crazy88

Karma: 328

crazy88 Mar 5, 2013, 2:38 AM
0 points
in reply to: AlexMennen’s comment on: Decision Theory FAQ
Point conceded (both your point and shminux’s). Edited for the next update.

crazy88 Mar 4, 2013, 8:08 PM
0 points
in reply to: AlexMennen’s comment on: Decision Theory FAQ
Thanks for the clarification.

Perhaps worth noting that earlier in the document we defined acts as functions from world states to outcomes so this seems to resolve the second concern somewhat (if the context is different then presumably this is represented by the world states being different and so there will be different functions in play and hence different acts).

In terms of the first concern, while VNM may define preferences over all lotteries, there’s a sense where in any specific decision scenario, VNM is only appealed to in order to rank the achievable lotteries and not all of them. Of course, however, it’s important to note as well that this is only part of the story.

Anyway, I changed this for the next update so as to improve clarity.

crazy88 Mar 4, 2013, 9:12 AM
0 points
in reply to: AlexMennen’s comment on: Decision Theory FAQ
My understanding is that in the VNM system, utility is defined over lotteries. Is this the point you’re contesting or are you happy with that but unhappy with the use of the word “acts” to describe these lotteries. In other words, do you think the portrayal of the VNM system as involving preferences over lotteries is wrong or do you think that this is right but the way we describe it conflates two notions that should remain distinct.

crazy88 Mar 4, 2013, 9:12 AM
0 points
in reply to: AlexMennen’s comment on: Decision Theory FAQ
My understanding is that in the VNM system, utility is defined over lotteries. Is this the point you’re contesting or are you happy with that but unhappy with the use of the word “acts” to describe these lotteries. In other words, do you think the portrayal of the VNM system as involving preferences over lotteries is wrong or do you think that this is right but the way we describe it conflates two notions that should remain distinct.

crazy88 Mar 4, 2013, 8:58 AM
2 points
in reply to: Sniffnoy’s comment on: Decision Theory FAQ
I think I’m missing the point of what you’re saying here so I was hoping that if I explained why I don’t understand, perhaps you could clarify.

VNM-utility is unique up to a positive linear transformation. When a utility function is unique up to a positive linear transformation, it is an interval (/cardinal scale). So VNM-utility is an interval scale.

This is the standard story about VNM-utility (which is to say, I’m not claiming this because it seems right to me but rather because this is the accepted mainstream view of VNM-utility). Given that this is a simple mathematical property, I presume the mainstream view will be correct.

So if your comment is correct in terms of the presentation in the FAQ then either we’ve failed to correctly define VNM-utility or we’ve failed to correctly define interval scales in accordance with the mainstream way of doing so (or, I’ve missed something). Are you able to pinpoint which of these you think has happened?

One final comment. I don’t see why ratios (a-b)/|c-d| aren’t meaningful. For these to be meaningful, it seems to me that it would need to be that [(La+k)-(Lb+k)]/[(Lc+k)-(Ld+k)] = (a-b)/(c-d) for all L and K (as VNM-utilities are unique up to a positive linear transformation) and it seems clear enough that this will be the case:

[(La+k)-(Lb+k)]/[(Lc+k)-(Ld+k)] = [L(a-b)]/[L(c-d)] = (a-b)/(c-d)

Again, could you clarify what I’m missing (I’m weaker on axiomatizations of decision theory than I am on other aspects of decision theory and you’re a mathematician so I’m perfectly willing to accept that I’m missing something but it’d be great if you could explain what it is)?

crazy88 Mar 3, 2013, 9:57 PM
0 points
in reply to: torekp’s comment on: Decision Theory FAQ

Does the horizontal axis of the decision tree in section 3 represent time?

Yes and no. Yes, because presumably the agent’s end result re: house and money occurs after the fire and the fire will happen after the decision to take out insurance (otherwise, there’s not much point taking out insurance). No, because the diagram isn’t really about time, even if there is an accidental temporal component to it. Instead, the levels of the diagram correspond to different factors of the decision scenario: the first level is about the agent’s choice, the second level about the states of natures and the third about the final outcome.

