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. 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. So, if the analogy works then what is the problem with the ‘what’s in the box?’ argument? Overstepping the analogy Meaning that as a visual analogy the ‘what’s in the box?’ argument works as an example. 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. For until we open it, the box is potentially the set of all objects containing the property ‘weighs three pounds’. 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. With this understanding, we can now see how the ‘what’s in the box?’ argument can be analogous to the above argument. 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! 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. It would contain all manner of animals, tables, chairs, Zimmer frames, and more. Consider the idea of a set containing all objects that have the property of four legs. 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. 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. 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. A set containing only animals that have the property of fur also falls foul of a similar argument. 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. Property (x) is no indication of a singular type of item in a set that contains multiple types of objects. 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. If we break it down into a syllogistic form, we can see it is not a valid argument: 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. Imagining this set shows us that the argument fails at the get-go. If we were to then make an argument something akin to ‘this object has fur therefore it must be an animal’. Most would agree that it would be a huge set of objects. We would have various different kinds of animals, and objects like coats, hats, rugs, and much more, contained in that set. Imagine how large a set would be if we were to insert all things that contained the property ‘fur’. 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. Where Sp(x) is the set of all things containing property x. If we consider it something along the lines of a giant set of objects, with each object containing some shared property. It is, on the face of it, a reasonable argument of course.
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