What Is Common Knowledge and Why Is It Important?

TL;DR

Common knowledge refers to information that all parties know and understand mutually, requiring infinite layers of awareness. It plays a crucial role in social coordination, as illustrated by the coordinated attack problem where unreliable communication prevents rational decision-making. Despite the theoretical challenges, intuition suggests that after enough exchanges, coordination could still be possible, creating a paradox between logic and intuition.

Transcript

Hi, my name is Liang Zhou Koh. I am a graduate student in philosophy at the University of Toronto, and today I want to talk to you about common knowledge. One distinctive aspect of human mind reading is our ability to entertain and reason about higher-order knowledge and belief that agents may have about the mental states of others. In other words,... Read More

Key Insights

• Common knowledge is not just widely known facts but a technical concept in philosophy, economics, and computer science, requiring infinite mutual awareness.
• The coordinated attack problem illustrates the challenges of achieving common knowledge due to unreliable communication channels.
• Without common knowledge, rational coordination between parties becomes difficult, as seen in the generals' dilemma in the coordinated attack problem.
• Even with multiple message exchanges, achieving common knowledge is theoretically impossible due to the infinite nature of mutual awareness.
• Despite the theoretical impossibility, intuition suggests that after a certain number of messages, rational coordination should be feasible.
• The paradox of the coordinated attack problem highlights the conflict between logical reasoning and intuitive decision-making.
• Common knowledge is crucial for social coordination, affecting decision-making in various fields like economics and computer science.
• Future discussions will explore potential responses to the paradox presented by the coordinated attack problem.

Questions & Answers

Q: What is common knowledge according to Liang Zhou Koh?

Common knowledge, as explained by Liang Zhou Koh, is a technical concept used in philosophy, economics, and computer science. It involves a situation where all parties know a fact, know that others know it, and know that others know that they know it, continuing infinitely. This infinite mutual awareness is crucial for rational coordination in social contexts.

Q: Why is common knowledge important in social coordination?

Common knowledge is essential in social coordination because it ensures that all parties involved have the same understanding and awareness of certain facts. This mutual awareness allows for synchronized actions and decisions, preventing misunderstandings and ensuring that all parties can act rationally based on shared knowledge. Without common knowledge, coordination becomes challenging, as illustrated by the coordinated attack problem.

Q: What is the coordinated attack problem?

The coordinated attack problem is a thought experiment that illustrates the challenges of achieving common knowledge. It involves two generals who must coordinate an attack on a city but can only communicate through unreliable messengers. The problem shows that without guaranteed message delivery, the generals cannot achieve the infinite mutual awareness required for common knowledge, making rational coordination difficult.

Q: How does unreliable communication affect common knowledge?

Unreliable communication affects common knowledge by preventing the infinite mutual awareness required for it. In the coordinated attack problem, the possibility of message interception means that the generals can never be certain that their messages are received and understood by the other party, preventing them from reaching the infinite levels of mutual knowledge needed for common knowledge, and thus hindering rational coordination.

Q: Why is it said that achieving common knowledge is theoretically impossible?

Achieving common knowledge is theoretically impossible because it requires an infinite series of mutual awareness, where each party knows that the other knows, and this continues indefinitely. In practical scenarios, such as the coordinated attack problem, communication channels are unreliable, making it impossible to achieve the infinite levels of mutual knowledge required for common knowledge.

Q: What is the paradox in the coordinated attack problem?

The paradox in the coordinated attack problem arises from the conflict between logical reasoning and intuitive decision-making. Logically, without common knowledge, rational coordination seems impossible, as demonstrated by the generals' dilemma. However, intuitively, it seems rational for the generals to coordinate after exchanging a certain number of messages, despite the lack of theoretical common knowledge.

Q: How does intuition conflict with logical reasoning in the coordinated attack problem?

Intuition conflicts with logical reasoning in the coordinated attack problem because, while logic dictates that without common knowledge, coordination is irrational, intuition suggests that after a certain number of message exchanges, the generals should be able to coordinate their attack. This intuitive belief challenges the theoretical impossibility of achieving common knowledge, highlighting a paradox between theory and practice.

Q: What future topics will be explored regarding the coordinated attack problem?

Future discussions regarding the coordinated attack problem will explore potential responses to the paradox it presents. These discussions will likely delve into alternative theories and solutions that reconcile the conflict between logical reasoning and intuitive decision-making, aiming to better understand how common knowledge can be achieved or approximated in practical scenarios despite theoretical challenges.

Summary & Key Takeaways

• Liang Zhou Koh introduces the concept of common knowledge, a technical notion in philosophy, economics, and computer science, requiring infinite mutual awareness. He illustrates the challenges in achieving common knowledge through the coordinated attack problem, where unreliable communication prevents rational coordination between two generals.

• The coordinated attack problem demonstrates the difficulty of attaining common knowledge due to the infinite nature of mutual awareness and unreliable communication channels. Despite theoretical impossibility, intuition suggests rational coordination should be feasible after multiple message exchanges, highlighting a paradox between logical reasoning and intuition.

• Common knowledge underpins social coordination, impacting decision-making across various disciplines. The paradox of the coordinated attack problem reveals the tension between theoretical reasoning and intuitive judgments. Liang Zhou Koh plans to explore responses to this paradox in future discussions, emphasizing the importance of common knowledge in rational coordination.