Plato Vs. Wittgenstein

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 ideasÐ'--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 usÐ'--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, SocratesÐ'--and subsequently PlatoÐ'--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 "Apology" Socrates introduces his style of argumentation when he says, "From me you will hear the whole truth, though not, by Zeus, gentlemen, expressed in embroidered and stylized phrases like theirs [his accusers], but things spoken at random and expressed in the first words that come to mind, for I put my trust in the justice of what I say, and let none of you expect anything else," (Cahn 29). Accordingly, Plato's writings take a character on a journey through their personally held beliefs, as Socrates endeavors to help them arrive at a conclusion that he has already reachedÐ'--consequently the reader is taken on this journey as well. One of the goals of this method, clearly, is to question many of the notions that most people tend to take for granted. Generally, Plato ventures to "demonstrate that uncritically accepted opinions about philosophically important matters could lead to logical catastrophe," (Cahn 1). Essentially, the early dialogues are like bright red corrections on a math exam; Plato shows his audience where they went wrong in order to bring them along the right analytical path.

Wittgenstein also seeks to correct the analytic errors of the past; but he believes that these errors have been introduced by deduction's misapplication, and not simply erroneous deduction (Kuusela). Perhaps Wittgenstein's most lasting contribution to philosophical discourse is his radical proposal that language, as it is used by human beings, is a fundamentally insufficient tool with which to approach the problems of the infinite. In other words, Wittgenstein contends that language was conceived of as a method to deal with everyday issues and go about everyday business; in this respect, it must be viewed as exceedingly successful. Human beings are able to convey important bits of information to one another regarding their goals, plans, needs, and wants within reasonable levels of accuracy. However, Wittgenstein sees a necessary distinction between the largely relativistic manner in which language is used on a daily basis, and the apparently universal problems posed by the first Western philosophers: language is not an analytic tool towards determining moral truth to the same degree that mathematics is an analytic tool towards determining physical truth. Fundamentally, language and mathematics are analogous; yet the errors associated with making mathematical assertions about the world are smaller than those associated with making linguistic assertions about the world. Ultimately, this is why Wittgenstein argues that the word "good" has continually eluded philosophers who have attempted to surmise its elemental nature.

In the early Socratic dialogues we are presented with a very different interpretation of why the human goodness is such an elusive notion. Repeatedly Socrates