Parmenides, in his prime in the early 5th century BCE, was a very influential pre-Socratic Greek philosopher. He was one of the leading figures of the school of thought named after his home city – Elea. According to 19th-century Scottish philosopher’s Thomas Davidson’s translation of the fragments available to us from the work of Parmenides, this leading representative of the Eleatic school held the following view: 

“Wherefore that that which is should be infinite is not permitted.” 

_{Parmenides in Davidson¹}

The idea captured in this complicated choice of words is what I try to unpack in this article. And it is no trivial idea. Central to Parmenides’ teaching was his belief that Being Is and Non-Being is not. Non-Being cannot be (exist) because the existence of nothing is absurd, a logical contradiction. When we speak of being, of existence, we can only properly apply such mental categories to something, not nothing. Therefore, the being of non-being is not permitted (not conceivable by reason). If so, then Being is All since there cannot be Non-Being and whatever is, thus, is Being. In the quote, it’s this part: “that which is”. Being. 

The quote goes on to say something even more counterintuitive – Being that is All is, somehow, not allowed to be infinite. If there is only Being and nothing else, then how can it not be infinite? Wouldn’t this imply that Being has an end and that after that follows Non-Being, which is a self-contradiction, as we just established that Non-Being cannot be? This was also the observation of one of Parmenides’ students, Melissus. According to professor Frederick Copleston’s A History of Philosophy, here is what Melissus thought about the matter. If Being is not allowed to be infinite, it must be finite. If it is finite, it would be limited by Non-Being or, in other words, by nothing, by void. But that cannot be true “for what is empty is nothing. What is nothing cannot be.”² So, has Parmenides made a mistake in his thinking here?

Perhaps not. Parmenides goes on to provide further explanation of his strange thought about Being that is All but is not allowed to be infinite: “For it is lacking in naught, or else it were lacking in all things.”¹ What is infinity lacking? Seems like nothing, it contains everything. Yet, if we try and think about infinity as a mental concept, not as an actual space, we see that this concept lacks an idea of ending, of completeness. When conceived as an all-encompassing principle of reality, Being must contain everything, lacking nothing. That includes the sense of being complete and, thus, not boundless.  

It is not an easy thought to grasp and feels rather counter-intuitive. Still, it indicates that Parmenides aimed at an ultimate truth about reality with his notion of Being Is, and I doubt that he saw this as being constituted solely of matter or space. Indeed, it seems that Parmenides’ idea of Being is even more complicated than might appear at first reading. He rejects separating material and immaterial (like body and thought) because, to him, Being is All, it is One. 

Therefore, I can tentatively presume Parmenides conceived of his ‘Being Is’ ultimate truth about reality as a perfect, complete thought in manifested existence. In his own (translated) words:

“One and the same are thought and that whereby there is thinking; Never apart from existence, wherein it receiveth expression, Shalt thou discover the action of thinking; for naught is or shall be Other besides or beyond the Existent”

^{_{Parmenides in Davidson}1}

It is an interesting way of thinking about reality – Being in its entirety is not and cannot be infinite exactly because it is unconditionally complete. There isn’t anything else. This opens further curious avenues of thought about the nature and possibility of change in the world, but that’s for another article.

keep exploring! 

Sources used:

1. Thomas Davidson, Parmenides. The Fragments, 1869
2. Frederick Copleston, A History of Philosophy. Greece and Rome, 2003
3. Image credit: By Raphael – http://www.newbanner.com/AboutPic/athena/raphael/nbi_parm.html, Public Domain, https://commons.wikimedia.org/w/index.php?curid=430442