What makes an argument valid · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Valid does not mean true

Personal & Social Development · Ethics & Philosophy · ages 16-18
Name ______________________   Date ____________

  1. What does valid mean for a deductive argument?

    • Its premises must all be true in the actual world
    • Its conclusion must be true in the actual world
    • True premises cannot yield a false conclusion

  2. Mara says: since the cafe uses fresh beans, and fresh beans taste better, you will love our coffee. Which claim is her conclusion?

    • The cafe uses fresh beans
    • You will love our coffee
    • Fresh beans taste better

  3. A valid argument always ends in a true conclusion.

    Circle one:   True   False

  4. In a story, the cafe is open, the library is closed and the bus is late. Someone argues: the cafe is open; the library is closed; therefore the bus is late. Why is this invalid?

    • The premises do not force the bus to be late
    • A true conclusion requires a false premise
    • A late bus makes both of the stated premises false

  5. All fish are birds. A salmon is a fish. So a salmon is a bird. Is this argument valid?

    • Yes: the salmon must be a bird if both premises hold.
    • No: the false fish premise prevents any conclusion from following.
    • No: a false conclusion rules out a valid inference.

  6. What must you add to validity to get soundness?

    • The conclusion must be long
    • All premises must be true
    • Extra premises are needed

  7. Which argument is sound?

    • All mammals breathe air. All whales are mammals. So all whales breathe air.
    • All birds speak English. All crows are birds. So all crows speak English.
    • All fish live on dry land. All salmon are fish. So all salmon live on dry land.

  8. If it rains, the grass is wet. The grass is wet. So it rained. Is this argument valid?

    • Yes. Wet grass is enough to establish rain.
    • Yes. Either premise alone establishes the conclusion.
    • No. A sprinkler could wet the grass without rain.
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Valid does not mean true W1-mt_W72nTJmeOI-s1

  1. True premises cannot yield a false conclusion · Validity concerns what follows from the premises. It rules out a possible case in which all the premises are true and the conclusion is false.
  2. You will love our coffee · Mara offers the bean claims as reasons for accepting that you will love the coffee. Identifying the conclusion does not show that her reasons prove it.
  3. False · A valid argument can have a false conclusion when a premise is false. Validity guarantees truth only if all the premises are true.
  4. The premises do not force the bus to be late · The cafe and library claims do not force the bus claim. Both could be true while the bus is on time, even though the bus happens to be late in this story.
  5. Yes: the salmon must be a bird if both premises hold. · Assume both premises: every fish belongs among birds, and the salmon belongs among fish. The salmon must then belong among birds. The inference is valid, although its false first premise makes the argument unsound.
  6. All premises must be true · A sound argument must be valid and have all true premises. More detail or more premises does not replace checking their truth.
  7. All mammals breathe air. All whales are mammals. So all whales breathe air. · Each argument has a valid form. Only the whale argument also has all true premises. The bird and fish arguments each contain a false universal premise.
  8. No. A sprinkler could wet the grass without rain. · The premises allow wet grass without rain. A sprinkler provides a possible case with true premises and a false conclusion.
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