What’s in the Box?: A Three-Pound Rabbit

Introduction

Imagine that someone presents us with a box. That box weighs three pounds. The person presenting us with the box says that there is a rabbit in the box, and the fact that it weighs three pounds proves that there is a rabbit in the box. This is not the case of course, just because a box weighs three pounds does not prove that there is a rabbit in the box. There could be some other explanation for why the box weighs three pounds. It could be a guinea pig, or a three-pound weight, or numerous other explanations for why the box weighs three pounds. So, the box weighing three pounds is not evidence that there is a rabbit in the box, and therefore we have no reason to believe that there is a rabbit in the box. This is an argument often put forward by a popular YouTuber when debating those that argue for God.

The rabbit and all three-pound things

It is, on the face of it, a reasonable argument of course. If we consider it something along the lines of a giant set of objects, with each object containing some shared property. Something along the lines of S(p(x))={O1, O2, O3 .. O997, O998, O999}. Where Sp(x) is the set of all things containing property x. Looking at it in this form gives us some indication of just how many things there might in any set containing objects with a common property. Consider something like ‘fur’. Imagine how large a set would be if we were to insert all things that contained the property ‘fur’. We would have various different kinds of animals, and objects like coats, hats, rugs, and much more, contained in that set. Most would agree that it would be a huge set of objects.

If we were to then make an argument something akin to ‘this object has fur therefore it must be an animal’. Imagining this set shows us that the argument fails at the get-go. Within that huge set of objects with the property of fur are things that are not animals, so the argument that it must be an animal is one that fails immediately. If we break it down into a syllogistic form, we can see it is not a valid argument:

P1) Animals, hats, coats, and rugs, are objects that have the property of fur.
P2) Object X has the property of fur.
C1) Therefore object X is an animal.

Claiming from a single observation

The fault in the argument should have been clear to begin with, but if not, then the syllogism shows the invalid nature of the argument. Property (x) is no indication of a singular type of item in a set that contains multiple types of objects. The same argument also holds true for a set that contains a single type of item, such as animals, but multiple tokens of that type, such as rabbit, dog, cat, bear, etc. A set containing only animals that have the property of fur also falls foul of a similar argument. If we were to imagine the same set containing only animals that have the property of fur, we can once again see how large that set would be. So, to make an argument like ‘This animal has fur therefore this animal is a bear’ contains the same problems of invalidity as the above argument.

This same problem can be found any time we try to narrow down a single object based on a single property in a complex set. Consider the idea of a set containing all objects that have the property of four legs. It would contain all manner of animals, tables, chairs, Zimmer frames, and more. Saying that an object has four legs is no guarantee that the object is a dog, or a cat, or an animal, or a table, or a chair. An object remains vague when using a single property to assess what it is, especially when that property describes multiple types of objects, let alone multiple tokens of different types of objects!

As an analogy…

With this understanding, we can now see how the ‘what’s in the box?’ argument can be analogous to the above argument. If we consider the box to be an analogy for the ‘set of all objects containing property (x)’ then we can see how the box weighing three pounds cannot tell us that it is a rabbit. For until we open it, the box is potentially the set of all objects containing the property ‘weighs three pounds’. So, just as an object weighing three pounds gives no indication that it is a particular item in the set of all objects weighing three pounds, the box weighing three pounds gives us no indication that it is a particular object in the box. Meaning that as a visual analogy the ‘what’s in the box?’ argument works as an example. So, if the analogy works then what is the problem with the ‘what’s in the box?’ argument?

Overstepping the analogy

One problem is the claim that just because the box weighs three pounds does not mean that it is evidence that there is a rabbit in the box. While the box weighing three pounds certainly does not give us sufficient justification to believe the claim that there is a rabbit in the box, the box weighing three pounds can be considered evidence that there is a rabbit in the box. The box weighing three pounds means that it contains at least one of the objects in the set of all objects that weigh three pounds. If a rabbit weighs three pounds, then it is included in that set of all objects that weigh three pounds. Therefore, the box weighing three pounds means that it has the potential to be a rabbit, meaning that it can be considered evidence towards the claim that there is a rabbit in the box.

We could argue here that the box weighing three pounds means it also has the potential to be any of the other objects in the set of all objects that weigh three pounds. This is true, and cannot be denied. However, this does not mean that it is not evidence that there is a rabbit in the box. As stated already, a rabbit is one of the objects in the set of all objects that weigh three pounds. It is just not, on its own, sufficient evidence to support the claim that there is a rabbit in the box. Just as it is not sufficient evidence to support the claim that it is any other particular object in the set of all objects that weigh three pounds. Evidence is simply any data that is used to raise the probability that a particular conclusion is true. It may be good evidence, it may be bad evidence, it may not be sufficient evidence. However, if it is used to point to that conclusion, and it supports that conclusion in some way, then it is evidence for that conclusion.

‘But evidence is conclusive’

There will be those arguing here that unless something points specifically towards a particular conclusion then it cannot be considered evidence. In other words, data that supports more than one conclusion cannot be evidence for any of those conclusions. Evidence either supports a particular claim, or it supports none at all. This simply is not the case at all. Yes, evidence that supports one particular conclusion certainly raises the probability that some conclusion is the case. It also helps give us sufficient reason to support one hypothesis over another in the case of competing hypotheses. However, it is not necessary that it must point to a single unique conclusion for it to be evidence. So long as the data supports the conclusion being argued for, and raises the probability of its likeliness, then it is evidence for the conclusion. It is also rarely a single piece of data. It is usually a collection of data that is used to make an argument to support the conclusion of a hypothesis. That collection of data is used to raise the probability that the conclusion is likely to be true.

