# How many "degrees" of knowledge is conceivable?

Not sure if this is the right place for this, but there's something I've been pondering about and can't wrap my head around.

Say person A knows something, that person B does not. Let's call that the 0th degree of knowledge.

Now imagine that person B knows that person A knows something, but person A does not know that person B knows that. Let's call that the 1st degree of knowledge.

Now imagine that person A knows that person B knows that person A knows something, but person B does not know that person A knows that. Let's call that the 2nd degree of knowledge.

Now extrapolate that loop to the nth "degree of knowledge".

My head can only wrap itself around the 2nd degree. For example:

0th degree: Adam knows who the killer is, but Brian does not.

1st degree: Brian knows that Adam knows who the killer is, but Adam doesn't know that Brian knows that Adam knows.

2nd degree: Adam knows that Brain knows that Adam knows who the killer is, but Brian doesn't know that Adam knows that Brian knows that Adam knows.

In all three scenarios, I can imagine how a conversation may play out. But past this, it is really straining to even conceive of what a 3rd degree or higher of "knowledge" would mean. Does it even have any meaning? Does the possible degrees of knowledge end at 2? or 3? Or can it theoretically be limitless? How does each additional degree impact how Adam and Brian may interact with each other?

I'm not sure if this question is too abstract or not but I hope what I'm asking makes sense. And is there a name for this type of "knowledge"? I've been using the term "degree" only because I don't know what else to call it.

• Inconceivable! (I think Vizzini from the Princess Bride may actually explore beyond the 3rd degree) Aug 7, 2022 at 2:38
• I think I just found the answer to my own question here. Aug 7, 2022 at 4:30
• Since there is a continuum of possible probability values or fuzzy degrees of confidence between 0 and 1 the conceivable quantity would be at least that. And one can use something like Conway's surreal numbers as probability values to jack it up to any desired cardinality. Our ability to "conceive" various degrees far outstrips our ability to distinguish between them in practice, where some finite number (perhaps large) is all that is ever needed. Aug 7, 2022 at 5:07