Belief and Knowledge - Part One
Introduction
In its general mathematical sense, congruency constitutes a particular kind of relationship between two expressions. The nature of this relationship is such that it involves a means of mapping the features of one expression onto the features of the other expression. This mapping procedure is accomplished through a transformational function(s) which permits one to determine points of coincidence between expressions despite the existence of overt or superficial differences in the structure of the character of the expressions being considered.
By indicating that congruency is to be construed in its general mathematical sense, a reference point, of sorts, has been provided for the reader. However, the character of the transformation function(s) which allows one to determine points of coincidence between expressions - especially in a hermeneutical context - is somewhat vague, because although the idea of ‘congruency’ in the mathematical sense does provide a valuable starting point, the character of the transformation(s) involved in non-mathematical senses of congruency needs to be developed.
In the ensuing discussion, an attempt will be made to delineate a few of the characteristics of the aforementioned transformation function(s) when considered in a concrete context. This aspect of a determinate context is an important consideration when examining the character of transformation functions.
It is through the specificity of context that a transformation function gives expression to its particular character. This character indicates: a) what is meant by a congruency mapping operation in that context; and, b) how the relevant expressions in that context are to be mapped coincidentally one onto the other. Thus, although, within certain limits, all congruency relationships share the general features, nonetheless the character of any given transformation function will be shaped and structured by the character of the specific context being considered. Consequently, there are, potentially, an indefinite number of transformation functions which may establish a basis for conducting mapping operations in various kinds of specific contexts.
Given the foregoing, trying to treat, exhaustively, the notion of a transformation function is neither feasible nor practical. However, by undertaking a relatively detailed exploration into one kind of transformation function, a certain amount of insight might be gained concerning the character, in general, of congruency relationships and their underlying transformation functions. For these reasons, I have decided to concentrate on a specific problem within which the issue of congruency arises.
The problem I have selected concerns questions about the nature of the distinction between belief and knowledge. Although intuitively we frequently have a sense of this distinction, it tends to be difficult to pin down in a way that would be defensible in all instances in which the distinction is made.
In any event, I don't propose to discuss this distinction in general terms. Rather, I intend to examine a particular in-stance of this distinction.
This instance involves an exploration into the sort of structures and structuring processes which are encountered when one tries to establish differences between the phenomenology of belief and the phenomenology of knowledge. More specifically, I intend to examine this problem in the context of some arguments that have been put forth by Norman Malcolm which attempt to cast doubt upon an individual's ability to distinguish within himself or herself the difference between knowledge and belief. In contradistinction to Malcolm's position in his article "Knowledge and Belief", I will try to show there is good reason to believe that one, in at least some circumstances, can distinguish within oneself between belief and knowledge.
Distinguishing Between Belief and Knowledge
In his article "Knowledge and Belief", Norman Malcolm is critically responding to a contention of H.A. Prichard that 'phenomenologically' (although neither Prichard nor Malcolm use this term) one cannot confuse belief with knowledge. In other words, according to Prichard, the two are distinct experiences. Malcolm wishes to question whether, in fact, an individual actually can differentiate within himself or herself between knowing something or only believing it.
In order to attack this issue, he poses, for consideration, a number of hard cases which are all variations on a central theme concerning claims about water being in a particular gorge. Malcolm suggests:
"Let us begin by studying the ordinary usage of 'know' and 'believe'. Suppose, for example, that several of us intend to go for a walk and that you propose that we walk in Cascadilla Gorge. I protest that I should like to walk beside a flowing stream and that at this season the gorge is probably dry. Consider the following cases.
"(1) You say 'I believe that it won't be dry although I have no particular reason for thinking so'. If we went to the gorge and found a flowing stream we should not say that you knew that there would be water but that you thought so and were right.
"(2) You say 'I believe that it won't be dry because it rained only three days ago and usually water flows in the gorge for at least that long after a rain.' If we found water we should be inclined to say that you knew that there would be water. It would be quite natural for you to say 'I knew it wouldn't be dry'; and we should tolerate your remark. This case differs from the previous one in that here you had a reason.
"(3) You say 'I know that it won't be dry' and give the same reason as in (2). If we found water we should have very little hesitation in saying that you knew. Not only had you a reason, but you said 'I know' in-stead of 'I believe'. It may seem to us that the latter should not make a difference - but it does.
