I disagree, but in any case you are not (nor is anyone else) an agent with a consistent set of beliefs, so it doesn’t matter if that is true or not.
The real issue here is that there is clearly some possibility that you are mistaken enough about the nature of belief that it is impossible for you to have a belief that consists of a million “I believe that I believe… that I exist.” And if that is the case, and you cannot have that belief, then you mistakenly assigned a probability of 1 to a false statement (since the statement that you believe that string would be false.). Which explains why you should not assign a probability of 1 in the first place, since this is supposed to never happen.
(Also, “I believe that I believe X” cannot be logically deduced from “I believe X” in any case.)
To deduce something you need to use two premises. Nothing follows from “I believe X” without something additional. The other premise would have to be, “In every case when someone believes X, they also believe that they believe X.” But that is not obviously true.
Most people would call that begging the question. I will refrain from that particular accusation since ordinarily people just mean if you agree with the premises of course you would agree with the conclusion. But there is something to the point they would be making: if you are sure of that in general, that is already claiming more than the claim that you believe that you believe that you exist. In other words, it can be “logically deduced” only by assuming even more stuff.
Also, in order to have a probability of 1 for the conclusion, you would need a probability of 1 for that claim, not just reasonable confidence.
I disagree, but in any case you are not (nor is anyone else) an agent with a consistent set of beliefs, so it doesn’t matter if that is true or not.
The real issue here is that there is clearly some possibility that you are mistaken enough about the nature of belief that it is impossible for you to have a belief that consists of a million “I believe that I believe… that I exist.” And if that is the case, and you cannot have that belief, then you mistakenly assigned a probability of 1 to a false statement (since the statement that you believe that string would be false.). Which explains why you should not assign a probability of 1 in the first place, since this is supposed to never happen.
(Also, “I believe that I believe X” cannot be logically deduced from “I believe X” in any case.)
To deduce something you need to use two premises. Nothing follows from “I believe X” without something additional. The other premise would have to be, “In every case when someone believes X, they also believe that they believe X.” But that is not obviously true.
“In the case where I (Dragon God) believes X, they believe they believe X”.
I am reasonably confident that is true.
Most people would call that begging the question. I will refrain from that particular accusation since ordinarily people just mean if you agree with the premises of course you would agree with the conclusion. But there is something to the point they would be making: if you are sure of that in general, that is already claiming more than the claim that you believe that you believe that you exist. In other words, it can be “logically deduced” only by assuming even more stuff.
Also, in order to have a probability of 1 for the conclusion, you would need a probability of 1 for that claim, not just reasonable confidence.