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In response to Parmenides’ argument, philosophers after him took one of four basic positions. Two groups said reality differs by “non-being” (atomists and Platonists) and two insisted that reality differs in “being” (Aristotelians and Thomists).

Atomism: Things Differ by Absolute Non-Being

The atomists, such as Democritus and Leucippus, argued that reality is constituted of

innumerable and indivisible atoms, which together fill the void of space. Besides differing in size and shape, the atoms differ in space. That is, each atom occupies a different space in the Void.

The Void is any empty container; it is literally nothing. Hence, the basic way one thing (atom) differs from another is by nothing or non-being.

The Void in itself is absolutely nothing—pure emptiness. And yet by occupying different places in this empty space each thing (atom) in the universe is really different from each other thing. So the atomist’s solution to Parmenides’ dilemma was to affirm that things do indeed differ by nothing or non-being—by absolute non-being.

Philosophers have noted a number of criticisms of atomism. First, atomists do not really answer Parmenides’ challenge that differing by absolutely nothing is not differing at all.

Second, most modern thinkers reject the atomistic concept of space as a container. Rather, space is thought of as a relationship. Finally, atoms, once thought to be hard and

unsplittable pellets of reality, have been both split and “softened” into energy by modern science.

Some modern pluralistic philosophers think of the ultimate units of reality as “monads”

(as did Leibniz), which are a kind of qualitative “atom.” Others speak of “eternal objects”

(as did Whitehead), which are unchangeable and potential qualities that may “ingress” into the real, changing world. These revisions of ancient atomism indicate a rejection of the atomistic solution to the problem of the one and many. However, modern pluralists do not escape the logic of Parmenides’ dilemma: how can these units of reality (actual or

potential) really differ in being or in non-being? Unless there is a real difference in being, then Parmenides wins—all is one.

Platonism: Things Differ by Relative Non-Being

Plato provides a somewhat different answer to Parmenides. He spoke of a “receptacle” in which the mixture of all things is contained (this is the analogue of the atomist’s Void). Later, however, he also used the principle of “otherness” to distinguish one thing from another. This has been called differentiation by relative non-being, because it affirms that all determination is by negation. For example, we define or identify the pencil by showing that it is not the table, not the floor, and not everything else. This does not mean that there is not anything else, but simply that the pencil is not everything else. Hence, this is called the principle of relative non-being, since relative to everything else the pencil is not everything else. All differentiation is by negation. A sculptor “differentiates” the statue from the stone by chiseling away (negating) all that is not the statue. In this same way, suggested Plato, everything in the real world (i.e., the world of Ideas or Forms) can be differentiated from everything else.

There are a number of ways this solution can be criticized. First, Parmenides would ask how differing by non-being (relative or not) can be a real difference. If being is what is real, then non-being would be what is not-real. Hence, if things differed only by non-being, there would be no real difference between them. Second, other philosophers would ask how all determination can be by negation. How would the sculptor know when to stop chiseling the stone unless he first had some positive idea of what the statue was to be? Finally, if all determination (and differentiation) were by negation, then it would take an infinite number

of negations (of everything else in the universe) in order to know the identity of anything.

But this is impossible for a finite mind.

Aristotle: Things Differ in Their Being (Which Is Simple)

After Plato the next most significant answer to Parmenides was that of Plato’s most famous student, Aristotle. The ultimate items of reality in the universe for Aristotle were not atoms (as for Democritus) or ideal Forms (as for Plato), but were Unmoved Movers (gods). There were forty-seven or fifty-five of these Simple Beings, depending on which astronomer was right (each Mover moved a different sphere of the heavens). These beings were simple (uncomposed of form and matter) or pure forms of Being. Each was a simple being in itself and yet differed from the others, which were also beings. They literally differed in being, since they were beyond space and moved everything in space. All forms in the material world differed in their matter (and space), but pure Forms (gods) had no matter, so they differed in their very being. Each was an uncomposed being and as such it differed from the rest.

A number of criticisms can be mentioned. First, Aristotle himself (or a later editor of his Metaphysics, book 12) noted a serious problem: in a universe with multiple gods there would be no unity. Indeed, it would not be a uni-verse, since each Being (Unmoved Mover) operates in his own separate sphere, uncoordinated with the others and unsupervised by a superior Being. Second, Aristotle does not really answer Parmenides’ problem of how things can differ in their very being if there is no real difference in their being, since each is a simple being. If each Being is the same in its being with the others, then there would be no difference between them.

Aquinas: Things Differ in Their Being (Which Is Composed)

Aquinas made a unique contribution to the problem of the one and the many. He argued for both unity and diversity within being itself. Aristotle thought of being as simple; Aquinas thought of finite being as compound or complex. Finite being for Aquinas was composed of actuality and potentiality. There can be different kinds of beings, depending on their potentiality.

Some beings (like men) have the potential for being rational; others (like tomatoes) do not. These different potentials are real. For example, there are real differences among the potentials of an acorn, a monkey, and an Albert Einstein. Potentials make a difference, argued Aquinas, in the kind of thing a being is.

Aquinas’s answer to Parmenides, then, was twofold. First, according to Aquinas, Parmenides begs the question by assuming a univocal view of being. If being is understood as meaning entirely the same thing, does not one necessarily end in monism? Second, if one understands being as analogous (similar), then there can be many different beings all sharing in being. The doctrine of the analogy of being, as used by Aquinas, shows how things can be many in their being (there can be many different beings) since they have different potentials.

There is unity in being since, for Aquinas, only one thing is Being (God); everything else has being with differing potentials. God is pure actuality; every other being has potentiality in its being. Hence, the actuality of every finite being is analogous to God’s actuality, since

it has actuality and He is actuality. However, finite beings have potentiality in their being and God does not.

Aquinas apparently gave an adequate Christian answer on the level the problem was posed, that is, on the level of being. In short, one must either (1) accept some kind of analogy of being, (2) accept monism, or (3) take the problem out of the category of being and place it in other terms. This latter alternative was taken by Plotinus.

Plotinus: