The Origin of Paradox and Its Relation to Philosophical Reflection

Abstract

In this essay, my primary intention is to develop some insight into the fundamental meaning of paradox. Consequently, I will not be concerned with providing an historical account or a survey of theories. Various commentaries are employed, but these are interpreted in accordance with my intention to discern what reveals itself as most original, i.e., the a priori conditions necessary for to be what it is. In short, I simply ask the question: How is possible? Needless to say, the phenomenon in question is especially elusive. Its reputation for being resistant to analysis is thoroughly warranted. Thus, it is most important not to disengage from its context in order to get it under control and make it more amenable to explanation. When this is done, a certain precision may be achieved; but then, the very thing sought is lost, and ends up being forced into categories that are over-imposing. This, in turn, only gives the appearance of clarity because the categories, not the phenomenon, become the priority. With this in mind, I attempted, as best I could, to let be what it is. Although this approach runs the risk of placing a considerable strain on communication, it is the only way that one can hope to give as radical an account as possible. As the title indicates, particular attention is also given to the matter of philosophical reflection. This was not part of my initial intention; but, as this project unfolded, it became clear that and the task of philosophy are so intimately connected that neither can be considered apart from the other. For, as I hope to show, is the vehicle that enables radical reflection to discover what is most original. Thus, the very phenomenon being investigated is that which makes the investigation possible in the first place. In other words, when thinking about paradox, it becomes necessary to address the paradoxical character of thinking. The essay begins by examining, in a general way, some well-known examples of in order to clarify, at least provisionally, the meaning of contradiction, the most obvious feature of This, along with some suggestions from Quine, provides the context needed for developing an understanding of crisis, doxic being and the other fundamental elements that make possible. Finally, with the help of Heraclitus and Parmenides among others, I proceed to articulate the relation between what I regard as the two most prominent characteristics of the philosophical process-radical reflection and therapy-and paradox. The Tension of Sustained Contradiction Let us first consider a particular kind of discovered by Russell in 1901, often referred to as the paradox of the self-membership of classes. Russell found that some classes of things are not members of themselves and some are. An example of the former would be, say, cups. Indeed, the class of all cups is not a cup. On the other hand, the class of all things that are not cups is an example of a class that is a member of itself. It and its members are not cups. But now Russell inquires further by asking: Is or is not the class of all classes which are not members of themselves a member of itself? With some thoughtful consideration it can be noticed that something peculiar occurs when one attempts to answer; and with this, the reputed connection between and self-contradiction becomes evident. We are given a set of circumstances, or premises, from which to derive a conclusion. One soon discovers, however, that, given these premises, we cannot conclude that it is or it is not. Instead, we are put in a position whereby we are compelled to answer: the class of all classes which are not members of themselves is a member of itself if it is not a member of itself. And, in accordance with this conclusion, a contradiction presents itself, namely: it is, if, and only if, it is not. Russell's dilemma is an example of a wherein the impending tangle is maintained by a conclusion that denies itself. …