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Assume that doubt is meaningfully defined. Or let's say we define doubt as , both the statement under doubt, and it's complement can be true or false, we do not know, the uncertainty exists.

Imagine an ultimate doubter.

In this scenario, the doubter can doubt everything, including him being in doubt.

The doubter can make the sentence “I doubt that I am doubting”.

This sentence does not break reasoning.

Let me explain how.

I doubt (A), that I am doubting(B).

These are two different levels of doubt. This is a self referential doubt.

Doubting that “I am doubting”, does not mean that the doubter is not doubting. Doubting entails both the possibilities, “I am doubting”, can be true, or “I am doubting” can be false.

So the chain of recursion goes something like this:

“I am doubting”, is True.                               (1)

“I doubt(A), that I am doubting(B)”, is also True.      (2)

But, in (2), (B) is true under doubt or statement (A), and since (B), is in doubt, it is not as True as (1).

Again, the order of statements matter quite a lot.

Consider the sentence,

“I doubt (A), that I am not doubting(C)”                (3), for example

This(C) is false, since we have already established in (A) that we are doubting, so it’s complement in a sense, that “I doubt, that I am doubting”, has to be True.

Or, am I wrong somewhere in logic? ( I get my obvious current mistake, but trying to reword it meaningfully)

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  • "It would require the doubter to observe himself in order to say "I cannot doubt my doubt"" presupposes reflective model of self-consciousness that Descartes and other traditionally used, but it is controversial today. If the "I" surmises are pre-reflective the second argument does not work. But I do not see the point, few today defend the validity of cogito anyway.
    – Conifold
    Commented Nov 10, 2017 at 19:22
  • Your notion of "doubt" is so obscure that it is impossible to say if this point was raised before (but it probably was multiple times). And in any case, on the pre-reflective model one does not have to "observe on the inside" to make surmises about oneself. The idea of assimilating "inner sense" to outer perception, so-called Cartesian theater, is largely discredited today.
    – Conifold
    Commented Nov 10, 2017 at 20:30
  • So far you do not have an argument, which is why it is impossible to say much about it. What is doubt? What is "the universe"? What questions can be asked? What are your premises, what are the inference steps? Since pre-reflective model is popular in modern psychology by assuming something that rules it out you already make your argument half-moot. And since cogito is not accepted by most anyway why care at all?
    – Conifold
    Commented Nov 10, 2017 at 20:52
  • Let us continue this discussion in chat.
    – Conifold
    Commented Nov 10, 2017 at 20:59
  • Your hypothetical universe is impossible and this is the problem. We cannot doubt 'I am' and if we doubt that we doubt then perhaps we don't. . .
    – user20253
    Commented Nov 11, 2017 at 12:44

5 Answers 5

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The reasoning breaks the definition. I made the blunder of assuming that doubt could be meaningfully defined in such a situation.

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A minor point but in (2) does the doubter need to say anything ? Why not just 'in order to think' ?

If the doubter has a language then doesn't the doubter have beliefs - beliefs about the use of language ? If so, this is not a universe is which there is, beside the ultimate doubter, only doubt.

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  • The question appears to be a logical fallacy arising from the idea of a universe that is impossible.
    – user20253
    Commented Nov 10, 2017 at 16:46
  • @novice - i cannot make sense of a universe that contains only doubt. We cannot doubt that we are aware so such a universe must be impossible. Setting up impossible worlds leads to endless problems, as we see from the zombie arguments that cause so much trouble in philosophy of mind.
    – user20253
    Commented Nov 12, 2017 at 12:44
  • @PeterJ : Can this be used as a proof for cogito? The one i put up now.
    – novice
    Commented Nov 12, 2017 at 22:19
  • @novice - Not sure what you are referring to here. A demonstrable proof of cogito is not possible.
    – user20253
    Commented Nov 13, 2017 at 13:13
  • @PeterJ proving that it is not possible to doubt that you are doubting. "I doubt, I exist"
    – novice
    Commented Nov 13, 2017 at 16:45
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Very good question.

you must make him believe he is in doubt.

In order to believe to be without doubt. Is impossible nearly. If I tell you-you're going to get $1000000 in an hour you won't believe me. But then if I show you a picture of the million dollars you still don't believe me but I have eliminated some of your doubt. Only when I hand you the million dollars and you experience it, in reality, can you ever believe without doubt. Now to remove belief and only leave doubt would seem rather simple. You must make him believe he is in doubt.

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  • Paradox. He believes in something now. That he is in doubt.
    – novice
    Commented Nov 17, 2017 at 22:23
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Forgive me from straying from symbolic logic, but I think your answer is found without it. Sometimes the system of symbolic logic can be a little deceitful when we are using it as more of an equation separate from the underlying meaning of the words.

To doubt something is to cast uncertainty towards something (idea, fact, conclusion, etc).

I doubt you are taller than me. I doubt "that" is a fact. I doubt "it" will turn out that way. etc.

This doubt comes from within your mind. In order to doubt something that is also within your (rational) mind you need to again be uncertain about whatever that is. For example, you can doubt your ability to do something.

To "doubt your own doubt" you must be uncertain if you are uncertain about something. It is incompatible. There may be a "certainty scale," however "certain" is an absolute while everything else is uncertain. When one begins to doubt their uncertainty, they are still uncertain and therefore their original doubt is not actually doubted. It becomes a redundancy. When the scale begins to tip towards your doubted doubt becoming a certainty (no longer in doubt), it eliminates the uncertainty of the doubt towards your original doubt.

Note: wording gets a little tricky with so many "doubts"... I will try to reword ASAP if not understood correctly.

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What is this trying to achieve? The point of Descartes is that at this point in his systematic doubt he reached a point from which he gained certainty of something: That he exists, at least as a thinking thing (res cogitans). This is still true when you doubt that you are doubting: Maybe there is an evil demon trying to trick me, but maybe there isn't. Whatever it is, I can be sure of at least one thing: my existence.

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