1 / 10

# Some Puzzles About Truth - PowerPoint PPT Presentation

Some Puzzles About Truth. (and belief, knowledge, opinion, and lying). Puzzle #1: the postcard paradox. Consider the following sentences: 1) the following sentence is true: 2) the preceding sentence is false. (examine the index card now circulating) Q: are these sentences true or false?.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

(and belief, knowledge, opinion, and lying)

• Consider the following sentences:

1) the following sentence is true:

2) the preceding sentence is false.

• (examine the index card now circulating)
• Q: are these sentences true or false?
• Is the following proposition true or false?

This proposition is false

• • If every proposition is either true or false then this proposition will be either true or false
• • If it is true, then it is true that it is false; so it must be both true and false
• • If it is false, then it is false that it is false; so it must be true; so it must be both true and false
• • So in both cases it is both true and false, which is impossible
Puzzle #3: On the island of knights and knaves
• On the island of Knights and Knaves, every inhabitant is either a knight or a knave. Knights always tell the truth. Knaves never tell the truth; any sentence uttered by a knave is false. A stranger came to the island and encountered three inhabitants, A, B, and C. He asked A, "Are you a knight, or a knave?" A mumbled an answer that the stranger could not understand. The stranger then asked B, "What did he say?" B replied, "A said that there is exactly one knight among us." Then C burst out, "Don't believe B, he is lying!" What are B and C?
• One day I went to the island of knights and knaves and encountered an inhabitant who said, "Either I am a knave or else two plus two equals five." What should you conclude?
Puzzle #4: the ‘well-named’ ‘ill-named’ paradox
• Have you ever noticed that some people are very well named? Martin Short is, after all, rather short. I once met a realtor named 'Isolde Haus' and a preacher named 'Mike Pentacost'. Just recently, I received a letter from an evolutionary biologist named 'Steve Darwin'.
• Let's call everyone else 'ill-named'. Some people who are ill-named are rather spectacularly ill-named. For example, Tiny Tim is really rather large. Most of us are ill-named in a less interesting way, though. In any case, let's just agree to call everyone who isn't well-named 'ill-named'.
• I used to play a game of classifying everyone I met as well named if their name is, somehow, particularly appropriate for them and ill named if it is not. I quit playing this game when a new neighbor moved in next door. His name is John Ill-named. Is he well named, or ill named? (due to Raymond Smullyan)
Puzzle #5: how to prove anything
• Let A be any arbitrary sentence, and let B be the sentence "If this sentence is true, then A is true". Suppose B is, in fact, true. Then, according to B, A is true. Thus, we have established that if B is true, then A is true. But this is exactly what B asserts! Thus, B must be true, from which it follows (by B) that A must be true. Hence, all sentences are true! (due to M. H. Lob)