Introduction to Logic (03:45)
In this film, computer scientist and professor Dave Cliff will explore the basic reasoning tool used in philosophy, science, language and math. He created a computer program using logic to replicate human traders in on the stock market.
Logician Beer Joke (02:38)
Logic involves the rules of correct reasoning. Cliff explains a riddle in which inference is used to determine what three men want to order. Logic provides rules for organizing knowledge, but conclusion quality depends on idea quality.
Defining Syllogism (03:05)
Aristotle developed formal rules governing reasoning, thought, and argument. A simple argument consists of three propositions; view an example of premises and conclusion. Of 256 syllogism types, 19 are logically valid. Hear a logical fallacy.
Popularizing Logic (03:16)
Mathematician Lewis Carroll promoted reason to a wider audience in "Alice in Wonderland." He wrote "Symbolic Logic" for women and young people so that they could detect fallacious arguments. Some of his syllogisms were anti-Semitic.
Calculus of Reasoning (03:24)
George Boole argued that logic is closer to mathematics than philosophy. Changing words to symbols in a logical argument allowed it to be solved like an equation. He introduced Boolean operators "and," "or," and "not" and made statements either true or false. A century later, his logic became computing.
Logics of Computing (04:49)
Computer science and software systems use combinations of zeros and ones to represent any number. Cliff maps out a circuit with Boolean Logic gates and uses first graders to demonstrate how a system calculates numbers.
Computer Programming Principles (03:42)
Math can be used to reason about anything; axioms and rules unify logic in applications. Students compete in IOI to solve three algorithmic problems. Algorithms turn real world problems into questions answered through logic, such as identifying marsupials among zoo animals.
Air Traffic Control Algorithms (03:25)
A control center in Southeast England uses computer logic to help guide planes over U.K. air space—reducing human error and increasing sector capacity. Students should learn logic to understand how complex systems work. IOI competitors write accurate, fast programs; Chinese students win.
Logical Paradox (02:23)
No logical algorithm can solve the statement "This sentence is false." Paradoxes are fundamental contradictions that have puzzled logicians for centuries. In early 20th century Vienna, modern thinkers threatened mathematics foundations.
Struggle for Modernity (03:00)
Early 20th century Viennese thinkers admitted limits to certainty and perception. The university commissioned a ceiling panel by Gustav Klimt; his work “Philosophy” attacked the idea that mathematics would provide complete knowledge founded on absolute truth. Boolean logic was too simple to describe all of mathematics.
Search for Mathematical Certainty (03:47)
Gottlob Frege used logical quantifiers to describe and analyze statements. Hear an explanation of the logical paradox that Bertrand Russell discovered in his work. Russell's "Principia Mathematica" took 360 pages to logically prove that 1+1=2.
Austrian Logical Empiricism (02:53)
Inspired by Albert Einstein and Russell, the Vienna Circle aimed to purge philosophy of anything that wasn't directly observable through scientific experiment or derivable through logic laws. They forbade metaphysics during discussions.
Logical uncertainty remained a challenge for the Vienna Circle. In 1930, Kurt Godel concluded that in any logical system, you could either be consistent or complete. In mathematical logic, there would be some truths that could never be proven. As fascism rose, the Vienna Circle dispersed.
Universal Computing Machine (03:59)
In 1936, Alan Turing envisioned a machine that could tackle any mathematical problem using a logical algorithm encoded in its own limitless memory—launching a technology revolution. He built a model to crack German codes and Tommy Flowers built the first electronic programmable computer.
Digital Revolution (03:06)
In 1946, science fiction writer Murray Leinster imagined an interconnected technology he named “alogic.” Complex computer systems use basic Boolean logic and logic provides a way to organize information on the internet.
Stock Exchange Technology (01:58)
The London Metal Exchange is the last venue for face to face trading. Algorithms are replacing traders and computers beat humans at pure logical reasoning, but humans still write algorithms.
Artificial Intelligence Debate (02:54)
In 1950, Turing wrote chess algorithms and predicted that a computer would be able to converse with a human. Supercomputers aid data-centric research, but don't yet rival humans.
Man vs. Machine (02:52)
In 1997, a computer algorithm defeated chess champion Garry Kasparov. Turing saw computers and the human brain as information processing systems governed by logical rules—suggesting that one day, we could code ourselves. Cliff believes altruism, creativity, and love are impossible to replicate.
Credits: The Joy of Logic (00:32)
Credits: The Joy of Logic
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