Given that this is how the diagram works, smearing out the triangles would mix up the levels and damage the clarity of the diagram. To model an agent as caring about whether they were insured or not, we would simply modify the text next to the triangles to something like “Insurance, no house and $99,900”, “Insurance, house and - $100″ and so on (and then we would assign different utilities to the agent based partly on whether they were insured or not as well as whether they had a house and how much money they had).

I think that forgetting this point sometimes leads to misapplications of decision theory.

I agree, though I think that talking of utility rather than money solves many of these problems. After all, utility should already take into account an agents desire to be insured etc and so talk about utility should be less likely to fall into these traps (which isn’t to say there are never any problems)

crazy88 Mar 3, 2013, 9:43 PM
2 points
in reply to: Pentashagon’s comment on: Decision Theory FAQ
Will be fixed in the next update. Thanks for pointing it out.

crazy88 Mar 3, 2013, 9:36 PM
0 points
in reply to: diegocaleiro’s comment on: Decision Theory FAQ
Thanks. Will be fixed in next update. Thanks also for the positive comment.

crazy88 Mar 3, 2013, 9:34 PM
0 points
in reply to: kilobug’s comment on: Decision Theory FAQ
Thanks, as you note, the linked comment is right.

crazy88 Mar 3, 2013, 9:34 PM
0 points
in reply to: somervta’s comment on: Decision Theory FAQ
Thanks, will be fixed in next update.

crazy88 Mar 3, 2013, 9:15 PM
0 points
in reply to: Vaniver’s comment on: Decision Theory FAQ
Fixed for next update. Thanks.

crazy88 Mar 3, 2013, 9:14 PM
0 points
in reply to: fortyeridania’s comment on: Decision Theory FAQ
Thanks, fixed for the next update.

crazy88 Mar 3, 2013, 9:13 PM
0 points
in reply to: Carwajalca’s comment on: Decision Theory FAQ
Thanks. Fixed for the next update of the FAQ.

crazy88 Mar 3, 2013, 9:10 PM
1 point
in reply to: ygert’s comment on: Decision Theory FAQ
Thanks. I’ve fixed this up in the next update (though it won’t appear on the LW version yet).

crazy88 Dec 17, 2012, 12:48 AM
0 points
in reply to: Qiaochu_Yuan’s comment on: By Which It May Be Judged
I think this conversation is now well into the territory of diminishing return so I’ll leave it at that.

crazy88 Dec 16, 2012, 9:44 PM
0 points
in reply to: Qiaochu_Yuan’s comment on: By Which It May Be Judged
Okay, perhaps I can have another go at this.

First thing to note, possible worlds can’t be specified at different levels of detail. When doing so we are either specifying partial possible worlds or sets of possible worlds. As rigid designation is a claim about worlds, it can’t be relative to the level of detail utilised as it only applies to things specified at one level of detail.

Second, you still seem to be treating possible worlds as concrete things rather than something in the head (or, at least, making substantive assumptions about possible worlds and relying on these to make claims about possible worlds generally). Let’s take possible worlds to be sets of propositions and truth values. In this case there’s no reason to find transworld identity puzzling. H2O exists in this world just if a relevant proposition is true (like, “I am holding a glass of H2O”). There’s also no room for this transworld identity to be relative to a context. Whether these things are puzzling depends on your account of possible worlds and it seems like if you’re account of possible worlds can’t account for transworld identity it can’t do the work required of possible worlds and so it is open to the challenge that it should be abandoned in favour of some other account.

Third, it’s important to distinguish questions about the way worlds are from questions about how they can be specified. It’s an interesting question how we should specify individual possible worlds and another interesting question whether we often do so or whether we normally specify sets of possible worlds instead. However, difficulties with specification do not undermine the concept of a rigid designator.

