Mathematic Logic

Logic (from Classical Greek λόγος logos; meaning 'speech/word') is the study of the principles and criteria of valid inference and demonstration. The term "logos" was also believed by the Greeks to be the universal power by which all reality was sustained and made coherent and consistent. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory. [1] Traditionally, logic is studied as a branch of philosophy, one part of the classical trivium, which consisted of grammar, logic, and rhetoric. Since the mid-nineteenth century formal logic has been studied in the context of the foundations of mathematics. In 1903 Bertrand Russell and Alfred North Whitehead attempted to establish logic as the cornerstone of mathematics formally with the publication of Principia Mathematica. However, the system of Principia is no longer much used, having been largely supplanted by set theory. The development of formal logic and its implementation in computing machinery is the foundation of computer science.  In logic and mathematics, or, also known as logical disjunction or inclusive disjunction is a logical operator that results in true whenever one or more of its operands are true. In grammar, or is a coordinating conjunction. Logical disjunction is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are false. More generally a disjunction is a logical formula that can have one or more literals separated only by ORs. A single literal is often considered to be a degenerate disjunction. Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician and advocate for social reform. A prolific writer, he was also a populariser of philosophy and a commentator on a large variety of topics, ranging from very serious issues to those much less so. Continuing a family tradition in political affairs, he was a prominent anti-war activist, championing free trade between nations and anti-imperialism. Did you know? ...that the Law of noncontradiction is the same as the Law of contradiction? ...that nand alone or nor alone make a functionally complete set of logical operators? ...that according to the continuum hypothesis, there is no cardinal number in between aleph null and the cardinality of the continuum? ...that all 24 valid syllogistic forms have names like 'Camestrop' and 'Felapton'? ...that if a statement P implies another statement Q, and a third statement R also implies Q, and either P or R is true; then Q has to be true? ...that the dunce hat was named after a logician? ...that the collective noun for a group of logicians is a "sequitur of logicians"