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Mathematics LibreTexts

17.8: Arguments

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    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 29

    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 30

    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.

    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.

    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

    A deductive argument is considered valid 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.

    17.8: Arguments is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.