Fourth, even if it were a relative matter whether H2O exists in a world this wouldn’t undermine the concept of rigid designation. Rigid designation would simply imply that if this were the case then it would also be a relative matter whether water existed in that world.

The summary of what I’m trying to get at is the following: you have raised concerns for practical issues (how we specify worlds) and epistemic issues (how we know what’s in worlds) but these aren’t really relevant to the issue of rigid designation. So, for example, I don’t think your claim that:

I think what I’m actually trying to say is that what constitutes a rigid designator, among other things, seems to depend very strongly on the resolution at which you examine possible worlds.

Follows from your argument (for the reasons I’ve outlined above, recap: from the fact that humans often specify sets of worlds rather than worlds nothing about rigid designation follows), even though I think your argument is an insightful one that raises interesting epistemic and practical issues for possible worlds.

crazy88 Dec 16, 2012, 9:26 AM
0 points
in reply to: Qiaochu_Yuan’s comment on: By Which It May Be Judged
I think this is getting past the point that I can useful contribute further though I will note that the vast literature on the topic has dealt with this sort of issue in detail (though I don’t know it well enough to comment in detail).

Saying that, I’ll make one final contribution and then leave it at that: I suspect that you’ve misunderstood the idea of a rigid designator if you think it depends on the resolution at which you examine possible worlds. To say that something is a rigid designator is to say that it refers to the same thing in all possible worlds (note that this is a fact about language use). So to say that “water” rigidly denotes H2O is just to say that when we use the word water to refer to something in some possible world, we are talking about H2O. Issues of how precisely the details of the world are filled in are not relevant to this issue (for example, it doesn’t matter what happens to the air molecules—this has no impact on the issue of rigid designation).

The point you raise is an interesting one about how we specify possible worlds but not, to my knowledge, one that’s relevant to rigid designation. But beyond that I don’t think I have anything more of use to contribute (simple because we’ve exhausted my meagre knowledge of the topic)...

crazy88 Dec 16, 2012, 8:05 AM
0 points
in reply to: gyokuro’s comment on: Open Thread, December 16-31, 2012
I can’t cite sources off-hand but this suggestion is reasonably standard but taken to be a bit of a cheat (it dodges the difficult question). For this reason it is often stipulated that no objective chance device is available to the agent or that the predictor does something truly terrible if the agent decides by such a device (perhaps takes back all the money in the boxes and the money in the agent’s bank account).

crazy88 Dec 16, 2012, 7:59 AM
0 points
in reply to: Qiaochu_Yuan’s comment on: By Which It May Be Judged
As I said, these are complex issues.

possible worlds are things that live inside the minds of agents (e.g. humans).

Yes, but almost everyone agrees with this (or at least, almost all views on possible worlds can be interpreted this way even if they can also be interpreted as claims about the existence of abstract—non-concrete—objects). There are a variety of different things that possible worlds can be even given the assumption that they exist in people’s heads (almost all the disagreement about what possible worlds are is disagreement within this category rather than between this category and something else).

Water is one of the examples I considered and found incoherent. Once you start considering possible worlds with different laws of physics, it’s extremely unclear to me in what sense you can identify types of particles in one world with particles in another type of world.

Two things: first, the claim that “water” rigidly designates H2O doesn’t imply that it must exist in all possible worlds—just that if “water” exists in a possible world then it is H2O. So if we can’t identify the same particles in different worlds then this just means that water exists in almost no worlds (perhaps only in our own world).

However, the view that we can’t identify the same particles in other worlds is a radical one and would be a strong sign that the account of possible worlds appealed to falls short (after all, possible worlds are supposed to be about what is possible and surely there are possibilities that revolve around the particles existing in our world—ie. surely it’s possible that I now be holding a glass of H2O. If your account of possible worlds can’t cope with this possibility it seems to not be a very useful account of possible worlds).

Further, how hard it is to identify sameness of particles across possible worlds will depend on how you take them to be “constructed”—if they are constructed by stipulation, ie. “consider the world where I am holding a glass of H2O” then it is very easy to get sameness of particles.

