Logic: The Structure of Reason (Great Ideas of Philosophy)

Logic: The Structure of Reason. As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle's Organon, Russell's Principia Mathematica, and other central works, this program tracks the evolution of logic, beginning with the basic syllogism. A sampling of subsequent topics includes propositional and predicate logic, Bayesian confirmation theory, Boolean logic, Frege's use of variables and quantifiers, Gödel's work with meta-mathematics, the Vienna Circle's logical positivism, and the Turing machine. Commentary by Hilary Putnam, of Harvard University; NYU's Kit Fine; and Colin McGinn, of Rutgers University, is featured. (43 minutes).
Origins of Logic (02:13)
Aristotle's "The Organon" establishes rules to distinguish valid and invalid arguments. His foundation on logic is the basic syllogism.
Deductive and Inductive Arguments (04:55)
The conclusion of the syllogism is reduced from the premises in deductive arguments. Inductive reasoning cannot guarantee this truth.
Stoic's Responses to Aristotle's Logic (02:59)
Propositional logic concerns itself with true or false sentences. Predicate logic goes deeper with inference rules.
Medieval Philosophers and Francis Bacon (02:28)
The advance of science demands new systems of thought. Bacon challenges the orthodoxy of Aristotle's logic
19th Century Modern Logic (03:15)
Applying the structures of mathematics to logic, George Boole creates the algebra of logic. Gottlob Frege becomes the Father of Modern Logic.
Boole's and Frege's Influences (06:09)
Scientists can now develop precise notations of analysis beyond Aristotle's "if/then" form. Russell's paradox tests the metal of all logicians.
Semantic Logic (03:05)
Alfred Tarski's semantic logic becomes the foundation for computer science language. Hilbert's Program brought logic into the realm of language.
Vienna Circle (02:08)
Group of logicians introduce Logical Positivism. Turing applies Boole's system to computer science with his new machine that follows mechanical rules.
Dialogue Between Philosophy and Logic (01:48)
Conflicts between philosophy and logic lie in what logic should emphasize, informalism and rigor or semantics and content.