Ad infinitum in the context of Common knowledge (logic)

👉 Ad infinitum in the context of Common knowledge (logic)

Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. It can be denoted as $C_{G}p$ .

The concept was first introduced in the philosophical literature by David Kellogg Lewis in his study Convention (1969). The sociologist Morris Friedell defined common knowledge in a 1969 paper. It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an interest in the subject of epistemic logic in general – and of common knowledge in particular – starting in the 1980s. There are numerous puzzles based upon the concept which have been extensively investigated by mathematicians such as John Conway.

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Ad infinitum in the context of Münchhausen trilemma

In epistemology, the Münchhausen trilemma is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without appealing to accepted assumptions. If it is asked how any given proposition is known to be true, proof in support of that proposition may be provided. Yet that same question can be asked of that supporting proof and any subsequent supporting proof. The Münchhausen trilemma is that there are only three ways of completing a proof:

The circular argument, in which the proof of some proposition presupposes the truth of that very proposition
The regressive argument, in which each proof requires a further proof, ad infinitum
The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended

The trilemma, then, is having to choose one of three equally unsatisfying options.

View the full Wikipedia page for Münchhausen trilemma

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Ad infinitum in the context of Common knowledge (logic)

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👉 Ad infinitum in the context of Common knowledge (logic)

Ad infinitum in the context of Münchhausen trilemma