4D, 3D and 2D

No three-dimensionalist has this ludicrous picture of the human being:

1. The human being is a three-dimensional whole whose functioning derives from the functioning of many two-dimensional slices that make her up.

But some four-dimensionlists have this picture of the human being:

2. The human being is a four-dimensional whole whose functioning derives from the functioning of many three-dimensional slices that make her up.

But it seems to me that (2) is not much better than (1). Just as we should be very dubious that there are any such things as two-dimensional slices of us—infinitely thin slices—we should be very dubious that there any such things as three-dimensional slices of us. And even if there are such slices, they are more like abstractions than components from which we derive our functioning.

So just as all three-dimensionalists deny 2D-slicism, all four-dimensionalists should deny 3D-slicism.

Now, let’s turn to three-dimensionalists. The following proposition is crazy:

1. The human being is two-dimensional.

But some think:

2. The human being is three-dimensional.

Why think (1) is false? The best reason is that the characteristic functioning of a human being requires more than just an infinitely thin section. Any thin section—whether infinitely thin or of non-zero thickness—through a human being is going to be quite unnatural, being intimately connected causally to other sections that are just as important to the characteristic functioning of a human being.

But the same reason applies against (2). Any temporally thin section—whether infinitely thin or of non-zero temporal thickness—through a human being is going to be quite unnatural, being intimately connected causally to other sections that are just as important to the characteristic functioning of a human being.

A secondary reason against (1) is that it is implausible that are privileged 2D slices. But likewise it is implausible (though maybe a bit less so) that there are privileged 3D slices.

Where does all this leave us? We should be at least four-dimensionalists (there might turn out to be more dimensions), and we should not think of ourselves as derivative from 3D or thinner slices. We should, indeed, be sceptical of the existence of such slices.