aaron - Aaron Leung Philosophy 290-6 Fall 2004 Week 9...

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

View Full Document Right Arrow Icon
1 Aaron Leung Philosophy 290-6 Fall 2004 Week 9 Handout 12 Unrolling from the Antecedent Time 74. CLOSENESS AND SIMILARITY Consider this claim about the closeness of worlds, along with a corresponding logical principle: C 1 : No world is closer to α than α is to itself. That is, the class of worlds closest to α includes α . P 1 : A>C entails A C C 1 stands or falls with P 1 ; P 1 implies C 1 because if C 1 is false, then there is some world w is closer to α than α is to itself; pick an A that is true in w and α , and pick a C that is true in w and false in α ; then A>C is true while A C is false, which falsifies P 1 . Now consider a stronger claim about closeness, along with another logical principle: C 2 : No world is as close to α as α is to itself. That is, the class of worlds closest to α contains only α . P 2 : A&C entails A>C C 2 implies P 2 (in addition to P 1 ); if A and C are true at α , then C is true at all the closest A-worlds because α is the only closest A-world according to C 2 . Everyone in the literature agrees that closeness involves similarity; when we think about A>C, we think about worlds in which A is true and everything else is pretty much the same. Our intuitive notions of similarity support C 1 ; certainly α should be one of the worlds most similar to α . But what about C 2 ? Is α the only world most similar to α ? What about the idea that there can be differences that make no difference? Similarity can be made to give us C 2 if we talk about similarity down to every last detail—‘all- in’ similarity, as Bennett puts it. Then any given world is closer to itself than any other world is to it. But it isn’t clear whether we want this result, or P 2 which follows from it. 75. A > BIG-DIFFERENCE It turns out that all-in similarity doesn’t work so well for the closeness relation because it requires us to declare false all subjunctives that have the form A>Big-difference, when many such subjunctives are intuitively true. For example: “If on July 20 1944 Stauffenberg had placed the bomb on the other side of the trestle, Hitler would have been killed.” This is almost certainly true, but all-in similarity arguably tells us to declare it false because any A-world in which Hitler survives the blast is more similar to α than any A-world in which Hitler dies early. Basically, we believe in many conditionals of the form A>Big-difference because it seems plausible that small differences in the vicinity of the antecedent can amplify and become big differences in the consequent. This suggests that we only want to consider similarity up to the time of the antecedent. So we start with:
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 (1) Worlds should be compared with respect to their states up to the time of the antecedent—call that time T A . Do not take into account differences between possible worlds and the actual world after T A . So, if we’re comparing two worlds in which Stauffenberg plants the bomb a little to the right, with Hitler dying one and not in the other, then the difference between
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/01/2008 for the course PHIL 290 taught by Professor Fitelson during the Fall '06 term at Berkeley.

Page1 / 8

aaron - Aaron Leung Philosophy 290-6 Fall 2004 Week 9...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online