Undistributed Middle: A Logical Fallacy

Undistributed Middle: Etymology, Literal and Conceptual Meanings

Etymology/Term:

The term “Undistributed Middle” originated in the field of logic and is associated with a fallacy in deductive reasoning. The term can be traced back to the mid-19th century and has its roots in formal logic and syllogistic reasoning.

Literal Meaning:

• The undistributed middle refers to a logical fallacy where the middle term in a categorical syllogism is not distributed to both premises.
• In a syllogism, the middle term is the one shared by the major and minor premises. When this term is not properly distributed, it can lead to faulty conclusions.

Conceptual Meaning:

• The undistributed middle fallacy occurs when the middle term, which connects the major and minor premises, fails to establish a connection between the two.
• It results in an invalid syllogism, as the conclusion drawn does not necessarily follow logically from the premises.
• The conceptual essence of the undistributed middle fallacy lies in the failure to adequately connect the terms in a way that ensures a sound and valid argument.

Undistributed Middle: Definition as a Rhetorical Device

The undistributed middle, as a rhetorical device, involves the misleading use of shared characteristics to create a false connection between disparate ideas or groups. It occurs when a speaker implies a commonality between two subjects by focusing on a trait they share, yet fails to demonstrate a direct relationship. This device aims to manipulate perceptions by exploiting superficial similarities without establishing a valid logical link.

Undistributed Middle: Types and Examples

Type	Description	Example
Superficial Similarity	Attributes or characteristics are shared, creating a deceptive connection without logical support.	All cats have whiskers. My car has whiskers (antennas). Therefore, my car is a cat.
Association Fallacy	Linking two subjects based on shared traits, implying a connection without addressing relevant factors.	People who like ice cream are generally happy. Mary likes ice cream. Therefore, Mary must be a happy person.
Ambiguous Language	The middle term is used in an ambiguous way, allowing for multiple interpretations and confusion.	Dogs are known for loyalty. This book is loyal to its theme. Therefore, this book is a dog.

These examples illustrate different manifestations of the undistributed middle fallacy, where the shared characteristics are insufficient to establish a valid logical connection between the subjects involved.

Undistributed Middle: Examples in Everyday Life

1. Coffee and Tea Fallacy:
   • Premise 1: Coffee wakes you up.
   • Premise 2: Tea wakes you up.
   • Conclusion: Therefore, coffee is tea.
2. Car and Bicycle Fallacy:
   • Premise 1: Cars have wheels.
   • Premise 2: Bicycles have wheels.
   • Conclusion: Therefore, cars are bicycles.
3. Vegetarian and Vegan Fallacy:
   • Premise 1: Vegetarians eat plants.
   • Premise 2: Vegans eat plants.
   • Conclusion: Therefore, vegetarians are vegans.
4. Book and Movie Fallacy:
   • Premise 1: Books tell stories.
   • Premise 2: Movies tell stories.
   • Conclusion: Therefore, books are movies.
5. Summer and Winter Fallacy:
   • Premise 1: Summer is hot.
   • Premise 2: Winter is hot (indoors with heating).
   • Conclusion: Therefore, summer is winter.
6. Language and Communication Fallacy:
   • Premise 1: English is a language.
   • Premise 2: Sign language is a language.
   • Conclusion: Therefore, English is sign language.
7. Fruit and Vegetable Fallacy:
   • Premise 1: Fruits are sweet.
   • Premise 2: Desserts are sweet.
   • Conclusion: Therefore, fruits are desserts.
8. Watermelon and Water Fallacy:
   • Premise 1: Watermelons contain water.
   • Premise 2: Water bottles contain water.
   • Conclusion: Therefore, watermelons are water bottles.
9. Dog and Cat Fallacy:
   • Premise 1: Dogs have tails.
   • Premise 2: Cats have tails.
   • Conclusion: Therefore, dogs are cats.
10. Bus and Plane Fallacy:
    • Premise 1: Buses transport people.
    • Premise 2: Planes transport people.
    • Conclusion: Therefore, buses are planes.

Undistributed Middle in Literature: Suggested Readings

1. Aristotle. On Rhetoric: A Theory of Civic Discourse. Translated by George A. Kennedy, Oxford UP, 2007.
2. Booth, Wayne C., Gregory G. Colomb, and Joseph M. Williams. The Craft of Research. 4th ed., University of Chicago Press, 2016.
3. Graff, Gerald, and Cathy Birkenstein. They Say/I Say: The Moves That Matter in Academic Writing. 3rd ed., W. W. Norton & Company, 2014.
4. Heinrichs, Jay. Thank You for Arguing: What Aristotle, Lincoln, and Homer Simpson Can Teach Us About the Art of Persuasion. 3rd ed., Three Rivers Press, 2017.
5. Lanham, Richard A. A Handlist of Rhetorical Terms. 2nd ed., University of California Press, 1991.
6. Lunsford, Andrea A., John J. Ruszkiewicz, and Keith Walters. Everything’s an Argument with Readings. 8th ed., Bedford/St. Martin’s, 2019.
7. Perelman, Chaim, and Lucie Olbrechts-Tyteca. The New Rhetoric: A Treatise on Argumentation. Translated by John Wilkinson and Purcell Weaver, University of Notre Dame Press, 1969.
8. Strunk, William, and E. B. White. The Elements of Style. 4th ed., Pearson, 1999.