INFINITY: Though we exist in an infinite continuum of time and space, human existence if characterized by limitation. Evolution bore human life, and one day humanity will come to an end. Each is born and each will die. The “Now” is the end of an infinite past and the beginning of an infinite future. With minutes, hours, meters and miles, we mark segments to cope with the ungraspable. And with mathematics and physics, we can describe infinity. But the paradox remains: the limited human mind is and probably will always be incapable of perceiving infinity.
ZENO’S PARADOXES: Around a century later, Zeno of Elea advocated several paradoxes known as the paradoxes of motion. Each of them rests on another kind of infinity, the infinitesimal. (fig. 1) The Arrow Paradox describes a flying arrow (fig. 2) which, when viewed in the infinitely smallest fraction of space and time, is stationary.
VAGUENESS: A mother gives birth to a perfectly functioning collection of cells. Once named, the name is virtually the only thing that remains constant until death. ‘We’ – our brains, thoughts, cells, appearances – experience the change in time. Our entire being is, at its end, nothing of what it was at its beginning. And each year that passes, we celebrate. But turning one year older doesn’t make us old, though each of us will eventually be old. So what does the word mean? Like ‘old’ we can only understand most of our words when they are placed in relation to external meaning. We manoeuvre through the world with the help of man-made constructs, creating a system of measurements to compensate for something that our reality doesn’t provide us with: definitude. The absence of boundaries that we experience, we call vagueness.
ORGANISMS: Before evolution masterminded sex and death, life began in aquatic climes and could be seen as one collective entity proliferating through (fig. 1) asexual reproduction. As an unbroken process, it can still be observed today, even on creatures more complex than monads. (fig. 2) On the seabed, when a starfish loses all its arms and each arm grows new ones, is this still the same starfish, or its young? Or on land, when a tree branch is broken off and planted in the ground where it continues to grow, (fig. 3) is this a new tree?
OUR WORLD: Discussed in parallel is the question of whether vagueness simply arises from language or is a feature of our world itself. For example, (fig.1) upon hiking up a mountain, one can see features of the valley left behind. And upon climbing down again, one sees the mountain looming up above. But to look back proudly on the path travelled, can we trace the beginning and end of each peak and trough? If we seek to find a valley line that separates two mountains, is the valley a string of atoms? A path wide enough for a pair of feet to walk through? It becomes a little absurd to debate the line between valley and mountain.
SELF-REFERENCE: The Ouroboros is an image of a tail-consuming snake found documented in several cultures, and it serves as an ancient symbol of self-referentiality. Today, self-reference is still a stylistic mean in artistic and cultural production. Yet not all self-reference leads to paradoxicality – for instance, a movie about movies, or a piece of writing about authors' self-referential qualities. Instead, what is of interest to philosophers is the kind of self-referentiality which circles around its own paradoxicality or traps one in an infinite loop, thus producing some of the deepest paradoxes. Take for example, the self-undermining statement, “This sentence is false”. Referring to itself, the sentence negates its own truth. Thus, if the meaning of the statement is true, then the statement itself is false.