Basics of Argumentation: Logic

Thinking Clearly

Aristotle articulated the basics of logical argument thousands of years ago. He taught about the syllogism (a statement in formal logic) and the enthymeme (a syllogism in which we all assume some parts). Here's what a syllogism looks like:

  1. All men are mortal. (Major premise)
  2. Socrates is a man. (Minor premise)
  3. Therefore, Socrates is mortal. (Conclusion)

However, because all the men we usually encounter are mortal, we usually assume the major premise, so an enthymeme would say:

  1. Socrates is a man.
  2. Therefore, Socrates is mortal.

Many times logical problems arise because of sloppy thinking. Consider, for example, the following attempts at syllogisms:

  1. Grass dies.
  2. Men die.
  3. Therefore, men are grass.
  4. Analysis: OK—this uses biblical language, but the Bible was being poetic. It was setting up a metaphor. What's really wrong is that #1 is supposed to set up a category and #2 is supposed to say that its members are part of the category. Instead, this one sets up two parallel predicates.
  1. No fish are dogs.
  2. No dogs can fly.
  3. Therefore all fish can fly.
  4. Analysis: any valid forms of categorical syllogism that assert a negative premise must have a negative conclusion. We're really stuck with this one. No fish can fly? We haven't proven that one either. The best we can do is:
  5. All dogs are canines.
  6. No fish are dogs.
  7. Therefore no fish are canines.
  1. No mammals are fish.
  2. Some fish are not whales.
  3. Therefore, some whales are not mammals.
  4. Analysis: At least one premise of a given syllogism has to be affirmative.

There are a lot of different syllogistic fallacies. The main point of bringing them out here is to show you that "A therefore B" doesn't always work if the structure of the argument is faulty. Things seem to be going so well, and then you find someone asserting the ridiculous conclusion that all fish can fly.

Some Fallacies of Logical Argument

Hasty Generalization

Faulty Causality

Begging the Question*

*Note: In modern, non-careful speech, "begging the question" has come to mean "bringing it up for discussion." This technical definition (assuming that the point you are trying to prove is already proven) is completely different.


Non Sequitur

Red Herring

Faulty Analogy

Circular Reasoning

Either-Or Choice (False Dichotomy)

1. "Red Herring Fallacy — Definition and Examples." Fallacy in Logic, Accessed 24 June 2020.

2. Bush, George W. "President Bush Addresses the Nation." Washington Post, 20 Sept. 2001, Accessed 24 June 2020.

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Revised 6/24/20 • Page author: Curtis Allen • e-mail: