Practical  Paradox #1991991:

I have no confession to make – there has been a problem. A delay, no less. It came about because I was trapped, practically. I was brought out of it by Andrew, a student at The University of Rummidge’s philosophy grad school, who diagnosed the following practical paradox:

Some delusional or confabulatory disorders involve the subject refusing to accept or believe that they have an illness, disability or injury. I’m not thinking about linguistic aphasias, where the subject struggles to communicate a belief, but cases where they’re convinced that there’s nothing to communicate. In these cases, there’s a practical paradox which can prevent the subject from getting diagnosed and treated: they don’t think that they’re ill, so they’ve got nothing to discuss with a physician.

Usually, friends or loved ones eventually take the subjects to be treated, often because the disorder is affecting their well-being. This fits the structure of practical paradoxes discussed so far: the way you get out of a practically paradoxical situation is through the intervention of an external agent.

Stones into the future

How Something Can Be Within Our Power Even Though We Can Have No Causal Effect On It, Or Maybe Not, With Apologies To Newcomb

A time traveller appears to you. (He really is one, you believe that he is, and you believe it for good reasons). He tells you that he is from the future. He just visited tomorrow, and saw that a certain man (call him Steve) is going to play the lottery. Steve is going to receive some number of millions of dollars. This number could be zero. It could be 100. It could be any other number. The time traveler does not specify.

The time traveller also indicates a box nearby, and points out all the stones on the ground around where you are. (You’ve been walking on the beach or something). The time traveller says he has also visited later today, and knows exactly how many stones are going to be in the box at that time. That number could be zero, or it could be any other number. The time traveller doesn’t specify. He does specify, however, that the number of stones that will be in the box is equal to the number of stones you are going to put in the box in the next five minutes.

The time traveller tells you it happens to be the case that the number of stones that will end up in the box is the same as the number of millions that Steve is going to receive. The time traveller also tells you that Steve is a very good, deserving individual who is sure to do a lot of genuine good with any amount of money he might receive.

“So,” you ask, “Whatever number of stones I put in the box, if any, that’s how much money Steve will get, if any?”

The time traveler hesitates. He doesn’t know that he would put it quite that way. The fact is that the number of stones that are going to be in the box is the same as the number of millions Steve is going to receive. But the time traveller clarifies that he isn’t saying you somehow cause Steve to win that amount of money by doing things with the box and the stones. Rather, Steve’s lottery results are completely the result of whatever the normal causal processes are that go into the determination of lottery results. The balls jiggle around in the basket, and are picked out one at a time, and so on. At no point is there a way for facts about this box and these rocks to have an effect on facts about the winning lottery numbers and the number of contestants playing and so on. It’s just a coincidence that Steve is going to get a number of millions equal to the number of rocks in the box. But it’s no less a fact for that.

So there you are–there’s a box nearby, and some stones. You could put some stones in that box if you wanted to.

The question is, do you want to? More specifically, does anything the traveller has just told you make you want to put stones in the box? Or perhaps, even make you think you should put stones in the box?

Having thought about this for a bit, try to pretend you had never read the above story. Now imagine the very same scenario, but imagine that the lottery takes place the day before, not the day after, your conversation with the time traveller. Does this change your intuition at all?

There are obvious similarities between these two scenarios and that found in Newcomb’s Problem. Do your intuitions about these scenarios match your intuitions about the Newcomb scenario? Should it? (There are also important differences, of course. The time travel element of these scenarios makes the relationship between the prediction and the thing predicted very different than in Newcomb’s problem. Is this a very important difference?).

I have no idea what this shows.

Kris Rhodes


I recently visited a local toy shop – I had a legitimate reason. Downstairs there were toys (lego, soft toys, dumper trucks, etc.); upstairs there were railway sets and model kits (planes, cars, boats, tanks, etc.). Upstairs, there were also small figurines of World War II soldiers, generals etc. Now, clearly the items downstairs were toys; that is to say, they were intended for playing with. The items upstairs were, for the most part, not for playing with. Model planes, tanks and ships, once constructed and painted, are generally too fragile to play with (something I learnt in childhood). Train sets, however, can be used in a more playful way – though enthusiasts probably would object to that description. The small (and very expensive) figurines of Hitler and other Nazi high officials could be played with (e.g. on a mock battlefield), but that is clearly not their primary function; they are rather intended to be displayed. (They are akin to ornaments; the sort of things my grandma used to show off in a glass-fronted cabinet). One corner of the shop had hundreds of ‘classic cars’ in boxes. These were not models insofar as they were ready-built. Again these could be used for playing with. But (again) given their price, it seems likely that they were intended for display purposes.

