Wittgenstein Ludwig Wittgenstein: Logic and Thesis

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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 out to user interfaces.

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This is a very basic understanding of Wittgenstein's contributions to computer science. 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.

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