Basics of Argumentation: Logic
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:
- All men are mortal. (Major premise)
- Socrates is a man. (Minor premise)
- 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:
- Socrates is a man.
- Therefore, Socrates is mortal.
Many times logical problems arise because of sloppy thinking. Consider, for example, the following attempts at syllogisms:
- Grass dies.
- Men die.
- Therefore, men are grass.
- 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.
- No fish are dogs.
- No dogs can fly.
- Therefore all fish can fly.
- 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:
- All dogs are canines.
- No fish are dogs.
- Therefore no fish are canines.
- No mammals are fish.
- Some fish are not whales.
- Therefore, some whales are not mammals.
- 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
- Definition: A conclusion based on inadequate evidence.
- Example: "I got sick after the first time I ate at Joe's Diner. Their food is always bad."
- Confusing sequence with cause: "My child swallowed a dime, then got measles; therefore dime-swallowing causes measles."
- Confusing coincidence with cause: "Gays are becoming very visible in the public space; America's marriages are falling apart; therefore gays are destroying America's marriages."
- Confusing necessary with sufficient cause: It's necessary to pass Freshman English if you want a degree, but it not sufficient. You have to take other courses.
Begging the Question*
- Definition: The proposition to be proved is assumed implicitly or explicitly in one of the premises.
- Example: "You always give me a 'C' on my papers, no matter how good they are."
- What's wrong with it: The unproven premise is that the papers are, in fact, good papers.
*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.
- Definition: Using the same word in different meanings in an argument, implying that the word means the same each time around.
- Example: "Bread crumbs are better than nothing. Nothing is better than cheesecake. Therefore, breadcrumbs are better than cheesecake."
- What's wrong with it: "Nothing" is being used in two different senses. In the first statement, "nothing" means "no food in the house." In the second, it means "no examples are above it."
- Definition: The conclusion does not follow from the premise.
- Example: If I am a human, then I am a mammal. I am a mammal; therefore I am a human.
- Note: The conclusion may be true or it may be false; the difficulty is in the reasoning process.
- Definition: An attempt to intentionally confuse or distract the audience by switching to another subject.
- Example: When Donald Trump was asked in 2005 about comments he made about women, he replied, "It's locker room talk, and it's one of those things. I will knock the hell out of ISIS. We're going to defeat ISIS. ISIS happened a number of years ago in a vacuum that was left because of bad judgment. And I will tell you, I will take care of ISIS."
- What's wrong with it: Trump never got beyond "It's locker room talk," and moved instead to a completely unrelated topic. It's quite possible for him to have said those things about women, yet take a strong position against ISIS. An uncareful listener might think he answered the question, but he really didn't.¹
- Definition: "Comparing grandmothers and frogs" in Serbian and "comparing apples and oranges" in English.
- Example: The universe is like an intricate watch. A watch must have been designed by a watchmaker. Therefore, the universe must have been designed by some kind of creator.
- What's wrong with it: While the universe may be like a watch in that it is intricate, this does not in itself justify the assumption that that watches and the universe have similar origins.
- Definition: Basing of two conclusions each upon the other (or possibly with more intermediate steps).
- Example: In one of Plato's dialogs, the philosopher Euthyphro presents himself as a religious expert. He says that the gods approve of things that are holy. When he is asked what makes something holy, he says that something is holy if the gods approve of it.
- What's wrong with it: The discussion is trapped in a loop. You must grant both of the speaker's assertions, and there is no development beyond agreement.
Either-Or Choice (False Dichotomy)
- Definition: Two alternative points of view are held to be the only options, when in reality there exist one or more alternate options that have not been considered.
- Example: "Every nation in every region now has a decision to make: Either you are with us or you are with the terrorists." George W. Bush²
- What's wrong with it: Some nations might neither support terrorists nor be American allies. By presenting an unacceptable choice as the only alternative to the speaker's position, the false dichotomy forces a choice rather than encouraging critical thinking.
1. "Red Herring Fallacy — Definition and Examples." Fallacy in Logic, fallacyinlogic.com/red-herring-fallacy-definition-and-examples/. Accessed 24 June 2020.
2. Bush, George W. "President Bush Addresses the Nation." Washington Post, 20 Sept. 2001, www.washingtonpost.com/wp-srv/nation/specials/attacked/transcripts/bushaddress_092001.html. Accessed 24 June 2020.
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Revised 6/24/20 • Page author: Curtis Allen • e-mail: email@example.com.