Monday, March 17, 2008

the success and failure of transitivity

John is taller than Jack; Jack is taller than Joey.
It follows that John is taller than Joey.


John likes Jack; Jack likes Joey.
But it doesn't follow that John likes Jack.


John thinks that he is taller than Jack; Jack thinks that he is taller than Joey. It doesn't follow that John thinks he is taller than Joey.

4 comments:

joshia said...

第一種是邏輯.
第二種是可惜.
第三種是複雜的心理轉折.

Anonymous said...

John thinks that he is taller than Jack, and John thinks that Jack is taller than Joey. Does John think he is taller than Joey?

joshia said...

無從推導

S said...

a: John
b: Jack
c: Joey

R1xy: x is taller than y

R1ab, R1bc => R1ac

************************

R2xy: x likes y

R2ab, R2bc =/=> R2ac

************************
R3xy: x thinks that x is taller than y

R3ab, R3bc =/=> R3ac

************************
************************


R4xy: John thinks that x is taller than y

R4ab, R4bc => R4ac


Can we do this?