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The reasoning behind this is fairly intuitive. If a person does not believe something to be true, it seems awkward to think they could have knowledge - for could someone really know that it is raining outside, but truly not believe that it is raining outside? Likewise, if some proposition about the world, such as "it is raining outside", is false, then it seems counterintuitive to say that a person knows it is raining outside. Finally, some sort of justification for thinking that the belief is true seems necessary - else any accidental true belief (that is, where a person believes something for no good reason and happens to be right anyway) would be considered knowledge, and that is also counterintuitive.
So this conception of knowledge at least has some intuitive appeal - for the most part, it seems to define as knowledge that which we generally consider knowledge. However, intuitive appeal alone is an insufficient basis for choosing a concept of knowledge. What else then should one look for in a theory of knowledge? The most common answer, and the one I will assume herein, is that an important factor is whether or not it can answer the skeptic; in other words, whether or not it can be demonstrated that knowledge, as defined by that conception, can be shown to exist about at least one proposition.
Before attempting to answer that question, it will be useful to clarify the justification aspect of the JTB conception. The JTB conception of knowledge is generally acknowledged as not requiring conclusive justification for a belief. Rather, at least some true beliefs can qualify as knowledge while being justified inconclusively (where the justification, however otherwise strong, still leaves some room for doubt on the part of the believer). The inconclusively justified conception of knowledge (from here on out referred to as simply JTB) is the primary focus of this paper, but the alternate conception of knowledge as conclusively justified true belief (CJTB) will be covered toward the end as well1.
Can Anything Be Known?
Once knowledge has been defined as JTB, it remains for an epistemologist to answer the question of whether or not any propositions can be known, i.e. whether or not a given proposition is known. If the JTB conception can be shown inadequate to answer this question, it is obvious that it fails to answer the skeptic, and another conception is needed. There are two approaches to answering the question: the first-person approach and the third-person approach:
The first-person approach asks the question from the inside: "Do I meet all the requirements for knowledge of the proposition (belief, justification, truth)?" The first-person epistemologist can, it seems safe to assume, determine whether or not they believe the proposition in question to be true. Assuming they do, they can presumably determine whether or not the belief is justified (whether or not this is the case is in fact immaterial to the argument to be offered below, but it will be granted as an assumption); keep in mind here that this justification need not be complete according to the JTB conception, else it would break down into the CJTB conception. Let us assume for the time being that the justification is inconclusive (the conclusive case will be covered at the end, but it suffices for now to cover the inconclusive case because the JTB conception, in order to remain distinct from the CJTB conception, must allow at least some inconclusively justified true beliefs to qualify for knowledge).
All that is left is to determine whether or not the proposition is true. Unfortunately, short of conclusive justification, no such determination can be made, for with inconclusive justification there is always the possibility of error, thus the possibility that the proposition is false, which means that the proposition's truth is not demonstrated. Therefore, the first-person approach of the JTB conception breaks down into the CJTB conception - for without doing so it seems that the truth aspect can never be demonstrated, and thus the JTB conception cannot answer the skeptic2.
The third-person approach asks the question from the outside: "Does some other person meet the requirements for knowledge of the proposition (belief, justification, truth)?" Analogous to the first-person epistemologist, let it be assumed that the third-person epistemologist can determine whether or not a person holds a justified belief. Granting that the epistemologist has identified a justified belief in a person, it remains to be determined whether or not that belief is true. By stepping out of the first-person perspective and into the third-person perspective, it might seem possible to avoid the problems that befell the first-person epistemologist.
The third-person epistemologist, in order to demonstrate the truth of the proposition in question, must consider reasons to think the proposition is true. If those reasons are inconclusive, there is a chance that the proposition is in fact false, and thus its truth cannot be determined (much as in the case of the first-person epistemologist). If, on the other hand, those reasons are conclusive, the third-person epistemologist has demonstrated that the proposition in question is known by the person holding the justified true belief.
Of course, because the epistemologist has conclusive reasons to accept the proposition as true, it seems absurd to deny that they would then of necessity believe the proposition to be true3. Therefore, what has been demonstrated is in fact (1) that the epistemologist knows the proposition, and (2) that the person that held the inconclusively justified belief that the proposition was true also knows the proposition.
