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2.4: Validity and Conditionals

  • Page ID
    1682
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    • 2.4.1: Validity
      An argument is Valid when without fail, if the premises are true, then the conclusion is going to turn out to be true also.
    • 2.4.2: Invalidity and Counter Examples
      An argument is valid just in case there is no possible case, no assignment of truth values to sentence letters, in which all of the premises are true and the conclusion is false. To be valid is to rule out any such possibility. Validity can be broken into two parts:  A Counterexample to a sentence logic argument is an assignment of truth values to sentence letters which makes all of the premises true and the conclusion false. An argument is Valid just in case there are no counterexamples to it.
    • 2.4.3: Soundness
      An argument is Sound just in case, in addition to being valid, all its premises are true.
    • 2.4.4: The Conditional
      A sentence of the form X>Y is called a Conditional. X is called its Antecedmt and Y is called its Consequent.
    • 2.4.5: The Biconditional
      Often we will want to study cases which involve a conjunction of the form (X>Y)&(Y>X). This truth function of X and Y occurs so often in logic that we give it its own name, the Biconditional, which we write as XGY. Working out the truth table of (X>Y)&(Y>X) we get as our definition of the biconditional.

    Contributors and Attributions

    • Paul Teller (UC Davis). The Primer was published in 1989 by Prentice Hall, since acquired by Pearson Education. Pearson Education has allowed the Primer to go out of print and returned the copyright to Professor Teller who is happy to make it available without charge for instructional and educational use.


    2.4: Validity and Conditionals is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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