Do we know whether we know something?

Question

Intuitively, it seems pretty obvious that, for a given proposition p, we know whether or not we know p.

I am not sure how to express this more formally (e.g. as a property of the relevant epistemic accessibility relation). I remember that belief, as opposed to knowledge, corresponds to a transitive accessibility relation. However, as far as I can see, transitivity would mean:

I know that I know p --> I know p

What I am looking for seems to be the reverse direction, though:

I know p --> I know that I know p

Has any philosopher ever explicitly stated something along these lines? What would be the relevant literature?

Thanks in advance!

Answer 1

I would suggest that you look at the literature on Gettier problems, as they would show why it is not always the case that

I know p --> I know that I know p

If one defines knowledge as "justified true belief" (i.e., JTB), then one can easily see situations where one knows something without one knowing that one knows; if one believes P to be true, and has a justification to believe P, and P is in fact true, it might still be the case that one does not have knowledge that the justification is good, and that P is in fact true.

Answer 2

In the latter period of his writings, a chap by the name of Ludwig Wittgenstein looked a second time at his earlier work and rather drastically changed his mind. In his first book, the Tractatus Logico Philosophicus, he argued, among other things, that

A logical picture of facts is a thought (Proposition 3)

This, when one unpicks to a decent enough approximation what he means by the terms, seems to make some sense- after all, it seems we cannot think anything truly illogical*, and I certainly seem to have an internal model of the things I am thinking about.

Indeed, if one hunts for the intuitive appeal in the claim "knowledge => knowledge of knowledge", one sees something similar, for:

If I know that p, and I know what I am thinking (this much, by hypothesis or 
apparent tautology)
*It is an immediate logical consequence* that I know that I know that p

Any logical picture shewing my knowledge of p occurring in my mind must logically shew its own presence.

As Wittgenstein demonstrated in his later work Philosophical Investigations, such accounts of thought are palpably false. To see why such accounts are false in full generality is rather a lot of work, so let's attack just the relevant bit of it. To adapt an example from section 60 (of PI): to bring a broomstick and brush attached as to make a broom, connotes a different thought than to bring a broom, although they are logically equivalent. That is to say exhaustive logical consequence is not a feature of thought.

Though one may derive second order knowledge of p from knowledge of p, one need not in knowing p.

To conclude, a thought experiment:

In a world where knowing state secrets is punishable by death; a man discovers, while walking in the park, an official document declaring the location of his children's school to be a nuclear testing site- at the bottom of the page; the words [top secret], the government seal, and a reminder of the law. Is his first thought for his own life, or his children's? Suppose somehow, both the reminder of the law, the secret itself and that it is a secret were conveyed simultaneously (for example, if there were a single monosyllabic word in the man's language containing all this information); what then?

*Although we may think plenty that is irrational or unreasonable. IMO the character Spock in the original Star Trek has a lot to answer for for confusing these three terms in the eyes of the public...

Answer 3

I don't have any profound philosophical insights for you, but I'll provide a referenced interpretation for my conclusion that by definition, knowing something does in fact imply knowing that you know.

First, the three criteria you listed for knowledge itself are corroborated by the SEP Article on epistemology (with the exception of the Gettier Problem, but that's another question entirely). I'll summarize each of these three and their relevant implications below (but not the details; the SEP has already accomplished that marvelously):

1. Truth. Now, there is a whole lot of extensive discussion on the nature of truth, but these are mostly ontological. People generally agree on what makes something true (although the conflict between Rationalism and Empiricism is pretty important) and regardless, I don't think it makes a big difference to the question at hand. Let it suffice that by definition (at least the one being used presently), knowledge simply must be true.

   Given this, I want to make the first point of my answer: we are not always aware of what is and is not true, regardless of our perceptions and beliefs. False beliefs aside, we may simply not realize that something is true because we have never given it consideration; note, however, that this does not keep it from becoming knowledge. It does not matter whether we know something is true or not, as long as it is true and the other two criteria are satisfied.

