The problem of the One and the Many, that is, explaining how one basic thing can be the source of many varied things.
The world contains an enormous variety of objects, some living, others inanimate; some solid, others liquid. It seems reasonable to suppose that all things come from a common source or type of stuff. Identifying that common source, though, is the challenge. This was an issue the Presocratics thinkers grappled with.The theories of the Presocratic philosophers were very daring, sometimes to the point of being bizarre. Being the first ones to venture into the uncharted territories of both philosophy and science, they explored virtually any explanation of things that seemed reasonable. They grappled with issues of the materiality and the non-materiality and their respective solutions to the problem of the One and the many. The Unlimited (the many) and the Limited (the one).
All entities can be thought to result from the Unlimited being limited or determined to some definite shape. This is best thought of mathematically.Unity limits plurality and gives it determinate shape. For instance, the soul is the harmony of the body. Since each number is associated with a determinate shape, we can think of things as being numerical and of mathematics as the key to understanding the world. The materiality was given the fundamental or primary qualities, which come in two pairs of opposites, hot/cold and moist/dry, there are four elements out of which all minerals are composed, each having its own set proportion of elements and from the minerals all other corporeal entities in general are formed fire= hot+dry; air= hot+moist; earth=cold+dry and water=cold+moist.The non-materiality was the changes in the world are produced by two active forces, an attractive force (such as Love or Condensation) and a repelling force (such as Strife or Rarefaction). According to the popular interpretation, each Presocratic philosopher tried to reduce the many to the one by positing one of the elements as the really real material principle and claiming that all the other elements are, appearances to the contrary, simply permutations of that really real one.
Interestingly, each chose a different one of the four. Thales: Water is the really real. (“Everything is full of gods. “) Anaximenes: Air is the really real. (Permutations result from condensation and rarefaction) Heraclitus: Fire is the really real.
(“Everything flows. “) Xenophanes: Earth is the really real. (Protested against theological anthropomorphism. ) What all of this raises, is the question of “the one and the many. ” How can there be any genuine unity in a world that appears to be multiple?To the extent that a satisfactory answer involves a distinction between appearance and reality, the distinction between the way things seem to be and the way they are. The merely apparent is often supposed to be internal, subjective, or temporal, but available for direct awareness, whereas the real is supposed to be external, objective, or eternal, but known only inferentially.
Drawn in different terms and applied in various contexts, the distinction is important in the philosophies of Plato and the use of dialectical reasoning, the process of thinking by means of dialogue, discussion, debate, or argument.