{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

section_2.02_answers

section_2.02_answers - PHIL12A Section answers 2 February...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
PHIL12A Section answers, 2 February 2011 Julian Jonker 1 How much do you know? The following arguments are given in the blocks language of Tarski’s World. Decide whether the argument is valid. If it is, find a way to persuade others that it is. (In other words, write an informal proof.) If the argument is not valid, think of a counterexample. 1. (Ex 2.9) 1 LeftOf(a,b) 2 b=c 3 RightOf(c,a) This argument is valid. We know that a is left of b , by premise 1. But b is identical to c , by premise 2. By the indiscernibility of identicals, we know that what is true of b is true of c , so a is left of c . Left of and right of are inverses of each other, so we have that c is right of a , which is the conclusion we want. 2. (Ex 2.12) 1 BackOf(a,b) 2 FrontOf(a,c) 3 FrontOf(b,c) This argument is valid. We know that a is in back of b by premise 1. But back of and front of are inverses of each other, so b is in front of a . We also know that a is in front of c by premise 2. By the transitivity of front of , it follows that b is in front of c – which is the conclusion we want. 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3. (Ex 2.14) 1 Between(b,a,c) 2 LeftOf(a,c) 3 LeftOf(a,b) When I put this problem on the handout, I had the following simple proof in mind: We know that a is left of c by premise 2. Furthermore, b is between a and c by premise 1. It follows that b is left of c and right of a , and so b is right of a . But left of and right of are inverses of each other, and so a is left of b , which is the conclusion we want. However, in section, I realized that this is not really good enough. The proof is valid, but it is not obvious that each step is convincing, since we assume that the reader is doing a lot of the work on her own when reading the proof. In particular, how can we go from stating that
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}