Wednesday Wisdom

Imagine a group of generals, each commanding their own portion of the Byzantine army, they need to come to a unanimous decision about whether to attack or retreat from powerful enemy city they have surrounded. They must come to a unanimous decision because they know a lack of synchronization would grant the city defenders an opportunity to attack and lead to their defeat. They communicate with runners who go back and forth. How can the general be sure the correct information has been reliably transmitted or that all the generals are loyal in their behavior or decision making? How can the generals reach a reliable consensus on a decision?

This is a logic question in philosophy which is applied to network systems known “The Byzantine Generals Problem”. This concept was introduced by Leslie Lamport, Robert Shostak, and Marshall Pease in their seminal 1982 paper, “The Byzantine Generals Problem”. In their paper, they formalized the challenges faced by distributed networks to reach consensus when a subset of participants cannot be trusted. They argue that these systems are only resistant to so many faulty or potentially malicious participants.

At its core, the “Byzantine Generals Problem” is a logical consistency challenge. It asks: How can multiple agents, with incomplete and possibly contradictory information, arrive at a single consistent truth? In classical logic, consistency means that a set of statements does not contain contradictions. In distributed systems like a computer network or the general’s problem, the statements are the messages the general’s exchange and decisions are made by the incoming information. If traitorous generals inject contradictions, telling one general attack and another retreat, the logical system breaks down unless there is a structured way to filter out falsehoods.

The problem also highlights the limits of deductive reasoning (conclusions drawn for principles or top dawn logic) under uncertainty. A loyal general cannot simply trust a single message, because the premise itself may be faulty (the sender could be a traitor or the communication is faulty). Therefore, the system must rely on redundancy and cross-verification and on logical proofs requiring multiple independent premises. This proof is known as the 3f + 1 rule (simply stated needing more than two-thirds honest participants to achieve consensus) and reflects a logical safeguard that provides enough overlapping truths must exist to drown out contradictory lies.

Philosophically, the Byzantine Generals Problem resembles the ancient logical issue of the liar’s paradox. The liar’s paradox is a statement that creates a contradiction of being both true and false at the same time for example “this sentence is false”. If a participant asserts contradictory things depending on the audience, the group must logically determine which propositions can be trusted. In logic, we resolve paradoxes by carefully defining rules of inference (drawing a conclusion or opinion based on existing information) and rejecting self-contradictory data.

In essence, the Byzantine Generals Problem shows that logic is not only about internal consistency of propositions, but also about trust in the sources of those propositions. Without mechanisms to verify truth, logic collapses into uncertainty. With verification, it becomes a powerful tool for coordination, whether in mathematics, organizations, or computer systems. In distributed computing like cloud and blockchains, it’s important to design consensus algorithms that enforce coherence (logically connected systems that are consistent) despite adversarial inputs from bad actors.

2025 -Does this apply to everyday world?

In the age of mass communication from television, podcasts and social networks, the world has been bombarded with information. The oncoming of artificial intelligence will only make our decision making on what is true or false only more difficult. The “Byzantine General’s Problem” provides an excellent framework on how to disseminate information in a logical way to find the truth.

During the nuclear forces treaty in 1978, Ronald Reagen famously said when dealing with the Soviet Union “Trust but verify”. As every good carpenter will tell you, measure twice, cut once- safe guarding the truth should be just as important.

And now you know...

Thanks, Dad, for the gift of curiosity!

Philosophy is the art of thinking, the building block of progress that shapes critical thinking across economics, ethics, religion, and science.

METAPHYSICS: Literally, the term metaphysics means ‘beyond the physical.’ Typically, this is the branch that most people think of when they picture philosophy. In metaphysics, the goal is to answer the what and how questions in life. Who are we, and what are time and space?

LOGIC: The study of reasoning. Much like metaphysics, understanding logic helps to understand and appreciate how we perceive the rest of our world. More than that, it provides a foundation for which to build and interpret arguments and analyses.

ETHICS: The study of morality, right and wrong, good and evil. Ethics tackles difficult conversations by adding weight to actions and decisions. Politics takes ethics to a larger scale, applying it to a group (or groups) of people. Political philosophers study political governments, laws, justice, authority, rights, liberty, ethics, and much more.

AESTHETICS: What is beautiful? Philosophers try to understand, qualify, and quantify what makes art what it is. Aesthetics also takes a deeper look at the artwork itself, trying to understand the meaning behind it, both art as a whole and art on an individual level. A question an aesthetics philosopher would seek to address is whether or not beauty truly is in the eye of the beholder.

EPISTEMOLOGY: This is the study and understanding of knowledge. The main question is how do we know? We can question the limitations of logic, how comprehension works, and the ability (or perception) to be certain.