What is a model? Well, models tend to be much smaller than the ‘real thing’, and tend also to not be functional. I take it that a ‘real’ boat one had on display in the front garden – a boat that was no longer sea-worthy – would not qualify as a model boat. Is this because it was once functional? What then about a life-size boat one built from assorted reclaimed wood and metal? This boat was never functional, but it seems odd to call it a ‘model’. Perhaps its scale is a determining factor here? But then imagine the same constructed, non-functional boat as one third or half the size of a ‘real’ boat. Would that be a ‘model’ boat?  Some ‘model’ planes can be flown (gliders or remote control), as can some model boats be sailed etc. So being functional – in some sense – does not seem to prohibit something being a ‘model’.

Here is the question: How does one distinguish between a model, a toy, a replica, and an ornament? What prompted this question was the following thought: If I was to say that I collect ‘model cups’, what might that mean? A very small cup is presumably still just a cup – albeit one that is hard to use – not a model of a cup. Even if this item had to be constructed (two halves glued together, or something more complicated) it is not clear it would be a model cup. Rendering this item unusable – e.g. by drilling a hole in the base – would not make it a model cup either. Perhaps then there are some things that are just not model-apt? What, if anything, makes something model-apt?

I have no idea what this shows.

Lonely and Helpless

[I have this inchoate idea about practical paradoxes that could benefit from being idly aired  – I think perhaps by regularly posting examples of such paradoxes we might help to eek out the kernel from within its shell. Let’s make this a running feature, with occasional reflections on the argumentative-state-of-play. Here I’ll just try to sketch the ballpark]

Thesis: A certain stripe of practical paradoxes seem to presuppose some sort of soliptical outlook.

Practical  Paradox #3172226:

I’ve had a rough night doing things I’d rather forget. I have the hangover of a Colossus crammed inside my averagely-and-fetchingly-proportioned skull. The first thing I must do is administer myself a huge dose of coffee. In fact, without any coffee I won’t be capable of doing anything at all. The problem is that I’m so hungover that I can’t even make coffee: I need a coffee before I’ve the capacity to make one.

Practical Paradox #00126823:

I’ll spare you the details, but last night I did something incredibly regrettable. Exceptionally regrettable. So regrettable that I think I’ve forced myself to partially forget it, and I don’t ever want to remember it – I certainly don’t want to see it again. But worse than that, I filmed it using a clunky old VHS camcorder. Worser and more worse, I taped over the middle (boring) part of my wedding video. I can’t throw the video away (it might end up in the wrong hands, and everyone’ll see what I did). I can’t destroy the video (I’ll lose the wedding footage). I should tape over the rebarbative part of the reel with some nice soothing snooker. But in order to ensure I censor only the reprehensible scenes, I’ll need to watch them: to see when the debauchery begins and for how long it persists. I have to see it again because I don’t ever want to see it again.


It can seem to be easy enough to think up ways out of practical paradoxes. With the first case, we imagine the sudden arrival of the local Star*ucks door-to-door representative, who prepares the recommended prescription of caffeine.

But it’s a bit trickier with the second case: the dilemma is between what I want (that no-one should see the footage) and what needs to happen (that the footage is deleted, which requires that it’s seen). We can’t just hand over the practical duties to another person, since we desire that no one else sees the footage.

Similarly with the coffee case. We can build the example in such a way that I would be so incapacitated by my hangover that I couldn’t even open the door to the coffee-delivery boy, much less invite his participation in curing me. The benevolent coffee deliverer would have to arrive unprompted and uninvited; in fact, he’d have to force his way into my house to give me the dose.

All of this seems a bit like cheating – it’s our example, why should Costa-dosemen be allowed to barge into it like this? It seems a bit like cheating because we feel the familiar intellectual pull of paradoxes, and we have a familiar sense of what is fair-play by paradoxes and what is not. I suppose this suggests that there’s a certain type of practical paradox that seem to have a soliptical attitude built in: we presuppose that the agent in the paradox is quite importantly alone if the paradox is to work. The latter case builds it in explicitly.

I have no idea what this shows. 

Should I Take The Key With Me?


Starting from a simple example, I argue that there are cases in which two equally plausible and important principles of practical rationality may conflict. The two principles are:

(R1) One should choose the option with the highest expected utility;

(R2) If an option is believed by the actor to be superfluous, then one should choose another option (which differs in this respect).