The third-person epistemologist thus escapes the complete breakdown into the CJTB conception, but leaves the JTB conception parasitic on conclusive justification. That is, the only way to answer whether or not a person with a JTB (but not a CJTB) knows a proposition is for someone else (the third-person epistemologist) to have a CJTB about the same proposition. Whether or not this solution is satisfactory will be taken up further below.
Failure to Establish Conclusive Justification
The preceding section show that inconclusive justification alone is insufficient to determine the truth of a proposition, and thus insufficient to answer the question of whether or not a proposition can be known. However, it has been shown that knowledge (under the JTB conception, specifically inconclusively justified true belief) is in fact possible, given that the third-person epistemologist can establish CJTB.
If this latter condition is met, it will mean that the JTB conception defines knowledge adequately - knowledge will be theoretically demonstrable, thus answering the skeptic - without breaking down into the CJTB conception. If the condition is not met - that is to say, if the third-person epistemologist cannot establish CJTB - it will be shown that the JTB conception fails to define knowledge adequately. In this case, it would be impossible to demonstrate knowledge (and thus answer the skeptic) under the JTB conception of knowledge - any attempt would be forced to break down to the CJTB conception. So the important question then is whether or not CJTB can, even theoretically, be shown to be possible.
The answer to that question appears to be negative. Imagine for a moment that someone claims they have conclusive justification for believing a proposition to be true. It can be asked of them how they conclusively justify their claim that their justification is conclusive (this meta-justification must also be conclusive, because inconclusive justification would leave open the possibility that the first-order justification is not in fact conclusive).
If that claim is justified by appeal to the nature of the first-order justification, say the fact that it is based on empirical observation or a priori reasoning, the question is only postponed. It can then be asked how they conclusively justify the claim that empirical observations or a priori reasoning (or literally any reason that is asserted for why the first-order justification is conclusive) provide conclusive justification for the proposition. Any explanation given must in turn be justified conclusively, and that justification must be justified conclusively, and so on ad infinitum.
As no human could possibly list out this infinitely long series of conclusive justifications, it can never be conclusively justified that the first-order justification is conclusive - i.e. it is always possible that the first-order justification is not conclusive. And if it is always possible that the justification for a proposition is inconclusive, one has failed to answer the skeptic. Therefore, both the JTB conception of knowledge (which depended on CJTB) and the CJTB conception of knowledge fail to adequately answer the skeptic - that is, fail to provide a reason to think that knowledge, as defined, exists about any proposition.
Thus the JTB conception of knowledge seems to offer little more than intuitive appeal. In fact, the underdetermination of the truth component makes it rather useless as a strict definition of knowledge since we can never be sure that we know a given thing, or for that matter that we know anything at all. Any definition of knowledge which allows for the possibility that we do not know anything at all seems to be an inadequate definition, and perhaps a new definition should be found which does not rely on a self-defeating component like the truth of the proposition.
1There is simply no universal agreement among JTB adherents as to the exact nature of what constitutes justification for a belief; and while the question is an important and interesting one, it will not be taken up in this paper because, whatever the answer, it seems inapplicable to the objection to the JTB conception which will be presented.
2It may be argued that demonstration of truth is unnecessary to answer the skeptic and that it is good enough to demonstrate that something is likely. However, that raises further questions, such as how to determine or judge whether or not something is shown to be likely, and how likely it must be shown to be accepted as knowledge, etc.? At any rate, no matter how these questions are answered, it appears that they will always leave open the possibility that any proposition is false, and thus the skeptic maintains a foothold and we cannot be sure anyone has knowledge.
3Some might argue that it is indeed possible for a person to hold conclusive reasons to believe a proposition is true without themselves believing the proposition is true. This argument is rejected on intuitive grounds based on what it generally meant by the term 'belief'. A more thorough investigation into the concept of belief might establish that conclusive justification does not imply belief automatically. However, this point is not crucial to the topic at hand, since all that is required for the argument presented is that the epistemologist has conclusive justification for a proposition's truth.