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Testing for validity

In this video, we see how we can test an argument for formal validity using a truth-table.

Here’s the truth-table for our representation of the argument:

Truth-table for Trump argument

Figure 1. The truth-table for our representation of the Trump argument

And here’s a breakdown of how the method works …

The procedure

  1. Construct a truth-table of the appropriate size for the number of basic sentences involved. (Make sure that there are rows for all the possible ways things could be with regard to the truth-values of those sentences.)
  2. Write the premises and conclusion of the argument we’re considering at the top of the right side of the truth-table, with the conclusion to the far right of the table.
  3. Work out the truth-values of premises and conclusion on each row.
  4. Check to see if there are any rows on which all of the premises are true and the conclusion false (counterexamples).
  5. If there are any counterexample rows, the argument is formally invalid. If there are none, it’s formally valid.

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This video is from the free online course:

Logic: The Language of Truth

University of York