Since there is no obvious way to rationally decide for one and against the other principle, we have a paradox here. It is similar to, but not identical with Newcomb’s problem. Our paradox is an important one and it is hard to see what a solution could look like.

The Example

I have just moved out of my office and handed over the key to Jones. As we leave the building, I wonder whether I “really” did lock the office door. I am quite sure that I did lock the office door but I am not absolutely sure. Since I want to be “really” sure, I decide to go back and check the door. Otherwise, I would keep on worrying about the door for some time. Jones has already stored the key in the bottom part of his backpack. He offers to get the key out of the backpack. I decline: I believe that most probably I did lock the door and I do not want to bother Jones just because of some remote possibility. However, if I should go back without the key and find the door unlocked, I would need to return to Jones, ask him for the key and go back to the door a second time. Jones tells me that I am being irrational: If I take the possibility of not having locked the door seriously, then I should take the key with me in order to be able to lock the door just in case I did not do so before we left the building. Is Jones right? Is my refusal to take the key with me irrational? I will start with an argument for a negative answer and the present an argument for a positive answer. Since both answers are equally good ones, we seem to have a paradox here.



Suppose my options are the following ones:

A) I do not go back;B) I go back without the key (if I find the door locked, I get back to Jones and we continue our walk; if I find the door unlocked, I go back to Jones, get the keys and return a second time to the office to finally lock the door, then get back to Jones to continue our walk);C) I go back with the key (if I find the door locked, I get back to Jones and we continue our walk; if I find the door unlocked, I lock it, get back to Jones to continue our walk).

Suppose further that:  

  • my subjective probability that I did not lock the door is .1;
  • my subjective (dis-)utility of leaving the door unlocked and keeping on worrying about the door for some time is -18;
  • my subjective utility of not going back but keeping on worrying about the door for some time even though it is locked is -3;
  • my subjective utility of making the effort to go back once and of letting Jones wait is -1;
  • my subjective utility of going back to the door twice and of bothering Jones with the key is -7;
  • my subjective utility of making the effort to go back once, of letting Jones wait and of bothering him with the key is -6.

Given these (not unrealistic) assumptions, the expected utilities of my options are as follows:

A: -4.5;

B: -1.6;

C: -6.

Hence, the best thing for me to do would be to go back without the key; going back with the key is even much worse than not going back at all. B is better than A and A is better than C (B>A>C). Rationality thus demands that I go back without the key.



This, however, contradicts a second argument put forward by Jones (see above). According to this argument, choosing B is blatantly irrational. Jones argues that if I go back, then I should take the key with me; going back and not taking the key with me is even worse than not going back at all. According to Jones, C is better than A and A is better than B. Jones thus argues for the “opposite” ordering of the options. But what exactly is the second argument?


According to Jones, plan B is problematic in a special way because its first part[1] (going back without the key) is problematic in a special way. There are exactly two circumstances here: Either the door is already locked or it is unlocked. If it is already locked, then my going back (with or without the key) is superfluous. If the door is unlocked, then my going back without the key is superfluous, too. Whatever the circumstances, my action of going back without the key is superfluous. And I know all that. Thus, my going back without the key “does not make sense” insofar as 

  • The actor believes that his action is superfluous.

Since it is irrational for an actor to perform an action that he believes to be superfluous, it is irrational to choose B. Hence one should rather choose A or C.[2] Rational actions must fulfil the “condition of making sense”: The actor must not believe that his action is superfluous. To be sure, it does not help to point out that only the first part of plan B suffers from this defect: No other part of the plan gives me a reason for not holding the action proposed by the first part to be superfluous.



But what then? The first argument led to the conclusion that I should rather go back and not take the key with me than go back and take the key with me. The second argument lead to the opposite conclusion that I should rather go back and take the key with me than go back and not take the key with me. The two conclusions contradict each other but both arguments seem (equally) convincing. Hence, we have a paradox here. How can we resolve it?


Let us look at the source of the contradiction. It seems that the two arguments rely upon different and conflicting principles of rationality. The argument for not taking the key with me relies on a principle that takes subjective probabilities into account:

(R1) One should choose the option with the highest expected utility.[3]

The argument for taking the key with me, however, relies on a principle of rationality that does not take subjective probabilities into account: 

(R2) If an option violates the “condition of making sense”, then one should choose another option (which does not violate this condition).[4]

In a way, our problem is similar to Newcomb’s problem: There are cases in which two (equally) plausible principles of rationality conflict. Furthermore, one of the principles is the principle of expected utility whereas the other principle does not take probabilities into account at all. And as in the case of Newcomb’s problem, it is hard to see how the conflict can be resolved. If rationality is a coherent notion (and we better hope it is), then there must be a solution. But what is it?

