I suggest that a primary cause of confusion about the distinction between "belief", "truth", and "reality" is qualitative thinking about beliefs.
Consider the archetypal postmodernist attempt to be clever:
"The Sun goes around the Earth" is true for Hunga Huntergatherer, but "The Earth goes around the Sun" is true for Amara Astronomer! Different societies have different truths!
No, different societies have different beliefs. Belief is of a different type than truth; it's like comparing apples and probabilities.
Ah, but there's no difference between the way you use the word 'belief' and the way you use the word 'truth'! Whether you say, "I believe 'snow is white'", or you say, "'Snow is white' is true", you're expressing exactly the same opinion.
No, these sentences mean quite different things, which is how I can conceive of the possibility that my beliefs are false.
Oh, you claim to conceive it, but you never believe it. As Wittgenstein said, "If there were a verb meaning 'to believe falsely', it would not have any significant first person, present indicative."
And that's what I mean by putting my finger on qualitative reasoning as the source of the problem. The dichotomy between belief and disbelief, being binary, is confusingly similar to the dichotomy between truth and untruth.
So let's use quantitative reasoning instead. Suppose that I assign a 70% probability to the proposition that snow is white. It follows that I think there's around a 70% chance that the sentence "snow is white" will turn out to be true. If the sentence "snow is white" is true, is my 70% probability assignment to the proposition, also "true"? Well, it's more true than it would have been if I'd assigned 60% probability, but not so true as if I'd assigned 80% probability.
When talking about the correspondence between a probability assignment and reality, a better word than "truth" would be "accuracy". "Accuracy" sounds more quantitative, like an archer shooting an arrow: how close did your probability assignment strike to the center of the target?
To make a long story short, it turns out that there's a very natural way of scoring the accuracy of a probability assignment, as compared to reality: just take the logarithm of the probability assigned to the real state of affairs.
So if snow is white, my belief "70%: 'snow is white'" will score -0.51 bits: Log2(0.7) = -0.51.
But what if snow is not white, as I have conceded a 30% probability is the case? If "snow is white" is false, my belief "30% probability: 'snow is not white'" will score -1.73 bits. Note that -1.73 < -0.51, so I have done worse.
About how accurate do I think my own beliefs are? Well, my expectation over the score is 70% * -0.51 + 30% * -1.73 = -0.88 bits. If snow is white, then my beliefs will be more accurate than I expected; and if snow is not white, my beliefs will be less accurate than I expected; but in neither case will my belief be exactly as accurate as I expected on average.
All this should not be confused with the statement "I assign 70% credence that 'snow is white'." I may well believe that proposition with probability ~1—be quite certain that this is in fact my belief. If so I'll expect my meta-belief "~1: 'I assign 70% credence that "snow is white"'" to score ~0 bits of accuracy, which is as good as it gets.
Just because I am uncertain about snow, does not mean I am uncertain about my quoted probabilistic beliefs. Snow is out there, my beliefs are inside me. I may be a great deal less uncertain about how uncertain I am about snow, than I am uncertain about snow. (Though beliefs about beliefs are not always accurate.)
Contrast this probabilistic situation to the qualitative reasoning where I just believe that snow is white, and believe that I believe that snow is white, and believe "'snow is white' is true", and believe "my belief '"snow is white" is true' is correct", etc. Since all the quantities involved are 1, it's easy to mix them up.
Yet the nice distinctions of quantitative reasoning will be short-circuited if you start thinking "'"snow is white" with 70% probability' is true", which is a type error. It is a true fact about you, that you believe "70% probability: 'snow is white'"; but that does not mean the probability assignment itself can possibly be "true". The belief scores either -0.51 bits or -1.73 bits of accuracy, depending on the actual state of reality.
From the inside, our beliefs about the world look like the world, and our beliefs about our beliefs look like beliefs. When you see the world, you are experiencing a belief from the inside. When you notice yourself believing something, you are experiencing a belief about belief from the inside. So if your internal representations of belief, and belief about belief, are dissimilar, then you are less likely to mix them up and commit the Mind Projection Fallacy—I hope.
When you think in probabilities, your beliefs, and your beliefs about your beliefs, will hopefully not be represented similarly enough that you mix up belief and accuracy, or mix up accuracy and reality. When you think in probabilities about the world, your beliefs will be represented with probabilities ∈ (0, 1). Unlike the truth-values of propositions, which are in {true, false}. As for the accuracy of your probabilistic belief, you can represent that in the range (-∞, 0). Your probabilities about your beliefs will typically be extreme. And things themselves—why, they're just red, or blue, or weighing 20 pounds, or whatever.
Thus we will be less likely, perhaps, to mix up the map with the territory.
This type distinction may also help us remember that uncertainty is a state of mind. A coin is not inherently 50% uncertain of which way it will land. The coin is not a belief processor, and does not have partial information about itself. In qualitative reasoning you can create a belief that corresponds very straightforwardly to the coin, like "The coin will land heads". This belief will be true or false depending on the coin, and there will be a transparent implication from the truth or falsity of the belief, to the facing side of the coin.
But even under qualitative reasoning, to say that the coin itself is "true" or "false" would be a severe type error. The coin is not a belief, it is a coin. The territory is not the map.
If a coin cannot be true or false, how much less can it assign a 50% probability to itself?
I am all too aware that I am 7 years late to this party, but coincidentally enough my beliefs from that time may fit the bill.
I too was born into a Christian family. Although I did not go to church regularly due to my parents' work, I was still exposed to religion a lot. My family was always happy to tell me about what they believed. I was told Bible stories since I was in diapers, and I began reading them myself soon after. I was even a huge fan of VeggieTales (and maybe I still am).
