3.3: Arguments
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3.3 Learning Objectives
- Identify inductive and deductive argument
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Evaluate the truth of inductive and deductive arguments
A logical argument is a claim that a set of premises support a conclusion. There are two general types of arguments: inductive and deductive arguments.
Argument types
An inductive argument uses a collection of specific examples as its premises and uses them to propose a general conclusion.
A deductive argument uses a collection of general statements as its premises and uses them to propose a specific situation as the conclusion.
Example 1
The argument “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 inductive argument.
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 a fairly weak argument, since it is based on only two instances.
Example 2
The argument “every day for the past year, a plane flies over my house at 2:00 P.M. A plane will fly over my house every day at 2:00 P.M.” is a stronger inductive argument, since it is based on a larger set of evidence. While it is not necessarily true—the airline may have cancelled its afternoon flight—it is probably a safe bet.
Example 3
The argument “Edgar Allen Poe must be a writer since all poets are writers and he wrote poems.”
The premises are:
All poets are writers.
Edgar Allen Poe wrote poems.
The conclusion is:
Edgar Allen Poe is a writer.
The argument uses the general premise that all poets are writers to conclude specifically that Poe is a writer since he wrote poems.
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 that it may be true.
Since the argument cannot be proven to be true the conclusions are called conjectures or hypotheses.
If there is one example that contradicts the conclusion, it proves the argument is false. This example is called a counterexample.
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. Common 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, such as when Einstein proposed the theory of general relativity.
A deductive argument is more clearly valid or not, which makes it easier to evaluate.
Evaluating deductive arguments
An argument is valid when the conclusion follows from the premises whether or not they are true.
A deductive argument is considered sound if, assuming that all the premises are true, the conclusion follows logically from those premises. In other words, when the premises are all true, the conclusion must be true.
An argument can be valid but not sound.
The argument becomes sound when it is valid and the premises are all true.
Example 4
Evaluate the deductive argument from above to determine if the argument is sound.
The premises are:
All poets are writers.
Edgar Allen Poe wrote poems.
The conclusion is:
Edgar Allen Poe is a writer.
First, determine if the argument is valid. Refer to the premises. Do those premises lead to the conclusion that is stated?
Yes they do. If all writers are poets and Edgar Allen Poe was a poet then the conclusion that he is a writer makes sense.
Second, determine if the argument is sound. Since the argument is valid, we just need to verify that the premises are true. The premises are true and the argument is valid, thus, this argument is sound.