlined the basic form of syllogism which represented the earliest branch of formal logic.6 For Aristotle, logic revolved around deduction: “speech in which certain things having been supposed something different from those supposed results of necessity because of their being so.” 7

If that sounds confusing – that’s ancient philosophy for you! Let’s break it down. “The things that have been supposed” are what we now call “premises.” “What results necessarily” from those premises being true is a conclusion.7

To Aristotle, if an argument was valid, it would be impossible for premises X and Y to be true and for conclusion Z to be false. Aristotle named this method of proving validity “reductio ad impossibile”: a syllogism is valid when the denial of the conclusion but acceptance of the premises would lead to a contradiction.8

Aristotle divided syllogistic propositions into four different categories: universal affirmative, particular affirmative, universal negative and particular negative.

A universal affirmative syllogistic sentence: All humans need food.

A particular affirmative syllogistic sentence: Some birds can fly.

A universal negative syllogistic sentence: No dogs are cats.

A particular negative syllogistic sentence: Not all cars have four doors. 10

During the rise of modern formal logic, German philosopher Gottlob Frege refined Aristotle’s syllogistic theory through the addition of non-categorical syllogisms. These are syllogisms that rely on premises and can be hypothetical, or which include disjunctions like ‘or’. The hypothetical form of syllogisms can be traced back to Stoic philosophy, but modern philosophers tend to attribute the theory to Frege. In the 19th century, British philosopher and economist John Neville Keynes also helped make non-categorical syllogisms popular.6

[To learn more about stoicism, check out our thinker profile on Seneca, one of the most well-known stoic philosophers.]

Here’s an example of a hypothetical syllogism:

  1. If it is sunny tomorrow, I can go running.
  2. It is sunny.
  3. Therefore, I can go running.

Here’s an example of a disjunctive syllogism:

  1. Patrick studies English or Linguistics.
  2. Patrick is not studying Linguistics.
  3. Therefore, he is studying English.

Another contributor to Aristotle’s system was Gottlob Frege. In the Begriffsschrift (German for “Concept-Script”), he refined Aristotle’s system by developing a logical system that explained how quantifiers (words like “all” and “some”) work.16,17 His system also became the basis for much modern computer science.18

Consequences

It has been argued that syllogisms are the strongest form of argument because they are truth-preserving: if the premises are true, and the syllogism is valid, the conclusion is undeniably true. To reject the argument, we need to either show that the syllogism is invalid or falsify one of the premises.

Usually, the premises are generally agreed upon, so syllogisms help clarify points that, while obvious, don’t have a justification.

There is evidence that syllogisms are understood across different cultures and languages. A study conducted by anthropologist James Hamill showed that speakers of Mende, English, Ojibwa and Navajo all were able to form valid syllogisms; and they agreed on which kinds of arguments were valid.12

Syllogisms can be a great starting point when making a complex argument. They help set out the basic principles and get everyone on board with basic assumptions. Polarizing views can limit discussion around controversial topics; it can feel impossible to speak to someone who strongly opposes your views. This is where syllogisms come in: they help establish or clarify common ground before you tackle more complex issues.

For example, if you want to argue that nurses deserve to have the COVID-19 vaccine first, you might start the argument with the following syllogism:

  1. All nurses work on the frontline against COVID-19.
  2. All people who work on the frontline against COVID-19 should get priority of access to the vaccine.
  3. Therefore, nurses should get the first priority of available vaccines.13

Your opponent would have to reject one of your premises if they wanted to disagree with your conclusion, which requires more thought than a knee-jerk disagreement.

Although syllogisms are usually only used in philosophy and formal logic because they can be quite pedantic (imagine deductively proving that your kids should eat their vegetables!), they can be useful thought exercises – even if they’re only for you! They can help you to evaluate an argument and see if your conclusion is valid or sound. 11

Controversies

There are two common ways a syllogism might go wrong. Sometimes, the syllogism might simply be invalid:

  1. Behavioral scientists conduct experiments.
  2. Bill conducts experiments.
  3. Therefore, Bill is a behavioral scientist.

Although premise one and two are both true, the conclusion could be false–Bill could be a physicist. For the argument to be valid, the first premise would have to say “Only behavioral scientists conduct experiments.”

Another common mistake is simply assuming that one of the premises is true when it is not:

  1. All mammals live on land.
  2. Whales are mammals.
  3. Therefore, whales live on land.

While intuitive, premise one is false – whales are mammals, but they live in water. The syllogism remains valid, because the conclusion does follow from the premises; but it is not sound, since one of its premises is false.

