In coherentism it is the beliefs in each set which are justified not the set itself and this leaves the theory exposed to objections. One objection raised is that justified coherent systems can bring about another set of efficiently coherent and justified system. E.g. fiction novels create a coherent world but they are nothing like the real world. This means that coherence can’t provide an adequate account of the justification of beliefs because there can only be one set of justified beliefs about the world and not more than one.
Coherentists respond to this that there can only be one coherent set and one coherentist who spoke about this further was FH Bradley. He intended that coherence should be a test of justification not of just any belief but something we have a motive to believe in. This means that coherence has the function to discriminate within those beliefs and get rid of some in favour of others. A similar notion has been said by Jonathan Dancy in defence of coherentism, he says that we scrutinise something we believe and retain this until we find something that goes against it, on the grounds that it is a belief already. This means that coherence is intended to be a test of the beliefs we already have or those we can add not to have multiple sets of coherent systems.
Another defender of coherentism called Donald Davidson has also responded to the criticism that coherentism could contain multiple sets of beliefs; he does this by considering the case of the Radical Interpreter. Imagine if you will and interpreter from the UK who speaks fluent English to come across a country that speaks the language Q, which no one outside of that country know. How will the English speaker ever understand the language Q? Davidson argues that the interpreter will have to operate with the principle of charity; this means he will have to assume that the beliefs of the speakers Q are true. This is true to the standards of the interpreter alone and he has to assume that they both share, roughly, the same standards of truth. Otherwise they would not share enough common ground for themselves to see where they disagree. However, if the interpreter assumes that they share the same standards of truth they could be both completely wrong and what guarantees that they are not mistaken? Davidson’s answer to this is to imagine an Omniscient Interpreter for the other interpreter, the Omniscient Interpreter to interpret the interpreter thane he will have to extend him to the same standard of truth as the interpreter had for the speakers. The Omniscient interpreter will then have to assume that he and the interpreter share, roughly, the same standards of truth like the interpreter had to do with the speakers. However, the Omniscient interpreter knows everything and this is true, his own standards of truth cannot be mistaken and this follows that the standards of truth between the interpreter and the speakers of language Q cannot be mistaken. If this is correct then the interpreter has to suppose that most of his basic beliefs are justified. This then means that there cannot be more than one coherent set of beliefs; however, there can be room to think that particular beliefs need to be investigated to see if they are justified. Therefore, according to Davidson, the coherentist can rebut the charge against themselves.
To conclude is about fitting beliefs together into a set, unlike foundationalism which is beliefs being inferred from a foundational belief. It comes with the criticism however; that there can be one more set of beliefs with is replied to by Coherentists such as Bradley and Davidson. These replies ensure that coherentism is backed up despite this one major criticism.