Tarski's World: II

MTHT 450: October 19, 1998



The next couple of sentences are nonsense because I don't know to print logical symbols in HTML. Try to fill in the gaps from other sources.

Let A and B be sentences (i.e. either true or false).

is the symbol for "and". A B is true if and only if both A and B are true.

is the symbol for "or". A B is true if and only if one of A or B is true.

is the symbol for "not". A is true if A is false.

1. Open wittgens.wld and Boole.sen. Verify which sentences in the Boole file are true in Wittgenstein's world. Don't go from one sentence to the next until you see why it is true. Do you see the importance of parentheses?

2. Open Shroeder's sentences. Build a new world where all the sentences in this file are true. As you work through the sentences you will modify your world. Whenever you make a change be careful that your earlier sentences are still true. At the end verify that all the sentences are true at once. Save your world as Shr.wld.

Homework for October 26.

1. Open the file DeMorgan.sen. Build a world where all the odd numbered sentences are true. Notice that no matter how you do this, all the even numbered sentences also come out true. Save this world as Demor1.wld. Now build a world where all the even numbered sentences are false. Save this world as Demor2.wld. What happens to the odd numbered sentences. Can you make any conjectures about the reason for this?

2. Harry claims that for every n, n² - 81 n + 1681 is prime? Do you agree? Explain how you thought about this problem and any steps you took to verify or refute the conjecture.