Logic

Key people

• Bertrand RussellBritish philosopher and logician (1872–1970)
• Kurt GödelAustrian-American logician, mathematician, and philosopher of mathematics (1906–1978)
• Jean PiagetSwiss psychologist, biologist, logician, philosopher and academic (1896–1980)

Read

• The Logic of Scientific DiscoveryKarl Popper · 1935Book
• The Game of LogicLewis Carroll · 1886Book
• Introduction to logicIrving Marmer Copi · 1953Book
• Philosophical essaysBertrand Russell · 1910Book

Watch

• Logic - Homicide ft. Eminem (Official Video)LogicVEVOVideo
• Logic - Homicide (feat. Eminem) (Official Audio)Visionary Music GroupVideo
• Kaun Bhoot hai ? Hindi Riddles | Hindi Paheliyan | Paheli | Mind Your Logic PaheliMindYourLogicVideo

Listen

• Logically SpeakingLogicPodcast
• Learning LogicMolly BPodcast
• The Art of Reasoning | Audiobook: A Practical Guide to Logic & ArgumentPedram KeshavarziPodcast
• Critical Reasoning: A Romp Through the Foothills of LogicOxford UniversityPodcast

Voices to follow

• Robert BrandomYouTubeAmerican philosopher
• David Kyle Johnson@kyle8425 · XAmerican university professor (born 1977)
• Sebastian Rudolph@sebrudolph · XGerman computer scientist and full professor
• Łukasz Kaiser@lukaszkaiser · XMachine learning researcher

Debates

• Is logic purely a formal system or does it have empirical grounding?One view: Logic consists of abstract rules and principles that are independent of any observation or experience. · Another: The principles of logic are ultimately derived from our experiences and observations of how the world works.Open question
• Is classical logic the only correct system of reasoning?One view: Classical logic, with its law of excluded middle, provides the fundamental and universal rules for valid inference. · Another: Alternative logics, such as intuitionistic or paraconsistent logic, offer better models for specific types of reasoning or handle paradoxes more effectively.Open question

Glossary

• PropositionA statement that is either true or false.
• SyllogismA type of logical argument where a conclusion is inferred from two premises.
• ValidityAn argument is valid if its conclusion logically follows from its premises, regardless of whether the premises are true.
• SoundnessAn argument is sound if it is valid and all of its premises are true.
• Deductive ReasoningA process of reasoning from one or more general statements to reach a logically certain conclusion.
• Predicate LogicA system for representing logical relationships between subjects and their properties or relations.

Careers

Roles this can lead toward

Threads 9

Where this connects to other fields — and why it's worth knowing.

• Non-Western Philosophy Philosophy

  Western logic long insisted every statement is either true or false, full stop. But centuries earlier, Jain thinkers in India built a system with seven values, including careful shades of 'maybe' and 'it depends on how you look.' They were doing 'in-between' logic long before Western math would even allow a maybe to exist.

• Artificial Intelligence & the Mind Psychology

  A logician named Godel proved that any rule-based system has true statements it can never prove about itself. A similar limit, the 'halting problem,' says no program can always predict what programs do. Some thinkers argue this means a purely computer-like mind could never fully understand its own reasoning, because no system can completely see inside itself.

• Elections & Voting Politics

  Every voting system feels like it should be fixable to be perfectly fair. A mathematician named Arrow proved it can't be done: no method can satisfy a few basic fairness rules all at once, once there are three or more choices. A flawless democracy isn't just difficult to build; it's logically impossible.

• Constitutions & Rights Politics

  A constitution wants to be a complete rulebook covering every case. But no set of rules can include the rules for how to apply itself, so gaps always appear, and judges must keep filling them forever. It's Godel's famous discovery in a robe: a system of rules can never fully close itself off.

• Does God Exist? Philosophy

  Godel is the man who shook math to its core by proving no system can prove everything true about itself. The same Godel also wrote a strict, step-by-step logic proof that God exists. In 2013, researchers fed it to a computer to check every step, and the logic came back valid.

• Constitutions & the Rule of Law Law

  Rule of law means the rules work the same whether a billionaire or a stranger invokes them, no favorites. Computer scientists have a twin idea called formal verification: proving a program gives the same correct behavior on every possible input. Both are really the same promise, that the outcome shouldn't depend on who happens to show up.

• Landmark Constitutional Cases Law

  While studying for his US citizenship test, the genius logician Kurt Gödel found a loophole in the Constitution that, he argued, could legally turn America into a dictatorship. It showed that a legal document, just like a math system, can secretly hide a contradiction inside it.

• Religion and Science Religion

  The old 'science versus religion' fight once turned into pure math. Kurt Gödel, one of the greatest logicians ever, took a medieval argument for God's existence and rewrote it as a formal proof, a chain of logic you can actually check line by line like a math homework.

• AI Governance Global Risks

  Engineers can mathematically prove a bridge or a computer chip will work, guaranteed. But an AI that learns on its own can only be tried out on examples, never fully proven safe. Using it means giving up the certainty engineering usually insists on.