Multiple observations and misrepresentations

Which examples the other problem with the ‘what’s in the box?’ argument. It misrepresents the arguments that it is trying to attack. It argues as if it is only a single data point that is ever presented in support of some argument or conclusion. While that is rarely often the case, even in the case of arguments for something like God. If we consider what Karl Popper had to say about observations and hypothesis formation, then we will see why the ‘what’s in the box?’ argument fails to be analogous.

Consider the idea of someone presenting us with said theoretical box. This someone tells us the box weighs three pounds and therefore there is a rabbit in the box. One of the things we might think will be similar to the ‘what’s in the box?’ argument of course. We will answer that just because the box weighs three pounds that does not give us an indication that there is a rabbit in the box. After all, it could be any object in the set of all objects weighing three pounds. Or could it? Would our observations even stop at the claim that the box weighs three pounds?

Observations and hypothesis formation

Of course not. As Popper says, if we are simply told to observe then we would not begin to form any kind of hypothesis about what is in the box. We would simply begin observing various properties of the box, and collecting data. From those observations, we may begin to form some kind of general hypothesis about the box, but it would not be directed in any particular direction. It would simply be data from which we could form a particular hypothesis. However, if we are told that there is a rabbit in the box, then we would begin to observe particular details about the box that enabled us to form a more detailed hypothesis. We would begin to look for specific details that would either confirm or disconfirm the claim that there is a rabbit in the box.

The box weighing three pounds might raise the probability that there is a rabbit in the box. However, if the box was only 3 inches by 3 inches by 3 inches, we would then use that observation to disconfirm the claim that there is a rabbit in the box. We might also say that if the box was about the size that we would expect to see a box containing a rabbit, then that might raise the probability further that there is a rabbit in the box. Or if the box had no lid, and there was no way to put anything in the box, then we would use that to lower the probability that there is a rabbit in the box. If we had just purchased a rabbit in a pet shop, and the member of staff brought us a box and said our rabbit was in it, then we would assume that the box had a rabbit in it. Multiple observations would be used to raise or lower the probability that there is a rabbit in the box.

+/- Probability

As stated previously, a single observation or property would not alone give us sufficient reason to believe that there is a rabbit in the box. Nor would that single observation or property alone give us sufficient reason to claim that there is not a rabbit in the box. Well, unless that single observation or property alone was a direct indicator of there being a rabbit in the box. An observation like seeing the rabbit being put in the box, or there being a see-through panel where we can observe the rabbit in the box, or buying the rabbit in a pet shop. An ambiguous observation or property can, at best, give us sufficient reason to suspend judgement about what is in the box. Belief formation with such an ambiguous observation at this point would be unreasonable or irrational.

However, as mentioned, in the case of something like that ‘what’s in the box?’ argument, there are multiple observations available to us. Those multiple observations when gathered together, and formed in a hypothesis, enable us to raise or lower the probability enough to form a belief about whether or not there is a rabbit in the box. If the probability that there is a rabbit in the box is low enough, then we have sufficient reason to disbelieve or deny that there is a rabbit in the box. The same is also true in reverse. If the probability is high enough, then we have sufficient reason to believe that there is a rabbit in the box. It might not be enough to claim knowledge of what is in the box of course. We may require further observations that give us justification to claim knowledge, but our observations may grant us reasonable belief if the probability is high enough.

In conclusion

As mentioned at the beginning of the article, as an analogy for what a single property cannot give us sufficient justification for believing the ‘what’s in the box?’ argument works well. It is a great visual analogy for why a single property of an object cannot give us sufficient justification to claim it is a particular object in a large set of objects all containing that property. As an argument for why we should suspend judgement on a claim based only on a single observation or property, it is an excellent analogy. The problem comes when it is used to argue for more than that. This is because it ignores how we would form a hypothesis about what is in the box. It ignores the fact that we would use multiple observations, multiple properties, and multiple arguments to either raise or lower the probability that there is a particular object in the box.

The ‘what’s in the box?’ argument will convince the already convinced of course. Those that argue that evidence is only evidence when it points to a particular conclusion will be convinced. However, that is to misunderstand hypothesis formation. While that kind of evidence can allow us to choose a particular hypothesis more easily, evidence is simply something that allows us to raise or lower the probability that a hypothesis is correct. When the probability of a hypothesis or claim is high enough then it grants us sufficient reason to believe that the hypothesis might be true. If we consider something like a bus timetable. The bus timetable indicates that there is a bus at 1:15pm every day. This evidence points towards a particular conclusion, that the bus will arrive at the bus stop at 1:15pm. Yet, if we were to catch that bus every day for several months, and each day that bus arrived 5 minutes late, then our observations would lower the probability that the bus timetable is accurate. Or say that we know that road works have started somewhere upstream of our bus route, and those road works are causing delays, then that too would lower the probability that the bus will arrive at the time stated on the timetable.

Our multiple observations allow us to separate the hypothesis that the bus will be late from the hypothesis that the bus will arrive at the time stated on the timetable. Even though the timetable points directly to the bus arriving at 1:15pm. We have more reason to believe the bus will be late then that the bus will be on time. The ‘what’s in the box?’ ignores this part of hypothesis formation. It makes a weak argument for why only things that point directly towards a particular conclusion should be considered evidence. It also makes a weak argument when it states that an observation or property that points towards multiple objects in the set of all things containing that property or observation is not evidence at all. For that observation or property is evidence that it is in that set of all things containing that property or observation. We would then use multiple observations and properties to either confirm or disconfirm the hypothesis, as we would in any other circumstance. To argue that we use only a single property or observation is a misjudgement about hypothesis formation. The ‘what’s in the box?’ argument most certainly has its place, but we should remember its place.