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.
All circular reasoning which is sound is tautological and cannot justify shifting expectation.
The point is, you have to live with at least one of:
No branch of this disjunction applies. Justifications for assumptions bottom out in EV of the reasoning, and so are justified when the EV calculation is accurate. A reasoner can accept less than perfect accuracy without losing their justification—the value of reasoning bottoms out in the territory, not the map, and so “survived long enough to have the thought” and similar are implicitly contributing the initial source of justification.
Circular arguments fail to usefully constrain our beliefs; any assumptions we managed to justify based on evidence of EV will assign negative EV for circular arguments, and so there is no available source of justification from existing beliefs for adopting a circular argument, while there is for rejecting them.
Coherentism: Circular justification is allowed in some fashion.
Only insofar as a reasoner can choose not to require that anything requiring cognitive work pay rent to justify the expenditure. Optimal bounded reasoning excludes entertaining circular arguments based on expectation of wasting resources.
circular justifications seem necessary in practice
I didn’t see any arguments which point to that unless you mean the regress argument / disjunction edit: or this?:
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.
Two independent justifications:
One starts with negative EV for having engaged in reasoning-that-requires-resources at all, and so the conclusion must at least pay that off to be a justified way to reason.
A circular argument does not constitute evidence relative to the premises, so conservation of expected evidence does not prescribe an update, except perhaps an extremely small one about the consistency of (and thus EV of) the assumptions that led up to that point—the argument is evidence that those rules didn’t lead to a contradiction, but not about the conclusion.
circular justifications seem necessary in practice
I didn’t see any arguments which point to that unless you mean the regress argument / disjunction
Yes, I agree: the essay doesn’t really contain a significant argument for this point. “Seem necessary in practice” is more of an observation, a statement of how things seem to me.
The closest thing to a positive argument for the conclusion is this:
However, in retrospect I think it’s pretty clear that any foundations are also subject to justificatory work, and the sort of justification needed is of the same kind as is needed for everything else. Therefore, coherentism.
And this, which is basically the same argument:
My reasons [...] are practical: I’m open to the idea of codifying excellent foundational theories (such as Bayesianism, or classical logic, or set theory, or what-have-you) which justify a huge variety of beliefs. However, it seems to me that in practice, such a foundation needs its own justification. We’re not going to find a set of axioms which just seem obvious to all humans once articulated. Rather, there’s some work to be done to make them seem obvious.
I also cite Eliezer stating a similar conclusion:
Everything, without exception, needs justification. Sometimes—unavoidably, as far as I can tell—those justifications will go around in reflective loops.
I think it’s pretty clear that any foundations are also subject to justificatory work
EV is the boss turtle at the bottom of the turtle stack. Dereferencing justification involves a boss battle.
there’s some work to be done to make them seem obvious
There’s work to show how justification for further things follows from a place where EV is in the starting assumptions, but not to take on EV as an assumption in the first place, as people have EV-calculatingness built into their behaviors as can be noticed to them.
Sometimes—unavoidably, as far as I can tell—those justifications will go around in reflective loops
I reject this! Justification results from EV calculations and only EV calculations, as trust values for assumptions in contexts.
All circular reasoning which is sound is tautological and cannot justify shifting expectation.
Does your perspective on this also imply that mathematical proofs should never shift one’s beliefs? It sounds like you are assuming logical omniscience.
Also, it is possible for a circular argument like “A; A → B; so, B; and also, B → A; therefore, A” to be sound without being tautological. The implications can be contingently true rather than tautologically. The premise A can be contingently true rather than tautologically.
One trusts proofs contextually, as a product of the trusts of the assumptions that led to it in the relevant context. Insofar as Bayesianism requires justification, it can be justified as a dependency in EV calculations.
We’re not going to find a set of axioms which just seem obvious to all humans once articulated.
People understand EV intuitively as a justification for believing things, so this doesn’t ring true to me.
The premise A can be contingently true rather than tautologically.
True, I should have indicated I was rejecting it on the basis of repetition. One could reject any repetition of what is already a given in a proof and not lose access to any conclusions. Repetitions contains tautologies (edit: more importantly, repetitions contains sound circular arguments), and I’m ruling out repetitions with EV as the justification. Anything updateful about an argument with circular reasoning is contained in the tree(s) formed by disallowing repetition.
Circular arguments fail to usefully constrain our beliefs; any assumptions we managed to justify based on evidence of EV will assign negative EV for circular arguments, and so there is no available source of justification from existing beliefs for adopting a circular argument, while there is for rejecting them.
As mentioned in AnthonyC’s comment, circular arguments do constrain beliefs: they show that everything in the circle comes as a package deal. Any point in the circle implies the whole.
Multiple argument chains without repetition can demonstrate anything a circular argument can. No beliefs are constrained when a circular argument is considered relative to the form disallowing repetition (which could avoid costly epicycles). The initial givens imply the conclusion, and they carry through to every point in the argument, implying the whole.
No branch of this disjunction applies. Justifications for assumptions bottom out in EV of the reasoning, and so are justified when the EV calculation is accurate. A reasoner can accept less than perfect accuracy without losing their justification—the value of reasoning bottoms out in the territory, not the map, and so “survived long enough to have the thought” and similar are implicitly contributing the initial source of justification.
