There's this paradox I had read about in a book of philosophical problems back when I was in high school. The paradox is about the impossibility of doing anything. The paradox is illustrated through the simple example of closing a door. Before you can close a door, you need to half-close it, but before you can half-close a door, you need to half-half-close it, and so on. Thus, the act of closing a door has to be accomplished through an infinite number of steps. But it is imposible to do a set of infinitely many tasks within a finite amount of time. Therefore, the paradoxical conclusion is that it is impossible to close a door, or to do anything for that matter.
Of course, the conclusion is paradoxical because we are consciously aware that we are able to close doors, among other things. Therefore, for the main premise of the paradox (that doing anything requires going through an infinite number of steps), it does not only have to make logical sense (which it does), but it also has to be reconciled with "reality." Let me take you through some of my thoughts on how the paradox can be resolved.
1. We never really get to do or finish anything. What we perceive as "accomplished tasks" are actually all unfinished work. Because we only have a finite amount of time, we only manage to do a fraction of the set of infinite steps. Maybe this is the origin of human imperfection and the futility of the human struggle. We strive to do things perfectly but we will always be doomed to fail. A person's life, mission, purpose, or search for meaning and happiness will always be unfinished and incomplete. Immortality, divinity, and eternal happiness will only be possible if we have in our possession an infinite amount of time.
2. We all know from basic geometry that a line (one dimension) is made up of infinitely many points (zero dimensions), and a plane (two dimensions) is made up of infinitely many lines (one dimension), and so on. Thus, a collection of infinitely many things, if made finite, will result to something that exists somewhere one dimension higher. Thus, one possibility is that when we do anything (close a door, for instance), the infinitely many steps that need to be accomplished are accomplished somewhere one dimension lower. The collection of the infinitely many steps, transcend to an existence that is one dimension higher, and results to something finite. One implication of this is that the "theory of everything" could be something based on fundamental entities in one or two dimensions. Another implication is that it is possible that finite and concrete existence exists in even higher dimensions than the three-dimensional (four, if you count time) world we are aware of.
3. The paradox can be resolved whether it is postulated that reality is independent from consciousness or that reality is dependent on consciousness. If reality is independent from consciousness, then perhaps in the "actual reality," it is possible to do infinitely many things within a finite amount of time, or maybe some other "reality laws" apply - the possibilities are endless. And regardless of this reality, our consciousness perceives the accomplishment of something finite within a finite amount of time. If reality is dependent on consciousness, then the "reality law" of finite things happening within a finite amount of time, despite the paradox, is merely a creation of consciousness.
Paradoxes are always interesting because they challenge the way we make sense of the world by presenting something that makes sense and doesn't make sense at the same time. Also, paradoxes are intrinsically conflicted and they provoke a conflict in the mind, and so they are representations of the human spirit, for is it not true that throughout history, it is conflicts, whether intra or inter-conflicts, that have pushed humanity forward?
In support of the paradox's conclusion that it is impossible to do anything, I will omit the last word in this
PS. But if I did that I would have been successful at omitting or not writing the last word in this post. I guess that's another paradox. Being unable to do something (complete a blog post, for example) leads you to being able to do something else (the opposite of what you were not able to do, among other things) and so it is impossible to not do anything.
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