Yet, as far back as I can remember (I think my diaries can testify I was as young as 6 or 7) I put God into the same bin as Santa Claus and the Easter Bunny. I can't recall my exact line of reasoning, but it was probably because all three consisted of fantastic tales full of morals, and all big kids knew the latter two were fake, so why not the first?
I don't remember ever being exposed to atheists or their beliefs, but I do remember the moment I realized all these people really DID believe in God. I remember the shock. All those years I had thought they were pretending to believe in God like they still pretended Santa came every year. Everyone knows Santa is a big fake, but apparently the same idea didn't seem to apply to the other big bearded guy who makes miracles.
I suppose I am what could be considered an innocent atheist. I chose my side on the Christianity/Atheism war long before I was even aware of such a dividing line.
I may write a full post on this to include further details and context. Because even after years of self reflection (honestly not too impressive since I'm currently a young adult) I can still agree with my younger self's conclusion.
I suggest that a primary cause of confusion about the distinction between "belief", "truth", and "reality" is qualitative thinking about beliefs.
Consider the archetypal postmodernist attempt to be clever:
No, different societies have different beliefs. Belief is of a different type than truth; it's like comparing apples and probabilities.
No, these sentences mean quite different things, which is how I can conceive of the possibility that my beliefs are false.
And that's what I mean by putting my finger on qualitative reasoning as the source of the problem. The dichotomy between belief and disbelief, being binary, is confusingly similar to the dichotomy between truth and untruth.
So let's use quantitative reasoning instead. Suppose that I assign a 70% probability to the proposition that snow is white. It follows that I think there's around a 70% chance that the sentence "snow is white" will turn out to be true. If the sentence "snow is white" is true, is my 70% probability assignment to the proposition, also "true"? Well, it's more true than it would have been if I'd assigned 60% probability, but not so true as if I'd assigned 80% probability.
When talking about the correspondence between a probability assignment and reality, a better word than "truth" would be "accuracy". "Accuracy" sounds more quantitative, like an archer shooting an arrow: how close did your probability assignment strike to the center of the target?
To make a long story short, it turns out that there's a very natural way of scoring the accuracy of a probability assignment, as compared to reality: just take the logarithm of the probability assigned to the real state of affairs.
So if snow is white, my belief "70%: 'snow is white'" will score -0.51 bits: Log2(0.7) = -0.51.
But what if snow is not white, as I have conceded a 30% probability is the case? If "snow is white" is false, my belief "30% probability: 'snow is not white'" will score -1.73 bits. Note that -1.73 < -0.51, so I have done worse.
About how accurate do I think my own beliefs are? Well, my expectation over the score is 70% * -0.51 + 30% * -1.73 = -0.88 bits. If snow is white, then my beliefs will be more accurate than I expected; and if snow is not white, my beliefs will be less accurate than I expected; but in neither case will my belief be exactly as accurate as I expected on average.
All this should not be confused with the statement "I assign 70% credence that 'snow is white'." I may well believe that proposition with probability ~1—be quite certain that this is in fact my belief. If so I'll expect my meta-belief "~1: 'I assign 70% credence that "snow is white"'" to score ~0 bits of accuracy, which is as good as it gets.
Just because I am uncertain about snow, does not mean I am uncertain about my quoted probabilistic beliefs. Snow is out there, my beliefs are inside me. I may be a great deal less uncertain about how uncertain I am about snow, than I am uncertain about snow. (Though beliefs about beliefs are not always accurate.)
Contrast this probabilistic situation to the qualitative reasoning where I just believe that snow is white, and believe that I believe that snow is white, and believe "'snow is white' is true", and believe "my belief '"snow is white" is true' is correct", etc. Since all the quantities involved are 1, it's easy to mix them up.
Yet the nice distinctions of quantitative reasoning will be short-circuited if you start thinking "'"snow is white" with 70% probability' is true", which is a type error. It is a true fact about you, that you believe "70% probability: 'snow is white'"; but that does not mean the probability assignment itself can possibly be "true". The belief scores either -0.51 bits or -1.73 bits of accuracy, depending on the actual state of reality.
The cognoscenti will recognize "'"snow is white" with 70% probability' is true" as the mistake of thinking that probabilities are inherent properties of things.
From the inside, our beliefs about the world look like the world, and our beliefs about our beliefs look like beliefs. When you see the world, you are experiencing a belief from the inside. When you notice yourself believing something, you are experiencing a belief about belief from the inside. So if your internal representations of belief, and belief about belief, are dissimilar, then you are less likely to mix them up and commit the Mind Projection Fallacy—I hope.
When you think in probabilities, your beliefs, and your beliefs about your beliefs, will hopefully not be represented similarly enough that you mix up belief and accuracy, or mix up accuracy and reality. When you think in probabilities about the world, your beliefs will be represented with probabilities ∈ (0, 1). Unlike the truth-values of propositions, which are in {true, false}. As for the accuracy of your probabilistic belief, you can represent that in the range (-∞, 0). Your probabilities about your beliefs will typically be extreme. And things themselves—why, they're just red, or blue, or weighing 20 pounds, or whatever.
Thus we will be less likely, perhaps, to mix up the map with the territory.
This type distinction may also help us remember that uncertainty is a state of mind. A coin is not inherently 50% uncertain of which way it will land. The coin is not a belief processor, and does not have partial information about itself. In qualitative reasoning you can create a belief that corresponds very straightforwardly to the coin, like "The coin will land heads". This belief will be true or false depending on the coin, and there will be a transparent implication from the truth or falsity of the belief, to the facing side of the coin.
But even under qualitative reasoning, to say that the coin itself is "true" or "false" would be a severe type error. The coin is not a belief, it is a coin. The territory is not the map.
If a coin cannot be true or false, how much less can it assign a 50% probability to itself?