Assignment 8. The Liar

For submission

1. Chef Boyardee on the space station can feed anyone on the space station. Give the chef a mischievous direction that leads to a self-referential paradox.

2. Recall the paradox of HAL. Recreate it in another scenario that has the same problem. How colorful can you make it?

3. (a) Is there anything unusual about these signs?

blue sign
Anything written on red signs should NOT be believed.

red sign
Anything written on blue signs should be believed.

green sign
Nothing written on green signs should be believed.

(b) What might Tarski say of them?

For discussion

Not for submission

A. Yablo arrives at a liar like paradox within an infinite set of sentence that refer to each others' truth without any circularities. Is the use of an infinite set essential? Can a liar paradox be set up in a finite set of sentence without using some sort of circularity?

B. If a three-valued logic is prone to a strengthened liar paradox, what about a four-valued logic?

C. Does it matter if Tarski's and Kripke's proposals are in an idealized formal logic? Should not ordinary language aspire to the precision of formal logic?

D. In the paradox of the unexpected exam, what sort of paradox is it? A true contradiction? Or is it merely something intuitively unexpected?