Correct vs. True?
What is the difference between something correct and something true? Is correctness the same as truthfulness? In other words, are all instances of correctness identical with truthfulness?
Correctness-Truth Alignment
For a Proposition P, where P is correct, P must also be true
At first glance, it seems like they must be. For example, consider a math test. On the test, if you solve an equation, you will be marked as correct.
Case 1:
Q: x + 5 = 12,
A: where x = 7
Case 1b:
Q: 2 + 2 = x,
A: where x = 4
It isn’t hard to find many cases where the correctness of a proposition aligns with truth. So according to these cases, the alignment seems to be clear. That which is correct must also be true. It may even be that any difference is merely in name alone, that both concepts point to the same thing. Now let’s go beyond, can we think about something that violates this alignment? Can we find an example that is correct but untrue?
Case 2:
Based on the orbital paths of celestial objects, The Earth is the center of the universe.
Back before the 16th century, nearly everyone would have assented to this statement as both correct and true. It aligned with the current understanding of astronomy and was accepted as extremely sound. Now we stand with our contemporary understanding in this field and we know that this statement is provably untrue it is taught as an example of a misleading belief.
So we can clearly and uncontroversially dismiss Case 2 as untrue. Can we dismiss it as incorrect? In this post, I am going to argue that in a way, we would be wrong to step in and simply dismiss this case as incorrect. Don’t jump ahead of me here. I just want you to for a moment realize with me that if we could successfully differentiate the values of correctness and truthfulness in this case, even slightly, it would disprove P1. I just want to show that the alignment between correctness and truthfulness is more complex than what we may have believed prior. This gets a little tricky so bear with me.
Checks and Xs :
Suppose, a similar mental framing that we used for Case 1. You are in a time before the 16th century, you are taking an astronomy exam. On this exam, it asks you, which planet is in the center of the universe. You then recall what you learned in a past lecture, and since you are a diligent student, you even rationalize your answer. You write:
Pre-16th Century Question 1:
“Based on the orbital paths of celestial objects, Earth is the center of the universe.”
Later upon reviewing the exams, the teacher looks at your question 24 and marks it with a big check. The check is the symbolic stand-in for what we all know as a correct answer.
Stand with me in this example and look for a moment. I feel a clear and overwhelming force to call the answer to question 24 demonstrably untrue. However, to call it full-stop incorrect seems to drift into rougher waters. Why? Well because it has that big check next to it. By all accounts, that check signifies its correctness. The teacher, who read the answer and is deemed the expert, reviewed it and signaled its correctness. It acts as a stand-in for that time and the knowledge they stood upon. It is this difference that I think captures the distinction.
Suppose you were in a contemporary science class. You are taking the exam and you follow suit with your (historical time period).
Contemporary Question 2:
“Based on the orbital paths of celestial objects, Earth is the center of the universe.”
The teacher when reviewing the exam graces your answer with a big red X. We all know the big red X is a symbolic stand-in for incorrectness. I think we are beginning to see the concept come apart a little bit, and it may have something to do with the teacher. So let me begin the propositions reformulate with the teacher included.
Grading with Different Teachers
Q1:
According to Teacher A, Case 2 is correct.
Q2: According to Teacher B, Case 2 is incorrect.
So we can see here, what changes is more than just the yielded verdict. Importantly the teacher grading the assignment is also changing. If you got teacher A to grade Question 2, you’d see Case 2 as correct again. The primary independent variable in this case seems to be which grader you have, and the correctness merely depends on that. This seems to provide the teacher with a little too much authority over what is correct. If a third Teacher C, was deeply confused and marked every answer even contradicting ones as correct, we’d see something wrong with correctness depending on the grader. So where does the Teacher get their authority? Let’s look at yet another formulation to clear this up.
Grading with Different Systems
Q1:
According to Teacher A, who knows the system of astronomy S1, Case 2 is correct.
Q2:
According to Teacher B, who knows the system of astronomy S2, Case 2 is incorrect.