2. Belief. The SEP defines belief as "the attitude we have, roughly, whenever we take something to be the case or regard it as true." Then it makes a very important point regarding your question:

   To believe something, in this sense, needn't involve actively reflecting on it: Of the vast number of things ordinary adults believe, only a few can be at the fore of the mind at any single time. Nor does the term “belief”, in standard philosophical usage, imply any uncertainty or any extended reflection about the matter in question (as it sometimes does in ordinary English usage). Many of the things we believe, in the relevant sense, are quite mundane: that we have heads, that it's the 21st century, that a coffee mug is on the desk.

   From this, I want to expand on the idea I expressed about truth: a belief does not require awareness either. You can believe something without thinking about it, and until you are confronted with the idea, you needn't even realize that you have the belief. However, you still had the belief the whole time.

3. Justification. As is explained in the SEP's article on epistemology (above), this is far from a simple matter. However, in the simplest view, a belief is justified when you have no obligation to believe otherwise (deontology). A more complex view is that a belief is justified when you have evidence for it (non-deontology). Although what actually qualifies as evidence is debated, what is and isn't justified does not seem to get much more complicated than having evidence.

   Here I want to bring my argument full circle. It would appear that every criteria for knowledge is achievable without active awareness. You can be justified in the belief that apples fall from trees on Earth either because you have no obligation to believe otherwise, or because you've seen apples falling. In either case, however, you can (as I explained about) be unaware of the belief, and by extension, the justification of the belief itself. You have evidence, but you don't think about it.

What this means is that you can have an unthought-of justification for an unthought-of belief in an unthought-of truth. I think the statement "knowing something does not imply knowing that you know something" must be using two different definitions of knowledge (or a different one entirely), because using the above argument one can observe the following:

Suppose I know that twice two makes four. Even if I haven't really thought about it, I still know it by the above definition of knowledge. Now, let's see whether I know that I know something:

• It is certainly true that I know something, because I know that twice two makes four.
• Is it a belief that I hold? It must be, because if I believe that twice two makes four, I must by extension believe that I know that - otherwise, I do not even know that twice to makes four, by default.
• Finally, is the belief that I know something justified? Whether I realize it or not, it is, because I either have no obligation to believe otherwise, or I actually have evidence that I know something: I know that twice two makes four.

Thus, it seems to me that to know something must imply knowing that you know something. Only semantically could it be possible to say that this is false; one may argue that you don't really think about knowing something, so you don't know that you know something (if knowledge is instead defined also as something that you must be aware of).

However, using the common epistemological definition, you must know that you know something if you know anything at all.

Answer 4

I think part of the confusion is that you are using "justified" to refer to the "truthiness" of the knowledge that you have, rather than your belief in the truth of that knowledge. Yes, it is tautological to justify knowledge as true by stating that you know something, on the merit of which, it is justified as true because that's what knowledge is. Beliefs are in need of justification, and the beliefs that are justifiable (by means that are contentious and debatable), may be said to amount to knowledge. The idea that there is an objective criterion called "Truth" that each belief can be held up to for reference begs the question (but this, too, is a focus for healthy debate). I am unsure of what you mean by "evidence" as opposed to "original evidence."

Also, why do you think that having beliefs means, by necessity, awareness of beliefs? Discussing specific beliefs probably brings an awareness of the belief in question, but how can you be sure that you are aware of every one of your beliefs - that you even have access to be aware of every one of your beliefs? Isn't this part of why reflection or contemplation or introspection are activities at all? To me, it seems that these activities help us consider those things we had not considered before and become aware of those things we had previously not been aware of.

Answer 5

In my mind believing something necessarily entails being aware of that belief, or a belief is just a conscious opinion (my philosophy professor has not said this). Given these criteria it seems that knowing implies that it is true and one believes it and has evidence for it. Therefore it is true that you know it, and it also true that you believe that you know it, by necessity.

I don't think that your professor is targeting the awareness of having a belief. I suspect that he targets the claim that one has proper knowledge of the fact that one knows (and not that one "believes" the fact that one knows.)

