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 ideasthese 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 usonly 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
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 ideasthese 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 usonly 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
Cited: Biletzki, Anat. "Ludwig Wittgenstein." Stanford Encyclopedia of Philosophy, Nov. 8, 2002. Cahn, Steven M. Classics of Western Philosophy: Fifth Edition. Indianapolis: Hackett Publishing, 1999. Feinberg, Joel and Russ Shafer-Landau. Reason and Responsibility. New York: Wadsworth, 1999. Kraut, Richard. "Plato." Stanford Encyclopedia of Philosophy, Mar. 20, 2004. Kuusela, Oskari. "Do the Concepts of Grammar and Use in Wittgenstein Articulate a Theory of Language or Meaning?" Philosophical Investigations, Vol. 29, Iss. 4, 2006. Pages 309-341. McGreal, Ian P. Great Thinkers of the Western World. New York: Harper Collins Publishers, 1992. Plato. Plato: Republic. Translated by G. M. A. Grube. Indianapolis: Hackett Publishing, 1992. Proops, Ian. "Wittgenstein 's Logical Atomism." Stanford Encyclopedia of Philosophy¸ Nov. 22, 2004. Russell, Bertrand. "Introduction." Lugwig Wittgenstein: Tractatus Logico-Philosophicus. Ogden Bilingual Edition, 2006. Available: http://www.kfs.org/~jonathan/witt/tlph.html. Wittgenstein, Ludwig. Lectures and Conversations on Aesthetics, Psychology and Religious Belief. Oxford: Blackwell, 1966.