Additionally, even if syllogisms are sound, they aren’t always that useful. Since the conclusion has to logically follow the premises, we don’t really learn anything new from them. To justify our argument, we usually need to go beyond why claims are logically sound – that is why scientific inquiry uses experiments so that we can obtain novel knowledge.

Shakespearean Syllogisms

The great writer and poet William Shakespeare was a big fan of syllogisms, and his plays are often cited as examples of syllogistic logic.

In Timon of Athens, a lesser-known play, the main character Timon uses a syllogism to explain why he has forgotten his chief steward:

Flavius: Have you forgot me, sir?

Timon: Why dost ask that? I have forgot all men; then, if thou grant’st thou’rt a man, I have forgot thee. 2

In The Merchant of Venice, Portia must choose between suitors her father has picked for her to marry. The test she gives her suitors is to correctly guess which of three caskets (a gold, a silver, and a leader) contains a portrait of her. One of her suitors uses an invalid syllogism when he reads on the gold casket, “who chooseth me shall gain what many men desire:”

  1. All men desire Portia.
  2. Many men desire what is in the chest;
  3. Therefore what is in the chest is (the portrait of Portia).

Portia’s suitor falsely equated ‘all’ to ‘many’. All men might desire Portia, but they also desire other things.2

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Sources

  1. IEP Staff. (n.d.). Deductive and Inductive Arguments. Internet Encyclopedia of Philosophy. Retrieved June 20, 2021, from https://iep.utm.edu/ded-ind/
  2. Syllogism. (n.d.). LitCharts. Retrieved June 20, 2021, from https://www.litcharts.com/literary-devices-and-terms/syllogism
  3. Nordquist, R. (2021, February 16). Definition and Examples of Syllogisms. ThoughtCo. https://www.thoughtco.com/syllogism-logic-and-rhetoric-1692167
  4. FORMAL LOGICAL STRUCTURE REVIEW. (n.d.). Humboldt State University. Retrieved June 20, 2021, from https://www2.humboldt.edu/act/HTML/tests/logic/review.html
  5. Syllogistic Fallacies. (n.d.). Logical Fallacies. Retrieved June 20, 2021, from https://www.logicalfallacies.org/syllogistic-fallacies.html
  6. Syllogism. (1998, July). Encyclopedia Britannica. https://www.britannica.com/topic/syllogism
  7. Aristotle’s Logic. (2000, March 18). Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/aristotle-logic/#SubLogSyl
  8. Ekthesis. (1998, July 20). Encyclopedia Britannica. https://www.britannica.com/topic/ekthesis
  9. Categorical proposition. (n.d.). New World Encyclopedia. Retrieved June 20, 2021, from https://www.newworldencyclopedia.org/entry/Categorical_proposition
  10. Medieval Theories of the Syllogism. (2004, February 2). Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/medieval-syllogism/#ArabLogiSyll
  11. Syllogism. (2019, March 29). Philosophy Terms. Retrieved June 20, 2021, from https://philosophyterms.com/syllogism/
  12. Hamill, J. F. (1979). Syllogistic reasoning and taxonomic semantics. Journal of Anthropological Research, 35(4), 481-494. https://doi.org/10.1086/jar.35.4.3629543
  13. Kearns, A. J. (2020). The principle of salvage in the context of COVID‐19. Nursing Inquiry, 28(1). https://doi.org/10.1111/nin.12389
  14. Distribution. (1998, July 20). Encyclopedia Britannica. https://www.britannica.com/topic/distribution-logic
  15. Examples of Syllogism. (n.d.). Your Dictionary. Retrieved June 20, 2021, from https://examples.yourdictionary.com/examples-of-syllogism.html
  16. Zalta, E. N. (2020). Gottlob Frege. In E. N. Zalta (Ed.),The Stanford encyclopedia of philosophy (Fall 2020). Metaphysics Research Lab, Stanford University
  17. Frege, G. (1997). Begriffsschrift: A Formula Language of Pure Thought Modelled on That of Arithmetic. In M. Beany (Ed.), The Frege Reader (pp. 47–78). Blackwell Publishing.
  18. Gillies, D. (2002). Logicism and the Development of Computer Science. In A. C. Kakas & F. Sadri (Eds.), Computational Logic: Logic Programming and Beyond (Vol. 2408, pp. 588–604). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-45632-5_23

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