Plato vs. Wittgenstein

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Plato and Wittgenstein have very different ideas concerning the nature and function of mathematical propositions. Outline one or more of these differences. Whose account do you consider to be more accurate, and why?

Plato and Wittgenstein possess contrasting views of what mathematics is, and how it can be utilized as a model within philosophy; nevertheless, they both agree that it represents more perfect model of philosophy. Whereas Plato was, perhaps, the first rationalist, Wittgenstein's forceful empiricism has left its indelible mark upon twentieth century philosophy (Biletzki). Plato conceived of mathematics as a scheme of knowledge that originated from observational inputs, but progressed into abstract ideas—these ideas, to Plato, represented the deep or hidden truth that mathematics possessed (Kraut). Wittgenstein, on the other hand, is far more skeptical of the form of knowledge that mathematics is capable of producing; he contends that math and language in innately inaccurate ways of describing the world around us—only to differing degrees. To him, math was designed to solve particular problems that arose in human life; therefore, it cannot be independently used to arrive at metaphysical conclusions. Still, overall both philosophers believe that the role of mathematics is analogous to the role of philosophy; they simply disagree over what these roles entail.

Plato believed that the physical world is in a state of constant flux, and therefore, cannot be the source of any true knowledge. Consequently, he held the position that philosophical thought progressed in a manner analogous to mathematics; rational judgments and arguments are drawn from the basis of sensory experiences. These inputs are changing and transitory, but to have true knowledge is to hold a definition that cannot be assailed by destructive argumentation. Fundamentally, Plato contended that it is possible to obtain real truth by understanding the essence of things, which is objective and universal: "These universals are objects of thought; horseness and triangularity are discovered, not created, by the thinking mind. Thus the form of good is what makes all things good," (McGreal 25). To Plato, these universal objects are "Forms" that are not merely verbal definitions bestowed upon objects, but are the distinctions between objects as utilized by thought itself. Accordingly, specifically what our senses perceive possesses a causal relationship to the truth of Forms, but the links to these truths are not altogether apparent.

Yet Plato was also very aware of the numerous false premises that pervade the world of man; people accept many notions, or believe they possess knowledge without logically assessing what they actually know. In this way, Plato attempts to demonstrate that most philosophers go about practicing philosophy without the technical know-how to find any real solutions. Because of philosophy's similarity to mathematics, these philosophers are like mathematicians who claim to know the laws of geometry, but actually make their own laws up as they go along. Deductive reasoning, to Plato, is the only key to metaphysical or moral truth (Feinberg 714). Accordingly, the destructive nature of the Socratic Method is employed by Plato in order to erase the deductive errors of the past, so that his own rational conclusions may eventually be unfurled. The Socratic Method is particularly interesting in that it, unlike most philosophic discourses, seeks to debase beliefs rather than build them up. Instead of offering a linear argument as to the nature of virtue, for example, Socrates—and subsequently Plato—begins with commonly held notions and analyzes them in an effort to debunk them. Philosophical reflection, to them, must first begin with a better understanding of our ignorance. Consequently, the reader of Plato's works is presented with a truly unique approach to philosophy that is based upon conversation and self-reflection. At the beginning of...
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