You can now clearly see why teachers A and B are disagreeing on the correctness of Case 2. They have different systems of astronomy. We can isolate this even further it has nothing to do with Teacher A or B, they stand in as a human version of the system. You could have the same teacher A who updates their astronomy system to S2, and it would align with Case 2’s incorrectness. We have learned something here that is useful to understanding correctness better. Correctness depends on a system and a particular proposition’s alignment with that system. In this way, correctness acts as a signal of coherence.
A Property of Correctness:
To determine the correctness of a proposition, a grader must base their verdict on how well the proposition coheres with a system.
Absolute truth instead aligns itself as some sort of real foundational fact about the nature of the world. Absolute Truth does not care about what system of astronomy we use. It may well be that both systems of astronomy mislead us from the truth.
A Moral Example:
Suppose someone asked you:
The Trolley Problem:
A runaway trolley is running down a single line of tracks. On that track are five people who will be killed. You stand on a footbridge above the tracks where you can push a large man off. Doing so would kill the large man, but save the five people. Is it right to push the large man?
You consider the problem for a while and render your verdict that:
Moral Verdict:
It is not right to push the large man.
Is it correct? Bad news for you, your teacher is a staunch utilitarian.
Moral Teacher (Utilitarian):
According to Utilitarianism, your moral verdict is incorrect.
You may try arguing with your teacher about how it can’t be incorrect. It feels wrong to push someone in this case. You may plead, but as you look toward the system it is hard to find how you could be correct. Utilitarianism explicitly states that the right action is that which has the consequences which produce the most utility. Therefore, killing one person to save five is the right and good thing to do. As you attempt to argue, it seems impossible to make your case. In your desperate pleading, you finally utter:
I know that you are correct, but it just can’t be true.
You realize you can’t find what it is about the Utilitarian system that is wrong you may even clearly understand the Teacher’s point of view. But despite all of that it still feels untrue. Now since we have our previous discussion laid out we can better understand what is happening. We disagree with the system that is asserted.
Systems are hard to argue against as we saw when our student pleaded. It can feel like a steel box you have been trapped within which provides no clear direction out of. It isn’t sufficient to disagree with the follow-on proposition, what to do in the trolley problem, you instead have to question the entire foundation of the system.
So while we may have an impulse to utter something like:
You are incorrect in the trolley problem! It is right to save 1 person instead of 5!
This is unsatisfying because it is non-sensical according to the system. It is the equivalent of stomping your feet. Instead, you have to completely break the foundation of the box.
Maximizing Utility is too reductive a view to consider what is right and wrong. Your whole system is wrong!
In The End
There may be times we meet others who purport to know what is right and wrong, true and untrue. It can feel off-putting to see someone advance an argument you don’t agree with. Even worse when you don’t know exactly why you feel so. You may follow the logic and the argument and find somehow the logic fails to capture or convince you. An intuitive pull prevents you from assenting to the reasoning. Those skeptical of our common sense intuitions may use examples like these to pull you into believing things that feel off. Instead, this feeling is an important aspect of our intuitive and cognitive abilities. We use our common sense as a way of verifying our systems, not the other way around. In these moments you may be dealing with a systematically correct proposition, but doubt its truth. In these cases, there is a piece of the argument which isn’t being clearly stated. It could be a disagreement on the belief system used, a snuck premise, or even a simple misalignment of word definitions. There is usually something that needs to be more clearly lifted into light.
Correctness appeals to how a proposition conforms to a certain system, whether that is mathematics, astronomy, morals, or politics. That is all it can purport to do. A proposition that generates its intellectual value on its coherence with a system of beliefs has value only insofar as you also take those beliefs as true. We ought to be careful in our appeals to systems, especially those which are epistemically controversial. On the other side, we ought to question those who make arguments implicitly with this plea to a system. As we saw prior, it can have the effect of boxing you into their own presupposed state of the world. A solution to this is not to try and disprove the proposition but to undermine the foundations of the belief system entirely.