Please note that this is part three of a three-part discussion

Significantly-built into the notion discussed in part two- is the concept that the inferential transmission of our justification does not need to be deductive, but rather can be probabilistic or inductive. Epistemologist Robert Audi, in The Foundationalism-Coherentism Controversy, states, “Superstructure beliefs may be only inductively, hence fallibly, justified by foundational ones and thus (unless they are necessary truths) can be false even when the latter are true.” (Knowledge and Inquiry, pg. 97) Thus, although we may have very good inductive evidence for holding a belief, we ultimately might have to reject it because of the introduction of new refuting evidence. For, no judgement aimed at finding truth can ever attain apodictic certainty. So, in the absence of infallible knowledge, as reasonable beings, we should be satisfied with less than that. As such, within this framework, fallibly justified beliefs are likely, but not guaranteed to be true, and for this reason, mutual coherence may also play a key role in our inferential justification.
Accordingly, a large part of mutual coherence, and its provision of justification for our basic beliefs, will depend on employing the principle of independence. The independence principle simply states that the larger the number of independent and mutually coherent factors one believes that support a truth, the stronger one’s justification will be for believing it. So, it is not enough to determine that one is having the internal perception of red; one must also have an external and independent factor corresponding to the perceptual state. For example, let’s say that a knower sees a red apple on the table:
(P1) I have a perceptual belief that I see a red apple (justified via introspection)
(P2) There is a red apple (justified via independent external factor)
(C1) Therefore, I have a true perceptual belief that there is a red apple
In this example, the knower infers deductively that their perceptual belief is reliable. And, since both P1 and P2 are justified, they jointly entail C1.
Conclusively, the individual appeals of foundationalism and and coheretism may lie in the fact that they provide answers to different questions. Or, it may simply be that we should let go of our traditional epistemological labels. Either way, the notion of fallibilist foundationalism seems superior to either ideology taken alone in isolation because it can give us an attainable theory of knowledge through an account of coherence as justification. Additionally, by making our theory of knowledge plausible, it avoids the impossibility of the skeptic because it grounds our beliefs in observation and past experience. So, again, although our perception may decieve us, it does not follow from this that we should abandon the realities of our senses altogether. Audi states, “In working from the experential and rational sources it takes as epistemically basic, fallibilist foundationalism (in its most plausible versions) accords with refective common sense: the sorts of beliefs it takes as non-inferentially justified…are pretty much those, that, on reflection, we think people are justified in holding.” (Ibid, pg. 123) As such, can we allow into our theory of knowledge, as privileged basic beliefs, those beliefs that are inferentially justified? Or, moreover, is it more accurate to question whether or not our immediately justified basic beliefs are infallible. Accordingly, if the answer to either of these questions is yes, should we further question whether or not our justification is strong enough?
I would argue that, as humans, the notion of achieving infallibilty is both impossible and unrealistic. The Cartesian, who proposes the goal of indubitability, ultimately ends up rejecting all inductions we make of the external world, which then leads us to a state in which we possess virtually no knowledge. And, clearly, the practice of making inductive inferences of the external world is reasonable and does constitute knowledge. Chisholm states, “It is difficult to think of any claim to empirical knowledge, other than self-justifying statements we have considered, that does not to some extent rest on an appeal to memory.” (Ibid, pg 24) Yet, although we must accept our fallibility as unavoidable, we should, perhaps retain the Cartesian concept as an unachievable ideal. Or, maybe the role of coherence in any theory of knowledge, simply becomes the negative role of incoherence. And, finally, perhaps it is enough that our beliefs, which arise from perception, memory, introspection and human reason, generate outcomes that are least likely to be true.