According to canonical epistemology, "knowledge" means "justified true belief". Therefore "to know" means "having justified, true beliefs". Do you think that everyone who knows that p knows that she has a justified true belief that p? In other words: Does one know, without having a complex theory of knowledge, what the conditions of knowing that p are? I would say this is highly unlikely. This is probably what your professor means when she claims that knowing does not imply knowing that one knows.

Secondly, even if we go by your weaker interpretation – knowing p implies believing that one knows that p – it seems that no such second-order belief is necessary in order to know that p. This is addressed in virtue epistemology (which tries to define knowledge not in terms of JTB). Here Ernest Sosa introduced the distinction between animal knowledge and reflective knowledge. Here's a brief overview:

Let's begin with Sosa's answer to the question "what is knowledge?" Knowledge, according to Sosa, comes at two levels. First, there is the kind of knowledge that human beings share with creatures who are not capable of theorizing: this is what Sosa calls "animal knowledge". Then, there is a kind of knowledge that is possessed only by creatures capable of theorizing: this is what Sosa calls "reflective knowledge". For a creature to have animal knowledge that p is for that creature to believe accurately that p, and for that belief to result from that creature's exercise of an epistemic competence (for the belief to be, as Sosa says, "adroit"), and for that belief to be accurate precisely because it is adroit (for the belief to be, as Sosa says, "apt"). In short, for a creature to have animal knowledge that p is for that creature to have an apt belief that p -- a belief that is accurate because it is adroit. For someone to have reflective knowledge that p is for her to believe that she aptly believes that p, and for this higher-order belief itself to be accurate because it results from the exercise of a competence that enables one to defend one's beliefs against challenges (including skeptical challenges). Thus, for someone to have reflective knowledge that p is for her aptly to believe that she aptly believes that p. To have such iterated apt belief requires being able to defend the content of one's belief against skeptical challenges. (This is of course not to say that possessing reflective knowledge requires actually defending one's belief against skeptical challenges: one can possess reflective knowledge without having skeptical challenges ever cross one's mind.)

(Review of Ernest Sosa: A Virtue Epistemology: Apt Belief and Reflective Knowledge, Vol. 1 by Frederick F. Schmitt)

In this sense one can certainly know (i.e. have animal knowledge) without knowing that one knows (i.e. having reflective knowledge).

Answer 6

First we should understand several assertions:

• i am aware of something and,
• i feel something

I am aware, it means i perceive difference. I feel something, it means i am not perceiving difference, but i am focusing on something.

I am aware is, when i am thinking, and i feel something is, when i am feeling of something without thinking, just doing things, enjoyment.

But indeed sometimes (mostly) we couldn't keep our feelings longer, and it will cause distraction and switched quickly from feeling of something to thinking about situation to maintain what we are doing (feeling of something itself). We may guess that feeling will involve thinking, but actually it won't. We just have to think deeper, strictly and see the border that may be very thin.

Conclusion: "i am aware" has nothing to do with focus. I am aware and it's merely our thinking that active to aware from one point to another point to see the differences. If we thought that while we were aware of something also we felt of something (aware = focus), it's wrong (aware is not focus). What really happened was, that we did, comparing, and (quickly) after that we switched to feeling (focus on something) and this will make us looks like thinking & feeling of something that is equal to aware of something, but it's wrong.

Now, we have two assertions:

• I perceive difference (aware)
• I focus on something (feel)

Further: "I know that I know something". This could be splitted into four:

• i am aware that i am aware of something, or
• i am aware that i am focusing on something, or
• i am focusing that i am focusing on something, or
• i am focusing that i am aware of something

But "i know" means "i am aware" rather than "i am focusing" on something, therefore "I know that I know something" is equal to "I am aware that I am aware of something". It asserts possibilities. Those are:

1. "I am aware" then "I am aware of something" = False, because,

   • "I am aware" then "I am aware of something", = "first, i am aware of nothing", but it asserts that i perceive nothing, and it's impossible, therefore it's fallacy (wrong)

   OR

2. "I am aware of something" then "I am aware" = False, because,

   • "I am aware of something" then "I am aware" = "first, i am aware of something" then "i am aware" of nothing, which is impossible, therefore this form is fallacy (wrong)

   OR

3. "I am aware of something" then "I am aware of something" = True, because,

   • "I am aware of something" then "I am aware of something" = "first, i am aware of something" then "i am aware" of something, which is possible, therefore this form is true.