I have no idea what this shows. [5]

Peter Baumann

[1]             The first part of a plan need not be the first stage of its two or more stages of the realization of the plan. If I find the door locked, then there is no more stage of the realization of my plan (there are more stages only if I find the door unlocked). This illustrates the fact that parts of plans are not the same as stages of plans.

[2]             Neither A nor C suffers from the above defect. – One can consider this defect to be a violation of the requirements of instrumental rationality.

[3]             If there are two or more options with the highest expected utility value, the principle must be modified:

(R1′) One should choose an option such that there is no other option with a higher expected utility.

For the sake of simplicity, I disregard this complication here.

[4]             There always is another such option – if only the option of not choosing a given option. – (R2) does not tell us which of several other options to choose but it is sufficient for our purposes here.

[5]             For discussion and comments I am grateful to Abdul Raffert, Thomas Schmidt, Barry Smith, Kyaw Tun, and Truls Wyller.

Rationality Locked Down

Suppose I was the kinda guy who’d work late at the office. As I’m coming out of the reprographics room and look down the corridor I spot a burglar trying the handles of the locked doors of the offices on either side. He’s tiptoeing along in his stripy sweater, absorbed in his stealth, so he doesn’t notice me. As he turns to try another door, I see he’s got a big bag with ‘SWAG’ written on it slung over his shoulder. I also see that this is my opportunity to act – I don’t have long, just a moment.

The range of possible actions I could carry out are severely limited. It seems that I could either:

a) reach out and lock my currently-unlocked office door,  or

b) reach out and unlock Bob’s office (immediately opposite mine)

but not both.

If I lock my office door, I’ll secure my ever-so-valuable possessions within. But I happen to know that Bob’s office has an impressively large cage mounted above the door: a hair-trigger automatic device means that anyone entering the room is immediately ensnared unless they’ve already deactivated the system. So if I unlock Bob’s room, the would-be-burglar would be caught.

A good case can be made for both a) and b). [I won’t consider the third case – doing nothing and leaving my door unlocked but Bob’s door locked].

By deciding to lock my own door [option a)], I prevent the would-be burglar from committing any crime. That is, although this pantomime figure may be thinking about committing theft, I can help to free him from any wrong doing by denying him any opportunity to do so. Moreover, I also secure my valuables – I remove the risk of having to suffer the unbearable consequences that my copy of Aqua’s stunning debut album ‘Aquarium’ might be handled by a stranger by placing it firmly behind a locked door.

By choosing to unlock Bob’s door [option b)], I prevent the would-be burglar from committing any crime. That is, although this pantomime figure may be thinking about committing theft, I can help to free him from any wrong doing by incarcerating him. Moreover, I also secure my valuables – I remove the risk of having to suffer the unbearable consequences that my copy of Aqua’s stellar second album ‘Aquarius’ might be handled by a stranger by placing him firmly behind bars.

So far, so even, or so it seems. Perhaps a little more analysis is called for. 

By taking option a), I leave it open that the burglar may head on into the world and commit other terrifying thefts. I may have protected his eternal soul (and the possessions of some other hapless citizens) this time, but tomorrow he could be bundling Britney LPs from babes-in-arms, depriving them of their one true joy and sending himself to hell. But at least my stuff is safe.

By taking option b), I might prevent the burglar from enjoying future freedom-of-theft, but by leaving my door open I leave my stuff at risk. For what if this sneak-thief tries my door before Bob’s? I guess I’ll just have to hope that once he’s grabbed my LPs he’ll be so swollen with self-assurance that he’ll try his luck on Bob’s door, and then he’ll be trapped. I’ll be able to reclaim my possessions in the morning (although I can’t imagine that I’ll feel the same way about them), and he’ll be looking at a lengthy stretch. But of course, it might be that once he’s acquired some Aqua, he’s no longer interested in taking any more risks, and he’ll hotfoot it away from Bob’s office before the fuzz get on his tail. In which case he’s got my Aqua and he’s a grand-theft-felon at-large.

If I lock my door, I’m acting out of self-interest: my stuff is definitely safe, but I’m contributing nothing to the security of the wider world. If I unlock Bob’s door, I’m taking a risk for the community: my stuff is much less secure, but I’ve raised the possibility that the thief will be caught.

I have no idea what this shows.