Learning Objectives
- Inductive Reasoning
- Deductive Reasoning
There are two general types of reasoning that we use when building and analyzing arguments: inductive and deductive.
Reasoning types
Inductive Reasoning uses a collection of specific examples as its premises and uses them to propose a general conclusion.
Deductive Reasoning uses a collection of general statements as its premises and uses them to propose a specific situation as the conclusion.
Try It
Example
“When I went to the store last week I forgot my purse, and when I went today I forgot my purse. I always forget my purse when I go the store” is an example of inductive reasoning.
The premises are:
I forgot my purse last week
I forgot my purse today
The conclusion is:
I always forget my purse
Notice that the premises are specific situations, while the conclusion is a general statement. In this case, this is fairly weak, since it is based on only two instances.
Example
“Every day for the past year, a plane flies over my house at 2pm. A plane will fly over my house every day at 2pm” is a stronger example of inductive reasoning, since it is based on a larger set of evidence.
Evaluating inductive arguments
An inductive argument is never able to prove the conclusion true, but it can provide either weak or strong evidence to suggest it may be true.
Many scientific theories, such as the big bang theory, can never be proven. Instead, they are inductive arguments supported by a wide variety of evidence. Usually in science, an idea is considered a hypothesis until it has been well tested, at which point it graduates to being considered a theory. The commonly known scientific theories, like Newton’s theory of gravity, have all stood up to years of testing and evidence, though sometimes they need to be adjusted based on new evidence. For gravity, this happened when Einstein proposed the theory of general relativity.
A deductive argument is more clearly valid or not, which makes them easier to evaluate.
Evaluating deductive arguments
A deductive argument is considered valid if all the premises are true, and the conclusion follows logically from those premises. In other words, the premises are true, and the conclusion follows necessarily from those premises.
Example
The argument “All cats are mammals and a tiger is a cat, so a tiger is a mammal” is a valid deductive argument.
The premises are:
All cats are mammals
A tiger is a cat
The conclusion is:
A tiger is a mammal
Both the premises are true. To see that the premises must logically lead to the conclusion, one approach would be use a Venn diagram. From the first premise, we can conclude that the set of cats is a subset of the set of mammals. From the second premise, we are told that a tiger lies within the set of cats. From that, we can see in the Venn diagram that the tiger also lies inside the set of mammals, so the conclusion is valid.
Try It
Analyzing Arguments with Venn diagrams
To analyze an argument with a Venn diagram
- Draw a Venn diagram based on the premises of the argument
- If the premises are insufficient to determine what determine the location of an element, indicate that.
- The argument is valid if it is clear that the conclusion must be true
Example
| Premise: | All firefighters know CPR |
| Premise: | Jill knows CPR |
| Conclusion: | Jill is a firefighter |
From the first premise, we know that firefighters all lie inside the set of those who know CPR. From the second premise, we know that Jill is a member of that larger set, but we do not have enough information to know if she also is a member of the smaller subset that is firefighters.
Since the conclusion does not necessarily follow from the premises, this is an invalid argument, regardless of whether Jill actually is a firefighter.
It is important to note that whether or not Jill is actually a firefighter is not important in evaluating the validity of the argument; we are only concerned with whether the premises are enough to prove the conclusion.
In addition to these categorical style premises of the form “all ___,” “some ____,” and “no ____,” it is also common to see premises that are implications.
Example
| Premise: | If you live in Seattle, you live in Washington. |
| Premise: | Marcus does not live in Seattle. |
| Conclusion: | Marcus does not live in Washington. |
From the first premise, we know that the set of people who live in Seattle is inside the set of those who live in Washington. From the second premise, we know that Marcus does not lie in the Seattle set, but we have insufficient information to know whether or not Marcus lives in Washington or not. This is an invalid argument.
Example
Consider the argument “You are a married man, so you must have a wife.”
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