"(4) You say 'I know that it won't be dry' and give a stronger reason, e.g., 'I saw a lot of water flowing in the gorge when I passed it this morning'. If we went and found water, there would be no hesitation at all in saying that you know.....
"(5) Everything happens as in (4), except that upon going to the gorge we find it to be dry. We should not say that you knew, but that you believed that there would be water." (pp. 58-59)
Malcolm goes on to say:
"Whether we should say you knew, depends in part on whether you had grounds for your assertion and on the strength of those grounds. [and] Whether we should say that you knew, depends in part on how confident you were." (pp. 59-60)
According to Malcolm, if a person does not feel absolutely sure something is the case, then, we, as onlookers or witnesses, are likely to refrain from saying the individual actually knew, even if the individual turns out to be correct. However, this position seems somewhat problematic.
The reason a person may be somewhat conservative or cautious in putting forth a claim about, for example, water being in the gorge could be because the individual knows of extenuating factors which might prevent water from flowing in the gorge. As a result, the individual may be marginally unsure whether those factors will come into play in the existing circumstances.
Therefore, on the one hand, on grounds which he or she considers to be very strong, the individual may have little reason to sup-pose water will not be in the gorge if the individual and his or her companions were to walk by the gorge at the present time. On the other hand, the individual also realizes that, on occasion in the past, there have been situations in which water was expected to run through the gorge but did not.
Let us suppose the individual making the claim about water being in the gorge was a geologist or long-time resident of the area who had considerable understanding of groundwater behavior in the environment containing the gorge. Let us suppose further that the understanding contained data which not only established how long water stays in the gorge under a variety of circumstances, but which also established that there were certain possibilities which could prevent water from being in the gorge.
Under these circumstances, the individual's claim, although couched in a degree of reservation, seems much more akin to a knowledge of water being in the gorge than it does to a mere belief that water is in the gorge. However, if an individual is willing to acknowledge the possibility that things could be other than what he or she claims them to be, one hesitates to label the claim as an instance of knowledge.
In the former instance, an individual's understanding is rooted in more than just true belief (one might even say the understanding indicates an expertise of sorts). In the latter instance, by acknowledging that things could be other than they are claimed to be, an individual's under-standing seems to represent something less than actual knowledge.
The deciding factor in whether the understanding in question constitutes belief or knowledge and whether an individual can recognize which is the case may be a matter of the extent to which an individual's understanding of the water-in-the-gorge issue allows a context of "connecting" insight to emerge or exist amidst all the principle conditions that are "known" to bear upon whether or not water will be in the gorge. For example, let us suppose there is only one known possibility which could prevent water from being in the gorge - namely, if Mr. Thoreau, who lives by the pond that feeds the gorge, closes the water gates of the dam he has built. If we are not present at the dam site, then, we can't know directly about the one factor which would determine whether or not water would be flowing in the gorge.
Without this sort of direct knowledge, one is forced to rely on other considerations. For instance, I might have seen Mr. Thoreau this morning, and he gave no indication, when asked, that he would close the dam's water gates this afternoon. Another such consideration might be that I saw Mr. Thoreau yesterday, and he was just going away at that time for a two-week fishing trip and had left the water gates open, and so on.
Let us assume someone is actually at the dam site. If someone were to ask: "Do you know if there is water in the gorge?" then, even if one were not at the gorge, an individual asked could say, quite appropriately: "Yes, I know there is water in the gorge."
This is so because we are assuming for the moment that there is only one possibility which could prevent water from being in the gorge. Since we are at the dam and have direct knowledge of the current status of that possibility, then, seemingly we could argue tenably that we know water is in the gorge.
Let us suppose another case in which one is neither at the dam nor at the gorge sites. Yet, let us also suppose one has information about Mr. Thoreau's behavior vis-a-vis the water gates at the dam.
Under such circumstances, if someone were to ask the same question as above, one also might appear to be able to say one knew water was in the gorge. However, there may be a few problems which one could encounter in attempting to do so.
