Feedback loop and circular reasoning fallacy are highly common, but they involve very different types of circularity.
Feedback loop: action induces further action, but the extra action also requires work, it doesn’t come from thin air.
Feedback loops typically weaken and end by themselves, although they can last longer as long as more work is put into the system. Feedback loop is essentially about amplification & second-order effects.
Think: deforestation that leads to land erosion, which leads to further deforestation.
Another example of a feedback loop is economic bubbles. Hype leads to more hype which leads to more hype, until all people who could be hyped up have been hyped up. Each stage in a hype cycle requires more work. Bubbles therefore could misallocate capital & cause waste.
Another example is the adoption curve of Bitcoin. Bitcoin was initially known only among geeks & cypherpunks. An early wave of early adopters built demand which raises the price. Rising prices in turn draws more attention and further increases adoption.
The important thing to remember about feedback loop is that feedback loop requires work. There is no magic.
Circular reasoning fallacy: the proposition is supported by the premise, which is supported by the proposition.
In terms of “work”, circular reasoning can also be generally described as creating work out of thin air. Work is the supposed “proof” that backs the argument, which for circular reasoning actually has zero substance.
So circular reasoning is essentially about creating something out of nothing.
Think: a hypothetical wheel that keeps spinning forever on its own.
This manifests in Proof-of-Stake protocols, for example, by naively moving the problem of distributed consensus from finding blocks to what is the source of randomness.
If the PoS source of randomness is external, it is circular reasoning because to agree on the same external randomness (without Proof-of-Work) also requires solving distributed consensus, which is the original problem.
If the PoS source of randomness is internal, it is not circular reasoning but the scheme breaks down for a different reason: if you use purely the content of a blockchain to determine the content of the blockchain, your process cannot be truly random. No good randomness means that your protocol is predictable and exploitable. For a detailed exploration of the role of randomness in Bitcoin, check out my other article: Bitcoin, Chance & Randomness.