LEGO Bricks and Fundamental Properties

So much for the metaphysics of LEGO. How does it compare to the metaphysics of the real, actual world—our universe? As with many other philosophical questions, there is no consensus view. For a long time, the world was believed to be made up of four elements—Earth, Water, Air, and Fire. On that view, the world bears very little resemblance to a MOC. But according to the view that has perhaps been most influential in metaphysics in the last few decades, our world is strikingly like a LEGO world. The view is called “Humean superve- nience” and was formulated and defended by the American philosopher David Lewis (1941-2001). Roughly, it is the claim that basically, the world is just an arrangement of fundamental properties.

A fundamental property is a property whose presence is not to be explained in terms of any other properties. Weight is not fundamental, since it is to be explained in terms of mass and gravitational attraction; the latter is in turn explained in terms of masses of other bodies. Plausible examples of fundamental properties are those that play a role in fundamental physics, such as mass, electric charge, and spin.

On Lewis’s view, the things of which the fundamental properties are properties are not familiar extended things like you or me. They are very small: points of space, or more precisely, of space-time. The fundamental properties obey a principle of re-combination: the instantiation of one of them is fully independent of the instantiation of another one, either by the same or by different points. This is sometimes expressed by the slogan that “there are no necessary connections”— things could be arranged differently.

Lewis introduced Humean supervenience as follows (using the term “qualities” for fundamental properties):

Humean supervenience is named in honor of the greater denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. ... We have geometry: a system of external relations of spa- tiotemporal distance between points. ... And at those points we have local qualities: perfectly natural intrinsic properties which need nothing bigger than a point at which to be instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else supervenes on that.1

The “greater denier of necessary connections,” after whom the view is named, is the Scottish philosopher David Hume (1711-1776). To say that something supervenes on something else is simply to say that you cannot change the former without changing the latter.

If Humean supervenience is true, then our world is fundamentally like a LEGO world. Space-time corresponds to the base plate, and the bricks correspond to fundamental properties. It is obvious that in a LEGO world, everything—how many houses and chairs and windows there are, for example—supervenes on how the bricks are arranged. To make another house, you will have to add to or modify the arrangement of bricks.

Lewis himself liked to compare the world to a mosaic or a dot matrix. But a LEGO world would be an even more apt comparison, because it is three-dimensional rather than two-dimensional. (His own passion was model railways, not LEGO creations. Perhaps this is why the LEGO metaphor did not occur to him.)

What reasons are there to believe that Humean supervenience is true? There is no particular observation to support it. Rather, the view is recommended by a very general methodological principle called the principle of parsimony or “Ockham’s Razor” after the fourteenth- century friar William of Ockham (1287-1347): “entities are not to be multiplied beyond necessity.” In other words, we should not believe in more things than we need to. Now it can be argued that we need to believe in the existence of fundamental properties and in space-time anyway—metaphysicians are ill-equipped to challenge the authority of physics on that point. If we accept Humean supervenience, then we do not acknowledge the existence of any further things beyond those. Hence we comply with Ockham’s Razor by accepting Humean supervenience.

This provides us with an argument for Humean supervenience only if rejecting the view is not also compatible with Ockham’s Razor. A metaphysician who rejects Humean supervenience would in effect accept further things beyond the fundamental properties and spacetime. His or her view would violate Ockham’s Razor unless these further things need to be accepted. Lewis argued at length that there is no such need—there are no features of the world that could not be explained using the resources of Humean supervenience.

But why, in turn, should we accept Ockham’s Razor as a methodological principle? This is actually a really difficult question, even though the principle is widely accepted in science as well as in philosophy.

We could motivate this principle if we saw the world as a testament to the skill of an ultimate master builder—traditionally called God. Suppose you are instructed to build a real-life scene. Would it take more skill to do that if you had only simple LEGO bricks at your disposal, or if you already had ready-made figures? Clearly the former. So the simpler the elements, the more glory to the creator.

This justification only works if you take it for granted that there is a builder. Once that is in question, Ockham’s Razor can be wielded against the existence of God. A theory that just says that there is a world, and describes it, appears to be simpler than one that says the same thing, and adds that there is also a God that created it. On Lewis’s view, at any rate, our world was not created by a God: it just is. This does not make the world in and of itself different from a LEGO world, however. Though LEGO worlds are built by someone, their builders do not belong to those worlds as parts.

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