Explain how Parmenides' Theory of the One challenged the existing pattern of philosophical investigation.
At its inception with the Milesians, Greek philosophy aimed at giving an account of the world as we experience it—that is, it aimed primarily at giving an explanation of the phenomena we perceive around us. The earliest philosophical thinkers took it for granted, in other words, that sense perception is not illusory and that an investigation of reality should take its data from experience. In attempting their unreflectively empiricist accounts of the nature of the cosmos, the Milesians set a pattern consisting of three general questions to be asked in any philosophic inquiry: What is the physis, or basic constituent/unifier/original source of matter? How does the plurality of existing things emerge out of the original unity of the physis? And how does the orderly cosmos maintain itself?
After almost a century of philosophy based on this general pattern, however, Parmenides cast the whole project into doubt by maintaining that the fundamental nature of reality has nothing to do with the world as we experience it. By rejecting the senses as entirely misleading and pressing on reason alone to reveal the truth, he came to conclusions about the nature of the world that seemed to suggest that not only were the theories that earlier thinkers proposed utterly unintelligible, but the very questions they asked were the wrong questions to be asking (based as they were on a complete misunderstanding of the nature of what was under investigation). His conclusions about the nature of the world can be grouped together under the heading of Parmenides' Theory of the One.
According to Parmenides, the senses are entirely deceptive, and reason alone can lead us to truth. The nature of the world, then, can only be gotten at through a rational inquiry. When starting out on a rational inquiry, according to Parmenides, there are only two logically coherent possibilities: either you begin your inquiry with the premise that the subject of your inquiry exists or you begin with the premise that it does not exist. But the second of these possibilities, according to Parmenides, is utterly meaningless. It is, therefore, not a real possibility at all. Parmenides bases this claim regarding the path of "it is not" on the assertion that, "that which is there to be thought or spoken of must be." What he seems to be getting at here is an idea that has had extraordinary pull for philosophers through contemporary times: one cannot possibly refer to what is not there to refer to.
Parmenides thus drastically restricts the rational inquiry through which one can get at the nature of reality; this rational inquiry cannot make use of any premise that involves non-existence. The rational inquiry must begin with the premise "it is" and deduce the nature of reality from out of it. What Parmenides ends up deducing is that "what is" is ungenerated and unperishable, unchanging, perfect, one and continuous. The general form of argument he uses for each of these conclusions is along the following lines: whatever is is X, because if not then it is not-X, and in order to explain what it is for anything to be not-X we must talk about "what is not." Since we have already seen the meaninglessness of any thought or statement involving "what is not" we can conclude that whatever is is X. Using this general form of argumentation Parmenides draws out the nature of "what is". He argues, first of all, against the possibility of generation, destruction, and change. In addition, he argues that "what is" has definite limits, is spherically shaped, and is one and continuous. Parmenides' theory led him to reject not only most of the content of all previous philosophical theories, but also the very questions asked. First, it is clear that Parmenides would object to the means by which prior philosophers arrived at their questions. The basic questions the earlier thinkers asked were at least partially motivated by observations they made about the world. They observed that a plurality of things existed, they observed that there were lawful and universal changes that seemed to maintain a certain stability in the cosmos, and they sought to account for these phenomena. Parmenides, of course, would reject the very notion of taking one's explanans from the world of experience since he maintained that there is no truth in what the senses tell us, and thus no reason to assume that the true nature of the world in any way resembles the world as we experience it.
