EXPLORING LOGICAL SPACE

1. Properties and Propositions

2. Connectives

3. Implication

4. Necessary/Sufficient/Necessary and Sufficient Conditions

5. Counterexamples

6. Top-Down and Bottom-Up Reasoning

7. Proof vs. Equilibrium Reasoning

THE FIFTH/SIXTH COMMANDMENT FROM THE OLD TESTAMENT

Let K = Killing

Let W = Morally Wrong

Literal-minded way of understanding the Fifth/Sixth Commandment:

K ® W [Being a killing implies that an act is morally wrong]

What does this statement mean?

It is not possible for something to be K & -W.

Can you think of a counterexample?

AN EXAMPLE OF A VALID DEDUCTION WITH A FALSE CONCLUSION

(1) The moon is made of green cheese à Professor Talbott is a blue-nosed gopher.

(2) The moon is made of green cheese.

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Conclusion: Professor Talbott is a blue-nosed gopher.