Gettier Cases and Epistemic Infallibilism

I wrote this a year ago, but never posted it. It is relevant to the preceding post. Epistemic infallibilism (EI) makes short work of Gettier cases.  But is this a compelling reason to accept EI?  You can guess what I will say: here we have another insoluble problem.

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In an earlier thread, Elliot writes:

I’m inclined to agree with you and Butchvarov that [propositional] knowledge entails objective certainty. Why? For one thing, the thesis of epistemic infallibilism seems immune to the epistemic luck present in Gettier cases. Or as Socrates might put it, objective certainty tethers true belief so that it doesn’t run away (Meno) at the sight of epistemic luck. For another thing, epistemic infallibilism explains why knowledge is more valuable than mere true belief.

The Gettier problem is old hat, and not just since 1963. The following from SEP:

Few contemporary epistemologists accept the adequacy of the JTB analysis. Although most agree that each element of the tripartite theory is necessary for knowledge, they do not seem collectively to be sufficient. There seem to be cases of justified true belief that still fall short of knowledge. Here is one kind of example:

Imagine that we are seeking water on a hot day. We suddenly see water, or so we think. In fact, we are not seeing water but a mirage, but when we reach the spot, we are lucky and find water right there under a rock. Can we say that we had genuine knowledge of water? The answer seems to be negative, for we were just lucky. (quoted from Dreyfus 1997: 292)

The above example comes from the Indian philosopher Dharmottara, c. 770 CE. The 14th-century Italian philosopher Peter of Mantua presented a similar case:

Let it be assumed that Plato is next to you and you know him to be running, but you mistakenly believe that he is Socrates, so that you firmly believe that Socrates is running. However, let it be so that Socrates is in fact running in Rome; however, you do not know this. (from Peter of Mantua’s De scire et dubitare, given in Boh 1985: 95)

A Chisholmian example from IEP:

The sheep in the field (Chisholm 1966/1977/1989). Imagine that you are standing outside a field. You see, within it, what looks exactly like a sheep. What belief instantly occurs to you? Among the many that could have done so, it happens to be the belief that there is a sheep in the field. And in fact you are right, because there is a sheep behind the hill in the middle of the field. You cannot see that sheep, though, and you have no direct evidence of its existence. Moreover, what you are seeing is a dog, disguised as a sheep. Hence, you have a well justified true belief that there is a sheep in the field. But is that belief knowledge?

A common objection to epistemic infallibilism is that it eliminates much of what we ordinarily take ourselves to know. For example, I justifiably believe that I am now looking at a lamp with a blue lampshade. But since it’s possible that I’m wrong, I don’t know that I’m looking at a lamp. Some will want to say that I know I’m looking at a lamp. The infallibilist can say that I know I’m having an experience as of looking at a lamp, or that I know I’m being appeared-to-lamp-bluely, but I don’t know (precisely speaking) that I’m looking at a lamp.

One point to discuss further: What is meant by “impossibility of mistake?” What sort of possibility is at work here?