The fragments of Parmenides provide the earliest formulations of the laws of thought that Aristotle later most famously formalized. (p. 58, 2.B2) His philosophy runs in direct contrast to that of Heraclitus who sought to create a philosophy that could accommodate the flux of the universe with the simultaneous paradoxes arising from change. Most likely influenced by the Pythagoreans and their conceptions of the capacity to reason, Parmenides sought to rely on understanding (capacity to reason) as a means of discerning the truth of what-is. This essay will begin by summarizing Parmenides’ account of what-is and what-is-not before exploring the question of why we cannot investigate what-is-not. It will conclude by discussing whether it is possible to learn about what doesn’t exist and delve into the potential implications of such a possibility.
Parmenides writings revolve around his effort to provide an account of the nature of truth, something that he referred to as what-is. He sought to distinguish between the genuine thought and knowledge that corresponded to truth and the belief that represented deception and error. For Parmenides believed that there are only two routes of inquiry for thinking; one that is and therefore cannot possibly not-be, and the one that is-not and cannot possibly be because it does not exist. (p. 58, 2.B2) He deployed a dualistic metaphor of day and night to illustrate his distinction between what-is and what-is-not and the truth and illusion they reflect. (p. 61, 9.B9)
According to his writings, what-is is that which is real and conceivable to the mind. In this way genuine thought and knowledge must be able to be imagined and conceived. He shunned the senses, equating sense-experience to mere illusions and delusions derived from erroneous opinions. For Parmenides what-is, or that which truly exists necessarily, extends beyond that phenomenal world and the various names and guises that follow from it. (p. 59, 8.B8.40) He lists the attributes of what-is as being whole and complete, universal and common, spread out evenly in every place. (p. 59, 8.B8) What-is is a continuous and indivisible plenum, since there can be nothing but what-is that separates it from itself. The truth of what-is corresponds to the idea of reality. Additionally, it is immovable and finite since what-is cannot move or extend beyond itself.
Seen in this light, Parmenides presents an account where time, and therefore change, does not exist. What-is is immutable, unchanging, and impervious to development: it is the irreducible essence of reality. Parmenides thought this perfectly balanced, complete and unbounded, finite and inescapable what-is represents a perfect sphere. One may conclude that Parmenides is essentially equating what-is with we now refer to as matter or, its equivalent via Einstein’s mass-energy equivalence equation, energy.
In contrast to what-is, Parmenides describes what-is-not as belief without understanding, saying that what-is-not is various and subject to change. In this way opinions about the sensory world are mere probabilities and not truth. He argues that one cannot even think or speak of what-is-not, otherwise it would be what-is.
Parmenides states very clearly throughout his fragments that what-is-not cannot be investigated, but the question is why? He explains that what-is-not simply doesn’t exist and, as a result, cannot be subject to the capacities of reason to yield any truth. If it did exist, it would be what-is. His characterization of beliefs and opinions and the deceptive what-is-not they render may be tantamount to our reliance on erroneous memories and past experience for determining what is true. Attempts to derive truth from beliefs about past sense experience may lead to inaccurate beliefs since there may presently be no veridical experience to refer to. For instance, one may recall a square and a circle, but there is no possible way to conceive a round square. According to Parmenides then, while it is possible to have knowledge of what-is-not, this knowledge is not genuine and true and, as a result, will lead one to fallacious conclusions. As mentioned, what-is-not is unimaginable and unconceivable, such as freezing fire, or dry water. What-is-not is sheer and utter nothingness and total absence and therefore cannot be the basis for any thought.
While this seems intuitive enough, the reasoning he provides hinges upon a static world where thought, and therefore consciousness, exist in a single continuous moment existing outside of time. For Parmenides, genuine thought is produced when thinking is actively conceiving what-is, when thought is absorbed with the what-is that constitutes the real and exists in the now. This conception of what-is does not allow for motion since motion as a coming to be is a process of passing from non-being into being.
In this way Parmenides dismisses the value of induction for yielding truths and genuine thoughts and therefore maintains a decisively deductive philosophy utilizing the laws of thought found in logic and mathematics that hold certain premises as immutable true. The corollary of this philosophy would lead to the study of pure mathematics or theoretical physics as a means of answering ontological questions of existence and reality.
However, this is not to say that Parmenides’ philosophy is an entirely realistic or pragmatic one. As a creature that relies on sense experience to navigate through the world, and the accretion of memories of past sense-experience to make predictions about the way things will continue to be in the world, we are indelibly bound to rely on certain conceptions of what-is-not when calculating the potential nature of things despite their absence. Humans are finite creatures that cannot possibly rely on perfectly sound logic and pure reason alone for determining the way things exist because we cannot be perfectly acquainted with what-is. As such, it appears necessary that one attempts to conceive what-is-not in an effort to establish and discover what-is, however difficult or alienating that attempt may be.
Entertaining creative thoughts about what-is- not may require accepting the very contradictions and paradoxes that Parmenides shunned as misleading delusions, illusions and deceptions, but that doesn’t guarantee that they will stay that way; nor does it destroy the possibility that such impossibilities, however logically irreconcilable and unimaginable they may initially appear, may pass into being what-is. Modern quantum superposition is such an example of such a previously inconceivable possibility. Attempting to learn about what-is-not may require that we revise our present conceptions of truth and what-is.
It seems that in Parmenides perfect world there people would rely on pure reason for establishing truths. However, the premises of these theoreticians could not accommodate any facts about the world derived by way experience since, as Parmenides held, sense experience is an erroneous and misleading guide to truth.
In conclusion, it seems that the most pragmatic manifestation of Parmenides philosophy that best preserves his axioms would be that of physics. Physics utilizes laws that, as far as we currently hold, assume immutable truth-like properties like those Parmenides sought to capture when he set out to delineate the nature of what-is. These true-laws allow for true premises and therefore the possibility of logically sound or true genuine knowledge regarding what-is which, in turn, may yield more true genuine knowledge. In this way Parmenides’ philosophy may be preserved as a coherent and consistent doctrine where reality is the single inescapable body we now refer to as matter.
 Law of identity (A⇔A) , Law of excluded middle (p v~p) , Law of non-contradiction ~(p •~p)
 This would initially appear to be a point of contention since that which is imagined doesn’t seem to be necessarily rooted in the reality of what-is, other than it is simply because it is conceived by your mind; one can imagine beliefs and opinions, something that Parmenides denies as being what-is.
 See the Laws of Thermodynamics