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Is it possible in any logical system to know what one doesn't know literally. I don't mean the daily usage of the phrase like "Sam doesn't know physics", where you are just ignorant about some topic or you know a little about it, etc. What I mean is, suppose I know a collection of propositions, let's call the collection C, then can I know something which is not in C (The answer, should I say 'intuitively' sounds no). Any articles, proofs, etc will be welcome.

Basically, the 'unknown unknowns'!

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  • Well, the true statements are fixed as soon as you say what the rules are and the starting assumptions are Jul 9, 2023 at 17:40
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    Your question needs to be clarified. In some ways, philosophy is all about knowing what you don't know. The identification and elimination of wrong or incomplete claims to knowledge begins with Socrates and extends to the Hegelian dialectic, at least. Similarly, the hard sciences can be seen not as certain knowledge, but as the elimination false claims. There are also, as Rumsfeld rightly quipped, the "known unknowns," such as the variable in an algebraic equation or the precise blank shape on a map designating unexplored territory. Jul 9, 2023 at 17:48
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    See: 'How do I know what I don't know?' philosophy.stackexchange.com/questions/99682/…
    – CriglCragl
    Jul 10, 2023 at 20:58
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    This question's importance grows with every passing second. I guess the shape of water varies ... for better/worse hypothesis non fingo. Jul 28, 2023 at 10:08
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    @AgentSmith I feign no apotheosis.
    – Scott Rowe
    Jul 29, 2023 at 13:04

4 Answers 4

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Let's model this conundrum with sets.

Let's assume to start with that you are aware of the contents of one set, call it set C. But your universe also contains sets A, B, D, E, F, ...

If you do not know that those extra sets exist, then you don't know what your areas of ignorance are.

Now if you do know that those other sets exist but you do not know what their contents are then it could be asserted that you do know what you don't know.

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  • Well, in classical logic, the answer to the question is no, as you presented it briefly too, I'm asking like what about the other logical systems, whose conclusions would make sense. Jul 10, 2023 at 17:00
  • This answer gets it right. Jul 27, 2023 at 15:58
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Depends on what you mean by don't know

The true statements in a logical system are fixed as soon as you say what the rules are and the starting assumptions are.

Related post on Math Stackexchange : Is Mathematics one big tautology?

However, still, it is not trivial to search for the meaningful true statements in a system and that's why we have so much Mathematics. So, while the truths are fixed , we have to learn and find them. But, I suppose this is not what you meant.

Now, one could also go on the meta level of asking what would be the truths of a different starting assumptions and rules too.

Analysis is also related to an important school of thought known as post modernism/post structuralism. Here is a nice discussion of it on youtube.

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  • I have edited the question to be more clear. Jul 10, 2023 at 5:26
  • @SiddharthChakravarty how did you know how to clarify it? :-)
    – Scott Rowe
    Jul 29, 2023 at 13:15
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    @ScottRowe because in the initial draft, the question was sounding ambiguous. Jul 29, 2023 at 13:29
  • @SiddharthChakravarty what is the sound of one ambiguous question?
    – Scott Rowe
    Jul 29, 2023 at 13:42
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    @ScottRowe I can't give you the exact frequency. Jul 29, 2023 at 14:12
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Is it possible to know what you don't know?

Yes. If you were to come in to the room with a bag, and tell me you have something in the bag, I would know two things:

  1. I don't know if there is actually something in the bag.
  2. If there is something in the bag, I don't know what it is.

I can justify both conclusions easily by citing the fact that people lie, and that when they the truth, my knowledge about the state of affairs in the world (like the content of your bag), are limited. So, knowing what we don't know is easy because we can justify our belief that we don't know things.

But, you have also invoked the question of unknown unknowns, and here's where things get more interesting. How do come to a state of knowledge about what we don't know. In the example of the bag, your having a bag and asking about the contents of the bag defines the scope of belief and knowledge. Specifically, you ask the question 'What is in the bag?', and that begins our journey of reason. But what about in the general situation?

First, we have to start with a recognition that reason is defeasible (SEP). From the article:

In philosophy of logic, defeasible reasoning is a kind of provisional reasoning that is rationally compelling, though not deductively valid.1 It usually occurs when a rule is given, but there may be specific exceptions to the rule, or subclasses that are subject to a different rule. Defeasibility is found in literatures that are concerned with argument and the process of argument, or heuristic reasoning.

So, our first strategy in determining unknown unknowns is to write out what we believe or know. Then we can use our intuition to explore the boundary of the known and unknown. For instance, do I know anything about the bag? Do I know anything about you who carries the bag? Do I know about what you have access to put in the bag? Do I know about what is possible regarding the bag holding particular contents? This can help separate unknowns that are and can be known from those that cannot. This might be considered an exploration of facts and defeaters.

But the more important question is, are there limits to this process? And the answer is yes. There are limits to knowledge, and therefore we are always confronted with the possibility of unknown unknowns. This rests on the basis that one cannot know everything. That there is no omniscience for human beings. What justification?

First, intuitively, through our own experiences, we are constantly discovering that our model of the world is inaccurate. We witness such an imperfection in others. We can examine people's mistakes in reasoning, and see that time and time again, people come to the wrong conclusion because they are confronted with unknown unknowns. We can examine the tentative nature of inductive and abductive logic. Is there an explanation? Perhaps. Perhaps we human beings are systems of physical computation (SEP) who have material limits to our ability to know. For instance, we can only know when we are alive, and we live a finite period. Whatever the justification, the conclusion helps to support the idea that knowledge is fallible (IEP). From the article:

Fallibilism is the epistemological thesis that no belief (theory, view, thesis, and so on) can ever be rationally supported or justified in a conclusive way. Always, there remains a possible doubt as to the truth of the belief.

If human reason is defeasible (it is), and there are inescapably unknown unknowns (there are), then reason itself is fallible (it is).

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  • "That there is no omniscience for human beings. ", and why won't it hold for any entity, would it render omniscience as self-refuting or, there could be some resolution for it. Jul 28, 2023 at 18:00
  • @SiddharthChakravarty That's an entirely separate question contingent upon the belief of entities that are sufficiently different from humans in physical or intellectual capacity to whom the question applies predicated upon the belief of their existence. As I do see reason to believe such entities exist at this time, I haven't given it much thought. IOW, I can't answer questions like is 'God omniscient' because the question 'Who or what is God?' seems to me too metaphysicalu speculative and the source of too much consensus to be of value to discussion .That being said... you're in the place!
    – J D
    Jul 28, 2023 at 19:54
  • philosophy.stackexchange.com/q/3252/40730 comes from the knowledge base and there are others
    – J D
    Jul 28, 2023 at 19:54
  • This is what makes airport security so challenging. People carrying bags, etc.
    – Scott Rowe
    Jul 29, 2023 at 13:11
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Goedel's incompleteness theorem can be thought of as knowledge of what one doesn't know, namely that it (that which one doesn't know) exists. Namely, in a logical system L incorporating the Peano Arithmetic, there will necessarily be an assertion that can be neither proved nor disproved by L.

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    Short n sweet. Except that I'd make a trinity: Gödel's incompleteness + Turing noncomputability + Tarski's Undefinability
    – Rushi
    Jul 28, 2023 at 9:37

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