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80-150 The Nature of Reason

Summer Two 2001, Dirk Schlimm
Homework No. 14
Friday, July 20 
  1. Reading.

    TTT, Chapter 6, pages 141-163.

    This is a hard read, since it's very technical and the concepts are not discussed in great detail. Read it once or twice, and try to get the most out of it!

    If you have questions about something explained in the text, write it up, bring it to class, and ask it at the beginning of next's class.

  2. Soundness and completeness. (6 points)

    • Read carefully TTT, page 153-4 again.
    • In yesterday's class we've seen a semantic way of testing the validity of an argument (truth tables) and a syntactic way (Natural deduction rules). An important question to ask is "How can we know that both ways are equivalent?"
    • Write a paragraph or two in which you explain as detailed as possible what soundness and completeness is. (Imagine that you explain these concepts to your friend who has never heard about logic before!)

  3. Natural Deduction. (4 points)

    • Give a proof using the rules of Natural Deduction (Handout) that from (A & B) v (A & not-B) you can derive A.
    • Show that the argument is valid using the semantic method.