Here is a set of claims, each of which one might take to be plausible. If any two of them are true, the third is false. Which one do you deny and why?
1. Propositional knowledge requires epistemic certainty.
2. To be epistemically certain that p is to be infallible about p.
3. The typical human person possesses many items of propositional knowledge about basic science, history, household management, automobile maintenance, etc. and yet these items are not matters of infallibility.
*Infallibility is the impossibility of one’s being wrong about a proposition given that one’s justification for believing that proposition is such that the proposition one believes cannot be false in virtue of the justification. If S is infallible about p, then p has an epistemic probability of 1 for S given S’s evidence for p, and hence S (insofar as he believes that p) cannot be wrong that p. For example, if Smith knows infallibly that 2 + 2 = 4, that he is currently thinking about arithmetic, that he feels soreness in his knee, or that if p entails q and p is true, then q is true, he cannot be wrong about that particular item of knowledge. (It’s important to note here that what guarantees the truth of p is S’s evidence or justification for p. The claim is not that p is a necessary truth. Rather, it’s that S cannot be wrong about p given S’s justification for p.)
Why accept (1)? Well, you might be an invariantist about propositional knowledge. Therefore, you might hold that the standards for propositional knowledge do not change according to epistemic context. In other words, the truth value of claims such as “Jones knows that his front door is closed” does not change according to context. (Epistemic invariantism is opposed to epistemic contextualism, which holds that such claims vary according to the situation: epistemically demanding situations require higher standards and epistemically relaxed situations have lower standards. Thus, the claim about Jones can be true in epistemically relaxed circumstances, but false in epistemically demanding ones.)
You might also hold that the best explanation for the cross-context uniformity of invariantism is that propositional knowledge requires epistemic certainty and hence that, in the majority of cases, human claims of knowledge are technically false. Claims that fall short of epistemic certainty are ruled out as items of knowledge; the remaining items are uniformly certain, which accounts for the invariance. ‘Knowledge’ might function like ‘straight’ and ‘flat.’ We speak loosely of drawing a straight line when in fact the line is not precisely straight. We talk of flat tables which are not perfectly flat. Similarly, we speak of knowing when in fact we do not precisely know anything for which we lack epistemic certainty, and we are epistemically certain perhaps only about some a priori propositions and items of introspection, such as matters of pure logic, mathematics, self-awareness, etc. In every case, then, knowledge requires epistemic certainty.
Moreover, you might hold — reasonably, in my view — that (a) the best solution (or at least one of the best) to the Gettier problem is to affirm that epistemic certainty is a necessary condition for propositional knowledge, (b) the best explanation for why cases of knowledge are more valuable than cases of true belief which fall short of knowledge is that knowledge guarantees certainty and thus prevents one from error, (c) holding that knowledge requires epistemic certainty enables one to avoid awkward concessive knowledge attributions such as “I know that p but I might be wrong that p,” and (d) if one knows that p, and knowledge requires epistemic certainty, then one can stop inquiring into whether or not p, whereas if one reasonably believes and yet lacks epistemic certainty that p, and yet one claims to know that p, one might be in the awkward position of admitting that “I know that p, and yet I’m still inquiring into whether or not p.”
What about (2)? One might hold that (2) is true by definition.
And (3)? One might accept (3) on the basis of common language usage and ordinary assumptions about what we know. We speak of knowing that the Earth orbits the Sun, that the Battle of Marathon occurred in 490 B. C., that the front door is closed, that the gas tank is full, etc.
If you accept (1) and (2), you are committed to the denial of (3). We do not know much of what we claim to know, which might strike you as odd. If you accept (1) and (3), you should deny (2). You might want to define ‘epistemic certainty’ in a way that is consistent with (3) — which is no easy matter. If you affirm (2) and (3), you’ll need to reject (1). But then you face the difficulties of defining ‘propositional knowledge’ in a way that avoids the many and dreaded Gettier-style problems. You would face other difficulties, too.
What is your move and why?
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