For an example, consider two alternative belief systems A and B consisting of beliefs A1, A2 and

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For an example, consider two alternative belief systems A and B consisting of beliefs A1, A2 and B1, B2 respectively. There are two beliefs in each system none of which can justify themselves alone. If A1 → A2 and A2 → A1, then there are 2 inferential connections in A and a high inferential density. Bonjour says this makes A likely. However, if only B1 → B2 and not vice versa, then there is only 1 non-mutual inferential connection in B and thus a low inferential density. Bonjour suggests that lack of mutual justification makes the whole system of B unjustified since B1 must act foundationally. From this example, we can see that the coherence of a system is defined to be inversely related to the number of beliefs in the system and…show more content…
Ironically, even Bonjour's own account does not fully live up to this claim in the end. For clarity, this initial account of Coherentism will henceforth be referred to as Non-foundational Coherentism. As is to be expected, the account of Non-foundational Coherentism is not without its flaws. Firstly, coherence is still too broadly defined by Bonjour to be useful. To illustrate the issue, consider two new belief systems A and B. If A is more inferentially dense but B is less anomalous in content, how do you decide which belief system is more likely? Curiously, Bonjour is largely silent on this point despite its dramatic consequences. The effect of this observation might lead one to the same skeptical conclusion as McGrew's linear foundationalism. In fact, this account may be even more troubling; the total number of possible coherent belief systems increases exponentially with the number of possible explanatory beliefs since such belief systems actually inhabit the powerset of these explanatory beliefs. Secondly, assuming Bonjour's account of Coherentism, one might encounter a few corner cases where such an account will fail to provide reliable justification entirely. Consider the case presented by Olsson wherein two eyewitness accounts A1 and A2 describe an event E having occurred. In this example it is assumed that we do not know if E occurred or who is telling the truth. We first assume that neither account
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