I can easily interpret this as falling into branches of the disjunction, and I am not sure how to interpret it as falling into none of the branches. It seems most naturally like a “justification doesn’t always rest on further beliefs” type view (“the value of reasoning bottoms out in territory, not map”).
Some beliefs do not normatively require justification;
Beliefs have to be justified on the basis of EV, such that they fit in a particular way into that calculation, and justification comes from EV of trusting the assumptions. Justification could be taken to mean having a higher EV for believing something, and one could be justified in believing things that are false. Any uses of justification to mean something not about EV should end up dissolving; I don’t think justification remains meaningful if separated.
Some justifications do not rest on beliefs
Justification rests on beliefs as inputs to EV calculations.
Some justification chains allowed to be circular
No conclusion requires its justification to be circular.
Some justification chains are allowed to be infinite and non-repeating
No infinite chains are required, they bottom out in observations as beliefs to be input into EV calculations.
All circular reasoning which is sound is tautological and cannot justify shifting expectation.
No branch of this disjunction applies. Justifications for assumptions bottom out in EV of the reasoning, and so are justified when the EV calculation is accurate. A reasoner can accept less than perfect accuracy without losing their justification—the value of reasoning bottoms out in the territory, not the map, and so “survived long enough to have the thought” and similar are implicitly contributing the initial source of justification.
Circular arguments fail to usefully constrain our beliefs; any assumptions we managed to justify based on evidence of EV will assign negative EV for circular arguments, and so there is no available source of justification from existing beliefs for adopting a circular argument, while there is for rejecting them.
Only insofar as a reasoner can choose not to require that anything requiring cognitive work pay rent to justify the expenditure. Optimal bounded reasoning excludes entertaining circular arguments based on expectation of wasting resources.
I didn’t see any arguments which point to that unless you mean the regress argument / disjunction edit: or this?:
Two independent justifications:
One starts with negative EV for having engaged in reasoning-that-requires-resources at all, and so the conclusion must at least pay that off to be a justified way to reason.
A circular argument does not constitute evidence relative to the premises, so conservation of expected evidence does not prescribe an update, except perhaps an extremely small one about the consistency of (and thus EV of) the assumptions that led up to that point—the argument is evidence that those rules didn’t lead to a contradiction, but not about the conclusion.
Yes, I agree: the essay doesn’t really contain a significant argument for this point. “Seem necessary in practice” is more of an observation, a statement of how things seem to me.
The closest thing to a positive argument for the conclusion is this:
And this, which is basically the same argument:
I also cite Eliezer stating a similar conclusion:
EV is the boss turtle at the bottom of the turtle stack. Dereferencing justification involves a boss battle.
There’s work to show how justification for further things follows from a place where EV is in the starting assumptions, but not to take on EV as an assumption in the first place, as people have EV-calculatingness built into their behaviors as can be noticed to them.
I reject this! Justification results from EV calculations and only EV calculations, as trust values for assumptions in contexts.
Does your perspective on this also imply that mathematical proofs should never shift one’s beliefs? It sounds like you are assuming logical omniscience.
Also, it is possible for a circular argument like “A; A → B; so, B; and also, B → A; therefore, A” to be sound without being tautological. The implications can be contingently true rather than tautologically. The premise A can be contingently true rather than tautologically.
One trusts proofs contextually, as a product of the trusts of the assumptions that led to it in the relevant context. Insofar as Bayesianism requires justification, it can be justified as a dependency in EV calculations.
People understand EV intuitively as a justification for believing things, so this doesn’t ring true to me.
True, I should have indicated I was rejecting it on the basis of repetition. One could reject any repetition of what is already a given in a proof and not lose access to any conclusions. Repetitions contains tautologies (edit: more importantly, repetitions contains sound circular arguments), and I’m ruling out repetitions with EV as the justification. Anything updateful about an argument with circular reasoning is contained in the tree(s) formed by disallowing repetition.
As mentioned in AnthonyC’s comment, circular arguments do constrain beliefs: they show that everything in the circle comes as a package deal. Any point in the circle implies the whole.
Multiple argument chains without repetition can demonstrate anything a circular argument can. No beliefs are constrained when a circular argument is considered relative to the form disallowing repetition (which could avoid costly epicycles). The initial givens imply the conclusion, and they carry through to every point in the argument, implying the whole.
I can easily interpret this as falling into branches of the disjunction, and I am not sure how to interpret it as falling into none of the branches. It seems most naturally like a “justification doesn’t always rest on further beliefs” type view (“the value of reasoning bottoms out in territory, not map”).
Beliefs have to be justified on the basis of EV, such that they fit in a particular way into that calculation, and justification comes from EV of trusting the assumptions. Justification could be taken to mean having a higher EV for believing something, and one could be justified in believing things that are false. Any uses of justification to mean something not about EV should end up dissolving; I don’t think justification remains meaningful if separated.
Justification rests on beliefs as inputs to EV calculations.
No conclusion requires its justification to be circular.
No infinite chains are required, they bottom out in observations as beliefs to be input into EV calculations.
Beliefs are required for EV calculations.