Parmenides was greatly influenced by the Pythagoreans. He invented formal logic by applying their mathematical methods of proof to the philosophical problem of the natures of being and not-being. Presenting his argument in the form of an epic poem, he used logic to show that being is unchanging and uncreated. This conclusion denied the possibility of any appearance of variety or change. A corollary to this positive, if mystical, conclusion was that human reason has the power to understand reality.
He is, then, not only foundational for understanding later generations of Greek philosophers, but also many modern philosophers, starting with Descartes: the philosophical admiration for the strength of mathematical reasoning has led a diverse set of people - from Spinoza to Hegel, from Wittgenstein to Quine - to model various branches of philosophy on the patterns of proof and theorem found in mathematics. Parmenides touches on another central point in philosophy: he poses a question about the strength and abilities of human reason. To be sure, he also answers that question - and thereby finds for himself both a number of allies and opponents. It is the question that is the beginning-point for Kant’s philosophy: which questions can human reason answer, and which ones can it not answer? Such a question is properly prior to any philosophizing, because before we can try to answer any further philosophical questions, we should first know whether or not those questions can be answered at all, and whether it is human reason, or some other faculty, which might be able to answer them.
Interestingly enough, Parmenides also wrote about astronomy, biology, and other sciences. Yet if his main insight was sound, the many changing things these sciences study could not be real. Vividly aware of change and the individuality in the world they observed about them
later Greek philosophers would try
to find ways to keep Parmenides’ logical method but to avoid his mystical conclusion.
It doesn’t bother Parmenides that the natural sciences must be, on his terms, dealing with what are illusions. He is content to deal with the parade of images presented by, as, or through sense-data, while realizing that they are merely images, that there is no underlying change behind the image of change, no underlying coming-to-be behind the image of coming-to-be, and no underlying passing-away behind the image of passing-away. Again, one sees here the seeds of Kant and phenomenology: the seeds of the former, inasmuch as the logic of causal relations in the phenomenal world does not apply to, or even entail the existence of, the noumenal world; the seeds of the latter, inasmuch as Parmenides brackets, even if he has already answered, the questions about the existence and natural of the noumenal world. Parmenides (as synopsized by the Brumbaugh) sets up his argument:
Suppose someone assumes that being is divided into many separate beings. Then what is it that separates them and holds them apart? It cannot be being, for then all of the parts would still all be together in one totality, and it not be distinct. On the other hand, if one says things are separated by not-being this leads to absurdity. For not-being, if it is the opposite of being,can only be a void, a kind of pure nothing: if one says that non-being is a separator, he is treating it as being, which by definition it is not. If one says that though it is nothing, it still separates the parts of being, this is the same as saying that “nothing separates being into parts,” which in fact is a statement denying that the parts are separated. How can nothing do something positive? The idea is self-contradictory.
Parmenides is both making a specific metaphysical statement here, and also laying down a principle for argumentation in general:
In explicitly recognizing that noncontradiction is a fundamental property of existence, as well as of thought, Parmenides hit a upon a most important principle. Once it is recognized that only consistent entities can exist, the truth of generalizations can be tested by examining their consistency.
It is worthwhile to sharpen the notion “that noncontradiction is a fundamental property ... of thought.” One might more specifically say “ ... of rational thought” or “ ... of logical thought” or even “ ... of significant thought,” for a self-contradictory sentence, and the proposition which is represents, cannot signify, i.e., cannot have a referent. The net impact on philosophy
was to reinforce philosophical formalism by showing that there is a close connection between reality and abstract logical form, and to make philosophers more conscious of the methods by which they arrived at their conclusions.
Future philosophers would appreciate “the value of precise logical form,” an impact which places Parmenides into the category of very important philosophers!
