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Computers, paradoxes and the foundations of mathematics: Some great thinkers of the 20th century have shown that even in the austere world of mathematics, incompleteness and randomness are rife
| Content Provider | Semantic Scholar |
|---|---|
| Author | Chaitin, Gregory J. |
| Copyright Year | 2002 |
| Abstract | Everyone knows that the computer is a very practical thing. In fact, computers have be come indispensable to mrvning a modern soci ety. But what even computer experts don't re member is that?I exaggerate only slightly?the computer was invented in order to help to clar ify a philosophical question about the founda tions of mathematics. Surprising? Yes indeed. This amazing story begins with David Hilbert, a well-known German mathematician who at the start of the 20th century proposed formalizing completely all of mathematical reasoning. It turned out that you can't formal ize mathematical reasoning, so in one sense his idea was a tremendous failure. Yet in another way, Hilbert's idea was a success, because for malism has been one of the biggest boons of the 20th century?not for mathematical rea soning or deduction, but for programming, for calculating, for computing. This is a forgotten piece of intellectual history. I will relate that history here without delving into mathematical details. So it will be impos sible to fully explain the work of the relevant |
| Starting Page | 164 |
| Ending Page | 171 |
| Page Count | 8 |
| File Format | PDF HTM / HTML |
| DOI | 10.1511/2002.2.164 |
| Alternate Webpage(s) | http://www.cs.ox.ac.uk/activities/ieg/e-library/sources/amsci.pdf |
| Alternate Webpage(s) | http://web.comlab.ox.ac.uk/oucl/research/areas/ieg/e-library/sources/amsci.pdf |
| Alternate Webpage(s) | http://pcfly.info/doc/Computers/21.pdf |
| Alternate Webpage(s) | http://www.umcs.maine.edu/~chaitin/amsci.pdf |
| Alternate Webpage(s) | http://www.cs.umaine.edu/~chaitin/amsci.pdf |
| Alternate Webpage(s) | http://www.cs.auckland.ac.nz/CDMTCS/chaitin/amsci.pdf |
| Alternate Webpage(s) | http://www.cs.auckland.ac.nz/~chaitin/amsci.pdf |
| Alternate Webpage(s) | https://doi.org/10.1511/2002.2.164 |
| Volume Number | 90 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
