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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.

Daniel
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  • 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 '16 at 05:41
  • basically this : https://www.youtube.com/watch?v=cDNCv-ob87E – shrey Sep 27 '16 at 06:31
  • I know I exist. I know I ignore. I know the two precedent statements are true. – Kii Sep 27 '16 at 08:49
  • @Kii: Do you know that you know you exist, or do you only believe you know you exist? – celtschk Sep 27 '16 at 09:52
  • I am sure I exist, and don't mind what "I" can mean. My own existence is a certainty, because otherwise I wouldn't be able to say so. IMO it is not a belief, it is a fact. – Kii Sep 27 '16 at 09:57
  • With this probabilistic approach, you will never catch the apple, and thus you will never eat it. So, for sure, you will starve to death attaining in this way at least a certainty about some fact. – Mauro ALLEGRANZA Sep 27 '16 at 09:58
  • @celtschk : even immersed in the Matrix, my own existence can not be denied. – Kii Sep 27 '16 at 10:48
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    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 '16 at 20:07
  • @Conifold: "no such thing as probabiliy having a probability"? Maybe, but there is certainly such a thing as "probability claims have probabities", which I think is what the question is about. consider "Joe say the probabiti –  Sep 27 '16 at 20:31
  • @Conifold: dadgummit, hit the wrong button again! ok, "Joe says the probability that X is .5. Joe is wrong about 50%of the time, and right the other 50%." then the probability that X is .25. –  Sep 27 '16 at 20:35
  • your real question is "Is it possible to know anything *with certainty*?", to which the answer is no. but that's not a problem. you "know" when you're hungry, or in pain, and you do not need a philosopher to explain that kind of knowledge. so to answer your last question: where the kind of thinking goes wrong is in presupposing that certain knowledge is a live possibility. –  Sep 27 '16 at 20:49
  • @mobileink This still doesn't make sense to me. Joe can be wrong 50% of the time about individual events, not about their probability, about the latter he is either right or wrong, 100%. I do not see what the sample space for "probabilities of probability claims" might be. It would make sense to attach subjective certainties to probability claims, but those aren't probabilities and their calculus works differently. This particular way to create a regress just doesn't work mathematically without any resort to knowledge-how, etc. – Conifold Sep 27 '16 at 21:40
  • @Conifold: Probability: the ultimate hairball. I meant Joe's probability claims are only half-right, not that what he claims as probabilities are half-right. does that even makes sense? ;) how can Joe not be wrong about the probability of an event, as you seem to say? why must Joe's probability claims be 100% righ –  Sep 27 '16 at 22:11
  • @Conifold did it again. :( Joe says the probability of getting heads with a fair coin is 75%. he says many similar things, half of which are right. so the probability that anything ha says is right, is .5. iow, forget probability claims, he's wrong half the time. his claims are just claims, not probabilities, even when they involve probabilities. "probability of a probability" may not make sense, but surely "probability that Joe's probability claims are true" does. or: truth claims, of which probabiliy claims are a species, have probabilities. –  Sep 27 '16 at 22:20
  • @mobileink Joe can be wrong that the probability is 1/2, if in fact it is 1/4, or he can be right if it is 1/2, but I don't see what it means that he is right that it is 1/2 with probability 1/2. Probability does not attach to individual events, truth claims included, it quantifies over series or ensembles, and once you quantified there is nothing left to quantify over for the "secondary" probability. I think levels of certainty about individual events are being conflated with probabilities here to apply formulas that do not apply. – Conifold Sep 27 '16 at 22:29
  • @Conifold: are you assuming that things (in the world not mathematics) have objective probabilities? I wouldn't go that far, personally. I would not agree that a real world event has an exact true probability. that would be un-pragmatistivalistic. :) btw have you by any chance read Huw Price on probabilities? it's on my list, alas, but I understand he treats the language of probability as just a coping device. Or sth like that. –  Sep 27 '16 at 22:31
  • @Conifold : I would not say that he is right that it is 1/2 with probability of 1/2. That's just one claim, which would be true or false as you point out. But I would say that only 1/2 of his claims are right, and thus if he claims that the probability is 1/2, there is a 50% chance he is wrong. we do not know ahead of time whether any particular claim of his is right or wrong, no matter what the "objective" probabilities are. –  Sep 27 '16 at 22:41
  • @Conifold: the sample space for "probabilities of probability claims" is probability claims. take a sample of n people and ask what the probability is of getting another heads if you've just got 100 heads in a row. x% != 100% will give the wrong answer. now pick any one from that population and ask the same question. what are the chances you will get the correct answer? I'm pretty sure it won't be 100%. Am I misunderstanding sth? wouldn't surprise me, given the subtleties of probability, but "probability of probability claims" seems very different than "probability of probabilities". –  Sep 27 '16 at 22:57
  • Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/45997/discussion-between-conifold-and-mobileink). – Conifold Sep 27 '16 at 23:49
  • There is also this answer on discussing Immanuel Kant's views on undoubtable thoughts. I am not sure how or if I should expand this into an answer. (https://philosophy.stackexchange.com/questions/8216/is-it-possible-to-know-anything-with-certainty/42465#42465) – Donate to the Edhi Foundation Oct 13 '18 at 16:32
  • Condifold's point appears to be correct. Your 'probability; is just a measure of your uncertainty. It is certainly possible to know with certainty, but only where this knowledge is 'by identity. I believe that Aristotle says somewhere 'True knowledge is identical with its object', although I can never track down this remark. –  Oct 15 '18 at 13:11

3 Answers3

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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.

virmaior
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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.

Rup7ur3
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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.

Harsh Chaitany
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