The Nonlinear Library LW - Circular Reasoning by abramdemski
Aug 5, 2024
20:35
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Circular Reasoning, published by abramdemski on August 5, 2024 on LessWrong.
The idea that circular reasoning is bad is widespread. However, this reputation is undeserved. While circular reasoning should not be convincing (at least not usually), it should also not be considered invalid.
Circular Reasoning is Valid
The first important thing to note is that circular reasoning is logically valid. A implies A. If circular arguments are to be critiqued, it must be by some other standard than logical validity.
I think it's fair to say that the most relevant objection to circular arguments is that they are not very good at convincing someone who does not already accept the conclusion. You are talking to another person, and need to think about communicating with their perspective. Perhaps the reason circular arguments are a common 'problem' is because they are valid. People naturally think about what should be a convincing argument from their own perspective, rather than the other person's.
However, notice that this objection to circular reasoning assumes that one party is trying to convince the other. This is arguments-as-soldiers mindset.[1] If two people are curiously exploring each other's perspectives, then circular reasoning could be just fine!
Furthermore, I'll claim: circular arguments should actually be considered as a little bit of positive evidence for their positions!
Let's look at a concrete example. I don't think circular arguments are quite so simple as "A implies A"; the circle is usually a bit longer. So, consider a more realistic circular position:[2]
Alice: Why do you believe in God?
Bob: I believe in God based on the authority of the Bible.
Alice: Why do you believe what the Bible says?
Bob: Because the Bible was divinely inspired by God. God is all-knowing and good, so we can trust what God says.
Here we have a two-step loop, A->B and B->A. The arguments are still logically fine; if the Bible tells the truth, and the Bible says God exists, then God exists. If the Bible were divinely inspired by an all-knowing and benevolent God, then it is reasonable to conclude that the Bible tells the truth.
If Bob is just honestly going through his own reasoning here (as opposed to trying to convince Alice), then it would be wrong for Alice to call out Bob's circular reasoning as an error. The flaw in circular reasoning is that it doesn't convince anyone; but that's not what Bob is trying to do. Bob is just telling Alice what he thinks.
If Alice thinks Bob is mistaken, and wants to point out the problems in Bob's beliefs, it is better for Alice to contest the premises of Bob's arguments rather than contest the reasoning form. Pointing out circularity only serves to remind Bob that Bob hasn't given Alice a convincing argument.
You probably still think Bob has made some mistake in his reasoning, if these are his real reasons. I'll return to this later.
Circular Arguments as Positive Evidence
I claimed that circular arguments should count as a little bit of evidence in favor of their conclusions. Why?
Imagine that the Bible claimed itself to be written by an evil and deceptive all-knowing God, instead of a benign God:
Alice: Why do you believe in God?
Bob: Because the Bible tells me so.
Alice: Why do you believe the Bible?
Bob: Well... uh... huh.
Sometimes, belief systems are not even internally consistent. You'll find a contradiction[3] just thinking through the reasoning that is approved of by the belief system itself. This should make you disbelieve the thing.
Therefore, by the rule we call conservation of expected evidence, reasoning through a belief system and deriving a conclusion consistent with the premise you started with should increase your credence. It provides some evidence that there's a consistent hypothesis here; and consistent hypotheses should get some ...
The idea that circular reasoning is bad is widespread. However, this reputation is undeserved. While circular reasoning should not be convincing (at least not usually), it should also not be considered invalid.
Circular Reasoning is Valid
The first important thing to note is that circular reasoning is logically valid. A implies A. If circular arguments are to be critiqued, it must be by some other standard than logical validity.
I think it's fair to say that the most relevant objection to circular arguments is that they are not very good at convincing someone who does not already accept the conclusion. You are talking to another person, and need to think about communicating with their perspective. Perhaps the reason circular arguments are a common 'problem' is because they are valid. People naturally think about what should be a convincing argument from their own perspective, rather than the other person's.
However, notice that this objection to circular reasoning assumes that one party is trying to convince the other. This is arguments-as-soldiers mindset.[1] If two people are curiously exploring each other's perspectives, then circular reasoning could be just fine!
Furthermore, I'll claim: circular arguments should actually be considered as a little bit of positive evidence for their positions!
Let's look at a concrete example. I don't think circular arguments are quite so simple as "A implies A"; the circle is usually a bit longer. So, consider a more realistic circular position:[2]
Alice: Why do you believe in God?
Bob: I believe in God based on the authority of the Bible.
Alice: Why do you believe what the Bible says?
Bob: Because the Bible was divinely inspired by God. God is all-knowing and good, so we can trust what God says.
Here we have a two-step loop, A->B and B->A. The arguments are still logically fine; if the Bible tells the truth, and the Bible says God exists, then God exists. If the Bible were divinely inspired by an all-knowing and benevolent God, then it is reasonable to conclude that the Bible tells the truth.
If Bob is just honestly going through his own reasoning here (as opposed to trying to convince Alice), then it would be wrong for Alice to call out Bob's circular reasoning as an error. The flaw in circular reasoning is that it doesn't convince anyone; but that's not what Bob is trying to do. Bob is just telling Alice what he thinks.
If Alice thinks Bob is mistaken, and wants to point out the problems in Bob's beliefs, it is better for Alice to contest the premises of Bob's arguments rather than contest the reasoning form. Pointing out circularity only serves to remind Bob that Bob hasn't given Alice a convincing argument.
You probably still think Bob has made some mistake in his reasoning, if these are his real reasons. I'll return to this later.
Circular Arguments as Positive Evidence
I claimed that circular arguments should count as a little bit of evidence in favor of their conclusions. Why?
Imagine that the Bible claimed itself to be written by an evil and deceptive all-knowing God, instead of a benign God:
Alice: Why do you believe in God?
Bob: Because the Bible tells me so.
Alice: Why do you believe the Bible?
Bob: Well... uh... huh.
Sometimes, belief systems are not even internally consistent. You'll find a contradiction[3] just thinking through the reasoning that is approved of by the belief system itself. This should make you disbelieve the thing.
Therefore, by the rule we call conservation of expected evidence, reasoning through a belief system and deriving a conclusion consistent with the premise you started with should increase your credence. It provides some evidence that there's a consistent hypothesis here; and consistent hypotheses should get some ...