Sign Up Now
Get instant access to over 1 million+ study documents
OR
Already registered? click here to login
By creating your account, you agree to our terms of service, privacy policy and student honor code.
This means that, according to Wittgenstein, math performs like language, or perhaps more simply language performs like math. There are certain established rules, both of grammar and of meaning, that allow language to be useful as long as statements are true, and anything that is not true or that cannot be spoken of using language (i.e. It does not fit into a logical system) must be discarded (Stanford, sec. 2.4). Mathematics and language are the same thing, then, simply with a different set of representational symbols.
The implications that these statements have on computer science should be fairly obvious. Though humans are capable of creating language, or at least of agreeing on new representational symbols, computers are (as yet) unable to take a creative hand in language development themselves. Far from calling into question the veracity of Wittgenstein's claims in relation to mathematics, the practice of computer science shows them to be vitally important -- computers must be taught language, including the grammar of algorithms and the representational symbols for numbers and countless functions in order to operate with any sort of usefulness. The most simplistic way of understanding this is Wittgenstein's proposal that language must obey rules in order to operate efficiently and effectively (Bagni, 216). This is exactly what computers are taught to do -- they obey rules as set by human programmers, using language that is mathematical at its heart and grows more "human" as the layers move...
His mathematical contributions can be understood on a far more technical level, especially in tandem with their famous (or infamous) interpretation by Bertrand Russell (Stanford, sec. 1; Bagni, 218). Much of this is due to the fact that Wittgenstein insisted that the obeying of rules in grammar and language must be a public thing -- thinking one was obeying rule automatically meant that the rule was not being obeyed; it had to happen automatically and in an externally observable way for it to have any meaning -- that is, for it to be logical (Bagni, 217). This has had a profound effect on set theory, which is itself integral to computer sciences and practical programming. Though Wittgenstein passed away before the field of computer science was firmly established, his thoughts on language and logic have had a profound effect on the field, and through it on our modern way of life.
Works Cited
Bagni, Giorgio. "Obeying a Rule': Ludwig Wittgenstein and the Foundations of Set Theory." The Montana Mathematics Enthusiast, 5(2&3), pp. 215-22.
Richter, Duncan. "Ludwig Wittgenstein." The Internet Encyclopedia of Philosophy. 2006. Accessed 11 April 2009. http://www.iep.utm.edu/w/wittgens.htm#H2
Stanford Encyclopedia of Philosophy. "Ludwig Wittgenstein." 2006. Accessed 11 April 2009. http://plato.stanford.edu/entries/wittgenstein/#Phi
Works Cited
Bagni, Giorgio. "Obeying a Rule': Ludwig Wittgenstein and the Foundations of Set Theory." The Montana Mathematics Enthusiast, 5(2&3), pp. 215-22.
Richter, Duncan. "Ludwig Wittgenstein." The Internet Encyclopedia of Philosophy. 2006. Accessed 11 April 2009. http://www.iep.utm.edu/w/wittgens.htm#H2
Stanford Encyclopedia of Philosophy. "Ludwig Wittgenstein." 2006. Accessed 11 April 2009. http://plato.stanford.edu/entries/wittgenstein/#Phi
Wittgenstein Ludwig Wittgenstein is particularly interesting because in Philosophical Investigations (PI) he repudiated all of his earlier work in logical positivism and the Tractatus Logico-Philosophicus (TLP), along with much of what was traditionally thought of as philosophy, and took a radically new track in the last twenty years of his life. Young Wittgenstein was more certain that he had solved all major philosophical problems, while the older Wittgenstein had completely lost
Wittgenstein is well-known for his philosophy with regards to the nature of language and the problems thereof in philosophy with regards to the nature of the language barrier. Words, according to Wittgenstein, are mere tools (Moore, 1990). The abuses of these tools create the concern of an imperfect language -- because there is no logically perfect language -- and thus an imperfect philosophy. Language is always "more or less vague,
Skepticism Bertrand Russel and Ludwig Wittgenstein's personal and professional relationship is well-known, with Russel having famously sponsored Wittgenstein's submission of Tractatus Logic-Philosophicus for PhD credit at Cambridge University. Both philosophers were important early contributors to the theory of logical atomism, and although they would both go on to reject many of the ideas central to logical atomism, their work nevertheless represented an important break from philosophical Idealism and set the stage
Karl Popper is arguably one of the greatest philosophers of the twentieth century because of his role as one of the pioneers of philosophy of science. Popper was a political and social philosopher of significant stature, a dedicated campaigner and strong defender of the Open Society, and a committed rival of all types of conventionalism, skepticism and relativism in human affairs and science (Thorton, n.d.). He considered one of the
Jean-Francois Lyotard (the Postmodern condition: A Knowledge Report 1979) describes postmodernism in the context of nature of social bond. He argues that due to the advent of the technology and with the invention of computer, information has been more restricted in the form of procedures and program. According to him some one must have access to all the information to check whether the decisions are madder correctly. He discuss in
One does this by using logical statements, if then, if a then b, etc. As a way to negate other hypotheses. Thus, the basis of critical thinking is a negative methodology in which one continually disproves alternative views, eliminating them one by one, resulting in a final truth that holds up to more contradictions. In utilizing critical theory, the status quo is critiqued and attacked. Actions are criticized because of