Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom
Download 9.31 Mb.
|
- Navigate this page:
- General summary: How the theory measures up against desiderata
SynthesisThe account presented here shows how we can to some extent accommodate both of the rivaling intuitions about what Beauty’s credence should be when she wakes up. On the one hand, the intuition that her credence of Heads should be 1/3 because that would match the long-run frequency of heads among her awakenings is vindicated, but only when there is an actual series of experiments resulting in an actual long-run frequency. For there are then many observer-moments that are outside the particular run of the experiment that  is in whilst nonetheless being in ’s reference class. This leads, as we saw, to  .
On the other hand, the intuition that Beauty’s credence of Heads should be 1/2 is justified in cases where there is only one run of the experiment and there are no other observer-moments in the awakened Beauty’s reference class than her other possible awakenings in that experiment. For in that case the awakened Beauty does not get any relevant information from finding that she has been awakened, and she therefore retains the prior credence of 1/2. Those who feel strongly inclined to answer P(Heads) = 1/2 on Beauty’s behalf even in cases were various outsiders are known to be present, are free to take that intuition as a reason for choosing a reference class that places outsiders (as well as their own pre- and post-experiment observer-moments) outside the reference class they’d use as awakened observer-moments in the experiment. It is, hopefully, superfluous to here re-emphasize that such a restriction of their reference class would also have to be considered in the broader context of other inferences that one wishes to make from indexical statements or observations about one’s position in the world. For instance, jumping to the extreme view that only subjectively indistinguishable observer-moments get admitted into one’s reference class would be unwise because it would bar one from deriving observational consequences from Big-World cosmologies. General summary: How the theory measures up against desiderataThe theory that I have presented in the pages of this book (and formalized in chapter 10) enables us to take observation selection effects into account in a systematic and precise way, and to accommodate them in a Bayesian framework. The observation equation, the centerpiece of the theory, implies the Carter and Leslie versions of weak and strong anthropic principles as special cases. The observation equation solves the freak-observer problem and makes it possible to model observation selection effects in real scientific applications. By relativizing the reference class, one can coherently avoid the counterintuitive consequences described in chapter 9; this requires taking into account additional indexical information beyond that covered by the Self-Sampling Assumption. We can thus see the Self-Sampling Assumption as a ladder that we have climbed and can now kick away (or better yet, retain as a simplified special-case version of observation equation). The observation selection theory does not imply the Self-Indication Assumption, which we criticized with the Presumptuous Philosopher gedanken and other arguments in chapter 7. The observation equation is itself neutral with respect to the reference class problem and can therefore be used independently of how one thinks the reference class should be defined. We have established a lower bound on the inclusivity of the reference class (  is incorrect) and we have identified considerations that can motivate choosing a reference class less inclusive than the universal reference class  . Between these limitations, there is scope for rational people to use different reference classes, and we argued that this degree of subjectivity mirrors the subjectivity in electing a prior credence function over (non-centered) possible worlds. There we have, thus, a framework for connecting up indexical beliefs with non-indexical ones; a delineation of the element of subjectivity in both kinds of inferences; and a method for applying the theory to help solve concrete practical philosophical and scientific problems, ranging from the question of God’s existence to analyzing claims about perceptual illusions among motorists.
Yet some issues remain mysterious. In particular, I feel that the problem of the reference class, the problem of generalizing to infinite cases, and the problem of attaining a more intuitively transparent understanding of the relation between the indexical and the non-indexical may each enclose deep enigmas. These mysteries may even somehow be connected. I hope that others will see more clearly than I have done and will be able to advance further into this fascinating land of thought. Directory: preprints preprints -> Digitally-assisted discovery and proof preprints -> Reorienting the Logic of Abduction preprints -> Supplementary Material Table 1 Download 9.31 Mb. Share with your friends:
|