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Common Patterns of Deductive Reasoning

Instructor: Christine Serva

Christine has an M.A. in American Studies. She is an instructional designer, educator, and writer with a particular interest in the social sciences and American studies.

In this lesson, you'll explore how some conclusions can be drawn with certainty. Learn about this type of logic through examples and a quiz, to check if you can match arguments to the patterns they use.

Reaching Certainty

Lorna, a scientist, is a major fan of deductive reasoning . Deductive reasoning involves taking valid premises and ultimately reaching a conclusion that is airtight. Unlike inductive reasoning, which aims to arrive at a conclusion that is simply likely or probable, deduction is all about premises leading to a certain, specific conclusion.

As a scientist, Lorna uses both approaches. In this lesson, we'll follow Lorna as she teaches her new intern, Pete, about deductive reasoning.

Syllogisms

Pete's first question for Lorna about this form of logic is, ''How can you possibly be certain about your conclusions? Isn't there always room for error?''

Lorna explains that since arguments can be flawed in many ways, deductive arguments can only occur in certain specific patterns that ensure the conclusions are more solid. Only certain circumstances call for this approach.

One common pattern of deductive reasoning is the syllogism. The basic format of a syllogism involves two premises, leading to a conclusion.

A particular type of syllogism, known as a categorical syllogism, would include an argument like this:

  • All spiders are arachnids. (Premise)
  • All arachnids have eight legs. (Premise)
  • Therefore, all spiders have eight legs. (Conclusion)

One way to spot a categorical syllogism is by taking note of the three categories, each used twice in the argument: spiders, arachnids, and eight legs.

Lorna points out that if the premises of this argument about spiders are true, then it follows that, without a doubt, the conclusion must be true. It's not a matter of it being likely or probable. Deductive reasoning leads us to only one logical conclusion in this case: If the first two statements are accurate, then spiders have eight legs, end of story.

It may help to remember that a syllogism includes two premises by noticing how there are two ''L's'' in the word itself.

Lorna tells Pete about another type of syllogism, the hypothetic syllogism. She gives an example:

  • If you make me hold a spider, I will definitely scream.
  • If I scream, I will hurt your ears.
  • Therefore, if you make me hold a spider, I'm going to end up hurting your ears.

Here, the ''if, then'' format is hypothetical, stating that ''If you make me hold a spider'' something will happen as a result. Another premise follows and, like a chain reaction, the conclusion will state that the first ''if'' will lead to the last ''then''.

Notice that there's only one logical conclusion here if the premises are true. The argument doesn't state, I might scream, or my scream might hurt your ears. Those premises are stated as true statements without exception. If they are accurate, the conclusion is also accurate.

Argument by Elimination

Pete wonders about another way to reach a logical conclusion. He's taking exams for college and has found that sometimes in multiple choice tests, he can be sure of the correct answer even when he doesn't know the material well enough to choose that answer.

Lorna asks Pete to explain more about what he means.

''Let's say you have answers A, B, C, and D,'' he says. ''And, let's say I know for sure that the answer is not A, B, or D. This means I am sure that the answer is C, even if I don't actually have the knowledge to confirm it. ''

Lorna nods her head. This is also a pattern in deductive reasoning. It's known as an argument by elimination. You essentially knock out all of the other possibilities. This only works in cases where there are no other options. In a fill-in-the-blank test, argument by elimination won't help you.

Mathematical Arguments

Pete has another example he thinks is deductive reasoning. ''What about when I'm calculating a number, like if I have to convert miles to kilometers? If I know how many kilometers are in one mile, I can deduce how many kilometers are in, say, seventeen miles through simple math, right?''

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