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How to tell the truth without knowing what you are talking about
| Content Provider | Semantic Scholar |
|---|---|
| Author | Anselma, Luca Cavagnino, Davide |
| Copyright Year | 2010 |
| Abstract | Introduction Is it possible to verify whether a statement is true, even without knowing the subject of the discussion? More precisely, is it possible to extract secure conclusions from a set of premises describing what you may not know? The answer is positive provided that the reasoning, from the accepted set of premises to the conclusions, is correct. The problem of verifying whether a reasoning is correct is one of the aims of logic since Aristotle. In particular, modern logic, that is logic since the Renaissance, aims at improving human reasoning and overcoming its fallacies, significantly by mechanizing reasoning. To this aim, it is necessary to improve logic passing from the syllogistic doctrine towards more powerful forms of reasoning and to devise a precise logical language free from the ambiguities of natural language: modern logic witnessed the birth of symbolic logic. Whereas Aristotelian and scholastic logic has a catalog approach, based on classification and categorization, modern logic is a calculus. In fact, in modern logic a symbolism must be devised, together with inference rules for manipulating symbols to discover new truths or to verify whether a conclusion can be derived from the premises. Today logic is considered a branch of mathematics and this mathematical entry into logic dates to the notable precursory works of Leibniz, who aimed at devising a lingua characteristica universalis, a universally characteristic language, and a calculus ratiocinator, a calculus of reason. However, Leibniz’s works on logic were published only at the end of the 19 century, so the influence of his ideas on the emergence of modern logic has been very limited. In the 19 century, there was a main paradigm shift in mathematics: the perception that algebra could deal not only with numbers but, more abstractly, with symbols. It was in this milieu that George Boole arrived at a mathematical treatment of logic by proposing an algebra not of numbers, but of logic. As Boole writes in the introduction of his The Mathematical Analysis of Logic: “... the validity of the processes of analysis does not depend upon the interpretation of the symbols which are employed, but solely upon the laws of combination.” Symbolic logic and in particular Boole’s Boolean algebra has had major repercussions on computer science. In fact, in the first half of the twentieth century many scientists showed that the Boolean logic could be easily implemented in electronic circuits and could be used to build the various functions of a computer. Moreover, it is used in search engines and in database management systems to query data. As an example to illustrate Boolean algebra, we will show that it is possible to solve the following simple detective mystery case and establish the truth as a valid conclusion by applying only Boolean algebra. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.di.unito.it/~anselma/pdf/preprintBoole.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
