Heraclitus and Parmenides were two Pre-Socratic philosophers who took radical steps to resolve the problem of ontological dualism which plagued the philosophical systems presented by earlier philosophers such as Thales and Anaximander. These earlier systems basically held that there are two fundamentally different types of being or existence, one level composed of or represented by all of the finite objects of daily experience, and one transcendent, eternal, infinite level which gives rise to all of these finite beings. However, such a conception of existence poses a problem when one attempts to work out how it is possible for the two different levels of being to interact with one another, an interaction which is a necessity if Being is to somehow give rise to all of the finite beings in the world.
Heraclitus' radical solution to this problem involves the elimination of Being, the arche, the transcendent, eternal fount of all finite beings. Instead, Heraclitus proposed that all there is in the world are the finite beings and the process of becoming, or change, through which all of them must go. All there is are the objects of our sensory perception, and, what is more, every single one of these objects is constantly changing on its road. Thus, for any given object, there is no moment of coming into existence or passing out of existence. Instead, every single moment is a moment of passing out of what previously existed and passing into what will exist.
Parmenides, on the other hand, resolves the ontological problem by eliminating the ontological category of individual, finite beings and the process of becoming through which they all go. Parmenides reached this conclusion through the use of nothing but pure reason. He argued that, since the mind cannot think about nothing, "nothing" cannot exist. The process of change and becoming, to which all finite beings are subject, involves their negation. If a being is something one moment and something else the next moment, then it is no longer what it was. What it was has been negated, that is, become nothing. However, since nothing cannot exist, the logical conclusion to which Parmenides' argument leads us is that the ontological category of finite beings, which depends upon nothingness and negation, cannot exist. This lead Parmenides to draw a further distinction between doxa, or everyday experience, and the Truth, which can only be discovered through the use of logos. To Parmenides, the Truth is that there is no change, no becoming, and no destruction. Instead, transcendental, eternal, unchanging Being is all there is. Furthermore, this Being is an undivided whole.
Heraclitus' position is far stronger than Parmenides', mainly because Parmenides' argument contains several logically problematic steps. First of all, Parmenides assumes that what cannot be thought does not exist. This is an unwarranted, unprovable reversal of the first step in Parmenides' argument. Just because what does not exist (nothingness) cannot be thought doesn't mean that only what can be thought exists. In order to take such a step, Parmenides must make a case for pure reason's ability to discern what exists being better than our empirical reason's ability to discern what exists. However, even if we grant Parmenides this point, his argument still contains a contradiction. Not only can a person not think of nothing, a person cannot think of infinity. The Being which Parmenides proposes to be the sole ontological substance of reality is, by his own description, infinite, unchanging, and eternal. All three of these qualities are unthinkable by the human mind. Thus, just as becoming was proved impossible by our inability to think of the nothingness upon which it rests, so is Being proved impossible by our inability to conceive of the infinitude upon which it rests, and poof!, all of existence vanishes.