Axiom 4 (Epistemic and Doxastic Logic)

A description of Axiom 4 in doxastic and epistemic logic and how this axiom may lead to the KK Regress, or the problem of knowing that you know.

Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!

Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!

[nathansalmon]

"Doubling possibility" makes a good deal of sense--so much so that the 4 axiom of the logic of metaphysical modality has an enormous number of false instances.

[louisng]

I don't think an infinite number of knowledge creates problems. For example, I know that 1 is odd. I know that 2 is even. I know that 3 is odd. I know that 4332857384069826850947 is odd. I don't actively think about 4332857384069826850947 is odd everyday, but if I need to figure out if 4332857384069826850947 is odd, I can always do so. Same for Axiom 4.

[louisng]

Infinitely many beliefs do not necessarily contain infinite information, just as 0.333... can be condensed to 1/3.

[Ansatz]

You don't need to hold an idea in your mind to believe it. Aside from issues of having infinite beliefs, even an ordinary number of beliefs is far too many for a person to be continuously thinking about. You believe something if it seems true to you when you consider it, and that will obviously apply to beliefs about beliefs about beliefs to an unbounded depth.

[homelylad]

It makes better sense when negating it tho

[DJK]

There's nothing wrong with having an infinite number of beliefs, when that infinite belief can be contained as a single belief including the idea of an infinite regression.. I agree with Ansatz66, and infinite series of beliefs does not mean an infinite amount of information, when in this case the series is repetitive. If there was inconsistency in the pattern, then it would be problematic, but there isn't. I can quite feasibly go and believe something including the idea of believing it regressively, I can comprehend and contain that idea right now.