In addition to using the wrong means by which to arrive at their questions, according to Parmenides' picture the questions previous Presocratics thus arrived at were, unsurprisingly, not good ones. The attempt to discover the unifier of all nature is fruitless since there is nothing to be unified - all that exists has always been and always will be unified since all that exists is one. The related attempt to discover that from which all else came is not only fruitless but also inconceivable, since it assumes the existence of generation and change. The plurality problem similarly involves the assumption of change and is based fundamentally on the assumption that a plurality in fact exists. Again, the maintenance problem assumes change, and since according to Parmenides there is no change there is no room for the question of maintenance to arise. In addition to the complete irrelevance of the questions with regard to the pursuit of knowledge regarding the nature of ultimate reality, the content of the theories developed in answer to these questions clearly offend horribly against the Theory of the One. These theories are the result of using a third path of enquiry that confuses the paths of it is and of it is not. This is the path that human beings consistently make use of despite the fact that it is not even a logically coherent possibility: the path that mixes being and not-being. Opposites (which very clearly demand the positing of "it is not")play an extremely large role in Heraclitus, a somewhat lesser role in Anaxagoras, and a small yet still extant role in Anaximenes. Motion (which is obviously a sort of change and thus strictly ruled out according to Parmenides) seems to appear in an explanatory role in almost all of these thinkers. Change is present in all theories, as is generation. And a plurality, both of kind and of number, is asserted regarding existing things.
How did later Philosophers respond to Parmenides' challenge? Show how each of the pluralists attempted to accommodate the Eleatic demands in their philosophical systems. Which demands did each of them accept? Which did they reject, and why?
While some philosophers, such as Zeno of Elea and Milesus of Samos, embraced Parmenides' theory wholeheartedly, attempting to extend and defend his conclusions, the natural philosophers Empedocles, Anaxagoras, and the Atomists returned to both the original aim and the original pattern of questions set by the Milesians. In formulating their theories in answer to those questions, however, they too were extremely influenced by the Parmenidian challenge.
First of all, where their predecessors had largely taken for granted the existence of motion and the trustworthiness of at least some sense-experience, after Parmenides' cogent attack on both these notions these issues had to be treated at length before they could be used in any natural philosophical system. Empedocles, Anaxagoras, and the Atomists, therefore, all sought to formulate an epistemological theory that allowed some credence to the deliverances of sense-experience. They also attempted to give a justifiable account of motion - Empedocles by positing the forces of love and strife, Anaxagoras by positing mind as the motive force, and the Atomists through describing the collisions and make-up of the atoms.
Secondly, in formulating all parts of their theories these philosophers were constrained by those Parmenidian metaphysical demands that they took to be legitimate. Their new challenge was to give an account of the world they experienced in such a way as to accommodate the Parmenidian metaphysical demands.
Both the pluralists—Empedocles and Anaxagoras—and the Atomists were convinced that Parmenides was right in claming that generation and corruption are impossible, and also took his arguments to correctly demonstrate that a plurality could not arise from a unity. But all also agreed that, contrary to what Parmenides claimed, change occurred, and a plurality of things existed. According to these later philosophers, there were certain elemental constituents of the cosmos that were, in some sense, Parmenidian ones (for instance they were ungenerated, indestructible, and changeless) and these are the only things that could truly by called real. In this way they were able to concede that being is eternal and unchanging while still allowing for the observable world of change and plurality. It was in attempting to allow for change, while insisting that generation, corruption, and the derivation of a plurality from out of a unity are impossible, that the two types of systems drastically diverged. The pluralists rejected the notion that what exists is one in kind (and in number). Empedocles posited the four elements as his version of Parmenidian ones, and Anaxagoras posited an infinite plurality of ones, making all natural substances the basic constituents of matter. The Atomists, on the other hand, retained the Parmenidian constraint that "what is" must be materially one in kind (the atoms were homogenous) and instead departed from the Theory of the One by asserting that non-being had reality - positing the existence of the infinite void in which the infinite number of atoms are dispersed.
How did Xenaphones arrive at his skeptical conclusions about the capacity for human knowledge?
Like the Milesians, Xenophanes was an empiricist, that is, he believed that all knowledge comes through observation and experience. In order to know something, according to Xenophanes, you need to see it or hear it for yourself. Unlike the Milesians, however, he discovered an unsettling consequence of this position: anything that cannot be observed, cannot be known.
Given the way that philosophy was set up at that time, it was impossible to directly observe the answers to any of the fundamental questions. The questions asked things like, "what is the fundamental constituent of the world?" and "how do various objects arise from this fundamental constituent?" In the days before microscopes and other powerful experimental tools, it was impossible to perform any observations that would bear directly on these questions. Therefore, according to Xenophanes, it was impossible to know the answers to these questions.