On the infinite:

Required Reading: Infinite divisibility, the paradox of infinite divisibility, infinity,

Any thing that is infinite can be divided into an infinite number of finite parts an infinite number of times. That is infinite divisibility. For example, measurements take an indeterminate volume and use an arbitrary value or increment to divide that indeterminate volume into smaller and smaller finite values.

Every thing can be divided in that way. There is nothing that is not divisible into smaller and smaller parts; nothing that is not infinitely divisible. This applies to the infinite - which by definition is of indeterminate value - like it does to any other thing.

There can only be one infinite thing. That which is infinite is all that there is by definition. Infinity as a quality is absolute, which means that it refers to limitlessness, endlessness, boundlessness, as opposed to a vaguer incapacity for human measurement, which is inherent in the infinite in the first place. An infinite thing extends forever, in all directions, and in all ways (an infinite thing which is not infinite in every respect is not infinite - more on this later). There can be no infinite object which occupies the same space (or non-spatial plane, if such a thing exists) as another, because the infinite is endless such that any other object/entity would be a part of it necessarily.

Whatever is infinite is the only thing there is. That is a confusing statement because as humans we live in terms of the finite; we see differences between ourselves and other objects and we don't normally think of those objects and ourselves as being one thing. You are not the same as a hammer; you are not the same as a giant robotic badger; you are not the same as your identical twin, even. So the idea of being a small part (a finite division) of something much larger would, to quote the vernacular, “blow your mind.” So, in terms of human experience, there is either no infinite thing (because of our perception of objects/entities as being separate and different), or our ideas about the relations between objects must be changed, and all things must be part of the one infinite thing.



Next Week: On infinite time and space, in which I make a really lame argument for why time is infinite, just for the sake of saying so. Then I make a slightly more convincing argument about space, maybe.