I’m not saying there’s not room for your criticisms but for them to hold requires substantial metaphysical work showing why your account, and only your account, of possible worlds works and hence that your conclusions hold.

crazy88 Dec 16, 2012, 6:43 AM
4 points
in reply to: Qiaochu_Yuan’s comment on: By Which It May Be Judged
Okay, so three things are worth clarifying up front. First, this isn’t my area of expertise so anything I have to say about the matter should be taken with a pinch of salt. Second, this is a complex issue and really would require 2 or 3 sequences of material to properly outline so I wouldn’t read too much into the fact that my brief comment doesn’t present a substantive outline of the issue. Third, I have no settled views on the issues of rigid designators, nor am I trying to argue for a substantive position on the matter so I’m not deliberately sweeping anything under the rug (my aim was to distinguish Eliezer’s use of the phrase rigid designator from the standard usage and doing so doesn’t require discussion of transworld identity: Eliezer was using it to refer to issues relating to different people whereas philosophers use it to refer to issues relating to a single person—or at least that’s the simplified story that captures the crucial idea).

All that said, I’ll try to answer your question. First, it might help to think of rigid designators as cases where the thing to be identified isn’t simply to be identified with its broad role in the world. So “the inventor of bifocals” is the person that plays a certain role in the world—the role of inventing bifocals. So “the inventor of bifocals” is not a rigid designator. So the heuristic for identifying rigid designators is that they can’t just be identified by their role in the world.

Given this, what are some examples of rigid designators? Well, the answer to this question will depend on who you ask. A lot of people, following Putnam would take “water” (and other natural kind terms) to be a rigid designator. On this view, “Water” rigidly refers to H2O, regardless of whether H20 plays the “water” role in some other possible world. So imagine a possible world where some other substance, XYZ, falls from the sky, sakes thirst, fill rivers and so on (that is, XYZ fills the water role in this possible world). On the rigid designation view, XYZ would not be water. So there’s one example of a rigid designator (on one view).

Kripke (in his book naming and necessity) defends the view that names are rigid designators—so the name “Thomas Jefferson” refers to the same person in all possible worlds (this is where issues of transworld identity become relevant). This is meant to be contrasted with a view according to which the name “John Lennon” refers to the nearest and near enough realiser of a certain description (“lead singer of the Beatles, etc). So on this view, there are possible worlds where John Lennon is not the lead singer of the Beatles, even though the Beatles formed and had a singer that met many of the other descriptive features of John (born in the same town and so on).

Plausibly, what you take to be a rigid designator will depend on what you take possible worlds to be and what views you have on transworld identity. Note that your comment that it seems difficult to imagine how you could go about identifying objects in different possible worlds even in principle makes a very strong assumption about the metaphysics of possible worlds. For example, this difficulty would be most noticeable if possible worlds were concrete things that were causally distinct from us (as Lewis would hold). One major challenge to Lewis’s view is just this challenge. However, very few philosophers actually agree with Lewis.

So what are some other views? Well Kripke thinks that we simply stipulate possible worlds (as I said, this isn’t my area so I’m not entirely clear what he takes possible worlds to be—maximally consistent sets of sentences, perhaps—if anyone knows, I’d love to have this point clarified). That is, we say, “consider the possible world where Bill Gates won the presidency”. As Kripke doesn’t hold that possible worlds are real concrete entities, this stipulation isn’t necessarily problematic. On Kripke’s view, then, the problem of transworld identity is easy to solve.

More precisely, I do not understand how one goes about identifying objects in different possible worlds even in principle. I think that intuitions about this procedure are likely to be flawed because people do not consider possible worlds that are sufficiently different.

I don’t have the time to go into more detail but it’s worth noting that your comment about intuition is an important point depending on your view of what possible worlds are. However, there’s definitely an overarching challenge to views according to which we should rely on our intuitions to determine what is possible.

Hope that helps clarify.