I am very sure this apple in front of me exists. I could be hallucinating however, so lets say:

  1. I am 98% certain the apple exists.

I am confident that (1) is a fair assessment, but I can't really be sure, so lets say:

  1. I am 99% certain that (1) is true

and then,

  1. I am 99% certain that (2) is true

and then,

  1. I am 99% certain that (3) is true

... etc, (I don't think one could be completely certain about any of these)

But I can only be certain about (1), if (2), (3), (4), ..., are all true.

Let A be the event that I am certain about (1)

But then P(A) = P(2) * P(3) * P(4) * ... = 0

(This would not mean that the apple does not exist, just that I can't really know that it does)

Now I don't actually believe this, but I haven't been able to pinpoint where this type of thinking goes wrong.

  • Actually my position is: I cannot be sure that the apple exist (as you say, I could be hallucinating, or I could be dreaming, or I might be in the Matrix, etc.) but what I can be sure is that I perceive the apple. There cannot be the slightest doubt that this perception exists, even though the perceived apple may not.
    – celtschk
    Sep 27, 2016 at 5:41
  • basically this : youtube.com/watch?v=cDNCv-ob87E
    – shrey
    Sep 27, 2016 at 6:31
  • I know I exist. I know I ignore. I know the two precedent statements are true.
    – Kii
    Sep 27, 2016 at 8:49
  • @Kii: Do you know that you know you exist, or do you only believe you know you exist?
    – celtschk
    Sep 27, 2016 at 9:52
  • 1
    There is something funny with the math. If 98% in "I am 98% certain the apple exists" is probability then this is not itself an event that has a probability. It is either true or false that "apple exists" has this probability, there is no such thing as probability of having a probability, so 2,3,etc. are undefined. Even if they were, the product rule only applies to independent events. If we rephrase your events to make sense, like "(2) (1) is true", etc., they are all in fact the same event, and you don't get to assign probabilities to them, they are all at 98%, and so is their conjunction.
    – Conifold
    Sep 27, 2016 at 20:07

3 Answers 3


I'd suggest two things.

First, what you're offering is similar to an argument that Descartes offers elliptically in the Meditations. In Med. 1, Descartes points out that he has at times been mistaken. And as a consequence should doubt all of his beliefs, but that checking the beliefs would take an infinite amount of time. His solution is to instead suspend belief until he can come up with a firm foundation. Ostensibly in his argument, this is the cogito, but more accurately it's a circle of (a) the cogito (Med 2), his argument for a good God (Med 3), and "clear and distinct ideas" (scattered throughout and not well defined).

In the process, Descartes highlights a problem for the sort of system you're suggesting. Namely, there's going to be a negative infinite regress. In his case, it's that we have to keep doubting our judgments -- including our judgments about our judgments. In your case, it's a continuous loss of probability.

This leads to the second issue. Maybe both you and Descartes are wrong about what it means to know something? A lot of recent work has suggested that knowing is an act. This research is spear headed by Ernest Sosa and John Greco. On their view, to know something is more similar to successfully baking a cake than justified true belief. You either end up with cake or you don't.

On such a model whether you arrive at knowledge depends on the techniques you're using and virtues of the knower, and your confidence levels don't really enter in. Moreover, once the knowing is accomplished, it's over, so there's no room for the sort of compounding probably you and Descartes face.

Maybe to state it more simply, knowing may not be the sort of thing subjectable to an infinite set of regresses about our confidence in each act of knowing. Instead, it might just be something that succeeds or fails.


It depends on the definition of knowledge. My definition of knowledge would come down to this: an assumption that a belief which is correct, is correct

Is it posssible to know apples exist? I'd say it could be possible. I'll explain why I think so.

According to my definition there are really two things you have to do: (1) to believe that apples exist, and (2) to assume that your belief is correct.

Then if apples really would exist, then you would have knowledge of it.

I see no reason why something could or couldn't exist. Also, I don't think anyone understands how to tell if something exists or not.

Also, regarding the approximation to infinity, it is due to the fact that knowledge is per (my personal) definition based on an assumption. So everytime you try to know whether or not the assumption is correct, you would make another assumption.

Again, I do not claim you cannot know. I do not claim that you can know. All I claim is that all by definition, knowledge is based on an assumption.

If you try to seek truth, you would have to create a perfect circle in which all assumptions are backed by knowledge. So your first piece of knowledge has to explain the assumption of the last piece of knowledge. I wish you health, strength and wisdom to seek such truth.


The basic problem with the OP is that the first numberic value of 98 percent or whatever already takes into account all possible assumptions. I am not saying the number is correct or whether arriving at any such value is even possible. But if it is at all possible. It has to be done in the first step itself. There is no need or possibility for further assumptions diminishing the number at all.

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