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3.1: Conditionals and their Parts

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    A conditional is a sentence that says something will be true, provided that something else is true. All these sentences are conditionals:

    1. If it is raining, then the lot is full.
    2. If Tom Brady lied about Deflategate, then he should be tried for perjury.
    3. If it doesn’t fit, you must acquit.
    4. If Wilbur had nothing to hide, he wouldn’t be so sneaky.
    5. If he builds it, they will come.
    6. If you bomb the final, you’ll fail the course.
    7. If a number is divisible by 2, then it isn’t a prime number.
    8. If you win the Publishers Clearing House Sweepstakes, then you will be rich.

    A conditional is a compound sentence that consists of two shorter sentences.

    When the sentence has an ‘if–then’ format:

    1. The sentence between the ‘if’ and the ‘then’ is called the antecedent.
    2. The sentence after the ‘then’ is called the consequent.

    The antecedent is the part that comes before (think about poker, where you ‘ante up’ before the hand begins).

    The antecedent of sentence 1. is:

    • It is raining.

    And the consequent is:

    • The lot is full.

    The words ‘if’ and ‘then’ are not part of either the antecedent or the consequent. They are just connecting words that glue the two simpler sentences together to form the conditional.

    A conditional is iffy. It does not claim that its antecedent is true or that its consequent is true. It is hypothetical: if the antecedent is true, then the consequent will be true too. As we noted above, it is true that if you win the Publishers Clearing House Sweepstakes, then you will be rich. But unfortunately, this does not mean that you will win the sweepstakes, or that you will be rich.

    Our first example of a conditional:

    1. If it is raining, then the lot is full.

    tells us what will happen if it is raining (the lot will be full). The biggest trouble people have with conditionals is thinking that they say more than they do.

    1. The conditional does not say anything about what happens if the lot is full. (In particular, it does not say that if the lot is full, it will be raining.)
    2. The conditional does not say anything about what happens if it is not raining. (In particular, it does not say that if it’s not raining then the lot isn’t full.)

    Our definition of validity is naturally stated as a conditional: if all the premises are true, then the conclusion must be true as well.

    Alternative Ways to State Conditionals

    There are various ways to state conditionals, and some of them require thought. Ask yourself: could we rephrase a sentence as an ‘if–then’ claim without changing its meaning? If we can, then the sentence is a conditional.

    The following sentences all have the same meaning, so we count all of them as conditionals.

    1. If it is raining, then the lot is full.
    2. If it is raining, the lot is full.
    3. When it’s raining, the lot is full.
    4. The lot is full, if it’s raining.
    5. It rains, and the lot is full.
    6. Should it rain, the lot will be full.
    7. The lot is full, provided that it’s raining.

    Two Notes on Terminology

    1. All arguments have premises and a conclusion. But no argument has an antecedent or a consequent.
    2. All conditionals have antecedents and consequents. But no conditional has a premise or a conclusion.

    Exercises on Conditionals

    Determine whether each of the following sentences is a conditional. If it is a conditional, draw a line under its antecedent and circle its consequent. If it’s not a conditional, write ‘not a conditional.’

    Example: If one more person tells me I must watch Game of Thrones, then I’m going to scream.

    1. This sentence is a conditional.
    2. (b.) One more person tells me I must watch Game of Thrones (antecedent)
    3. (c.) I’m going to scream (consequent)

    Note: the words ‘if’ and ‘then’ are not part of either the antecedent or the consequent, so should not be underlined or circled.

    1. If we run out of gas out here in the desert, we’re as good as dead.
    2. If you have the time, we have the beer.
    3. If Marlena goes to the movies, Ivan will stay home and watch the kids.
    4. Marlena will stay home and watch the kids, if Ivan goes to the movies.
    5. Ivan will stay home and watch the kids, provided that Marlena calls him on time.
    6. When it rains, it pours.
    7. Should OU win the rest of their games, they’ll win the Big 12 Conference.
    8. Give peace a chance.
    9. Give me a place to stand, and a tall frosty Bud Light.
    10. Give me a place to stand, and I’ll move the world.
    11. Ivan went to the movies and Marlena watched the kids.
    12. Wilbur will fix your car only if you pay him what you owe.
    13. Wilbur will fix your car if only you pay him what you owe.
    14. If wishes were trees the trees would be falling.
    15. If you want to hire Jim Rockford it’ll cost you $200 a day plus expenses.
    Answer

    1. If we run out of gas out here in the desert, we’re as good as dead.

    1. This is a conditional.
    2. Antecedent: We do run out of gas in the desert
    3. Consequent: We’re as good as dead

    2. If you have the time, we have the beer.

    1. This is a conditional.
    2. Antecedent: You have the time
    3. Consequent: We have the beer

    4. Marlena stayed home and watched the kids, if Ivan went to the movies.

    1. This is a conditional.
    2. Antecedent: Ivan went to the movies
    3. Consequent: Marlena stayed home and watched the kids

    6. When it rains, it pours.

    1. This is a conditional.
    2. Antecedent: It rains
    3. Consequent: It pours

    8. Give peace a chance.

    1. Not a conditional.

    9. Give me a place to stand, and a tall frosty Bud Light.

    1. This is not a conditional.

    In fact, it’s not even a declarative sentence.

    10. Give me a place to stand, and I’ll move the world.

    1. Although this looks a lot like the previous sentence, this is a conditional. You must focus on what it means. The key is to see that it says the same thing as “If you give me a place to stand, then I’ll move the world.”
    2. Antecedent: You give (gave) me a place to stand
    3. Consequent: I’ll move the world

    11. Ivan went to the movies and Marlena watched the kids.

    1. Not a conditional.

    12. Wilbur will fix your car only if you pay him what you owe.

    1. This is a conditional.
    2. Antecedent: Wilbur will fix your car
    3. Consequent: You pay him what you owe

    13. Wilbur will fix your car if only you pay him what you owe.

    1. This is a conditional.
    2. Antecedent: You pay him what you owe
    3. Consequent: Wilbur will fix your car. [Note the difference between this and the preceding problem]

    The conditional does not say anything about what happens if it is not raining. (In particular, it does not say that if it’s not raining then the lot isn’t full.)

    Our definition of validity is naturally stated as a conditional: if all the premises are true, then the conclusion must be true as well.

    This page titled 3.1: Conditionals and their Parts is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jason Southworth & Chris Swoyer via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.