   The notation is: P -> P = FOCUS

   It asserts prolong the same event. It's equal to focus.

   The correct statement related to this (P -> P) is "I am focusing on something"

Focus or Aware (Perceive Differences)

• But since "I know" is not focusing on something, because "I know" assert aware of something, therefore "I know" is equal to "I am aware".

• And if we insist to use this form as P -> P that has no relation with focus, then one of this proposition (P) must be replaced with ~P, and it must be in line with "I am aware of something" then "I am aware of something". The possibilities are:

  • ~P may represent:

    1. "I am not aware of something", but it's not in line with "I am aware of something", or
    2. "I am aware of nothing", and it's not in line with "I am aware of something", or
    3. "I am aware of something else", and it's in line with "I am aware of something"

  Therefore, ~P must be asserted as "I am aware of something else".

Conclusions:

• The correct notation: P -> ~P or P -> Q, with:

  • P = "I am aware of something"

  • ~P = "I am aware of something else"

  • Therefore: "(I know) that (I know something)" must be understood as = "(I know something) that (I know something)" = "(I know something) that (I know something else)"

• It's a strong assertion to ourselves. It's introspection, self awareness and similar to these.

  Examples for more familiar conversations represent this, are:

  ("I am aware of something") and it asserts -> ("I am aware of something else") =

  • ("I am aware about my illness") and it asserts -> ("i am aware that i should go to medical check up")

  • ("I am thinking of you") and it asserts -> ("i am thinking to make a phone call on you")

  • ("I know something on you, ... as i saw you yesterday") and it asserts that -> ("i know, you fall in love with her")

  • ("I know something on you, ... as i saw you last night") and it asserts that -> ("i know, you should sing a song to make you happy")

  • ("I know myself, ... as i live everyday") and it asserts that -> ("i know, i should learn piano")

• It's P -> Q for introspection. It's P -> Q for self awareness. It's P -> Q for strong assertion.

Answer 7

There are two aspects to this, depending on what you mean by 'to know'.

One aspect is the mental mechanics of awareness and consciousness and how the brain processes statements.

The other aspect is the mathematical idea of knowledge, the symbolic manipulation of mathematical propositions.

First, being able to articulate consciously a statement about the world also means being able to articulate consciously your confidence in your internal state about it. Once you're aware, you're aware that you're aware and so on, it's all in the same conscious mental space. But there's lots of knowledge and ability that we have as organisms that we can't articulate consciously. I have a lot of awareness of my physical surroundings that I am not aware of but I tend not to bump into the door frame when I walk though it.

Mathematically though, logic has stipulated very well a lot of these things very distinctly. There are facts (propositions) that are 'known' and can be inferred from, but there is a separation in some logics whether one can know about these facts. Provability logic, a particular kind of Modal logic, helps to separate between things that are known (elementary propositions) and things that are known to be known (i.e. proven). For example, there is a rule of inference (which is not necessarily used by all modal logics) that "If p is true, then 'p is provable' is true".

So for everyday things that you talk about, things that you know, yes, you know that you know them, because things that you know are all in the same mental space, your consciousness. If you know it, you know that you know it, and you know that you know that you know it, and so on. But for that infinite regress, you probably didn't know that, since you're asking. In some sense that really proves there are some things that you knew that you didn't know that you knew. But informally, that's probably not what you're talking about.

But in mathematical logic, one can choose your logical properties such that in one proof system you may know things but don't immediately know that you know those things but in another your self-knowledge is infinite.