One obvious problem with the foregoing concerns the problem of answering the sceptic who asks: "How do you know something didn't happen, accidentally or intentionally, between the dam site and the gorge which prevented the water from reaching the gorge, even though you can now see that water is flowing past the dam and toward the gorge? Or, how do you know Mr. Thoreau is telling the truth or whether he might have changed his mind between the time you spoke with him and now, such that he actually did close the water gates unbeknown to you? Or, how do you know someone else didn't close the water gates when Mr. Thoreau was away?" The skeptical possibilities virtually are endless with respect to the hypothetical situations which could be imagined that might occur outside one's sphere of understanding and experience, and, thereby, cast doubt on any claim of knowledge one might make with respect to water being in the gorge.
Moreover, problems surrounding claims to knowledge are multiplied considerably when one allows more than a single factor (e.g., the water gates of the dam) to affect whether or not water is in the gorge. To begin with, an individual cannot be everywhere at once in order to examine directly the factors which bear on whether or not water will be in the gorge.
As a result, the indirect indices one must rely on in assessing whether water is in the gorge are all vulnerable to skeptical ambush. Thus, even if one personally checked, within a short period of time, on every known factor which could affect the outcome, one could be asked: "How do you know the conditions which exist now at each site are the same as when you checked them ten minutes or five or two minutes ago?"
Ultimately, one could be asked: "How can one know for certain whether or not the reality of something might change its nature as soon as one turns away from it?" Alternatively, one might be challenged as to whether or not reality might be totally different from what one experiences it to be. Similarly, what if one's understanding and sensory input were immersed in error and deception, but one is deluded into thinking one can understand and sense, with some degree of accuracy, the reality which one is encountering?
The skeptical game, however, is a two-edged sword. One side of that sword cuts away the basis of epistemology, and this is the side which many philosophical discussions focus upon and are worried about. The other side of the sword actually cuts away the basis of at least radical scepticism.
When the sceptic asks, for example: "How do you know: Mr. Thoreau didn't change his mind about the dam's water gates, or whether he is telling the truth, etc."?, the obvious reply is: "What reason do I have for maintaining otherwise?" The thrust of this reply has the potential to carry one past a mere philosophical standoff in which one side says: "How do you know such and such isn't the case?" and the other side says: "How do you know it is the case?"
Unless the sceptic can provide a substantial argument as to why some given claim should not be maintained, there is no obvious reason necessitating the abandonment of the position one is maintaining. Of course, unless the latter position is itself supported by a well-documented and well-reasoned case, there may be no good reason for maintaining it either.
Yet, to raise doubts, of whatever hypothetical nature, in order to force an individual to reconsider his or her position is not enough in and of itself. The doubts which are generated must be capable of being considered as real challenges.
Mr. Thoreau may be known, far and wide, for the telling of lies. Or, perhaps, he is known as one who changes his mind frequently about decisions he has announced.
In either event, the sceptic's reminding one of these factors represents much more of a challenge to one's being able to tenably maintain one's position vis-á-vis knowledge claims concerning the gorge than if the sceptic were to say something like the following: "How do you know that little purple men from Pluto didn't secretly set down on Mr. Thoreau's dam and shut off the water while Mr. Thoreau was away fishing?"
Even though it seems logically possible that little purple men from Pluto could have done what the sceptic suggests, the mere logical possibility of something may not be enough to sustain a plausible challenge to one's epistemic claim (even if based on indirect evidence, to some extent) about water being in the gorge. In other words, the challenge need not be true or even something one could say is probably true or very likely true. Nonetheless, the challenge must have a certain believability about it such that it would be entertained for consideration as a factor which actually could be conceived, on the basis of past experience, as something that, on occasion affects whether or not water was in the gorge at any given instance.
The notion of "logical possibility" being used here means only that our existing understanding of "reality" or of our experience does not contain anything which automatically would preclude the possibility of, say, little purple men from Pluto closing the water gates of Mr. Thoreau's dam being true. Yet, as indicated previously, absolute necessity is entirely a function of what is empirically true with respect to reality, not just logically possible.
This function is independent of (because it is more fundamental and encompassing than, although not entirely unrelated to) what we think we know. More importantly, this function is independent of our ignorance about what the nature of reality actually is. Therefore, 'logical possibility' can be construed either in terms of: a) what actual reality permits as being possible, given that reality has the character it does; or, b) what our understanding believes reality permits as possible, although this sort of 'possibility' may not be possible in ontological actuality (i.e., aside from its reality as a belief).
One needs to draw a distinction between, at the very least, rooted and un-rooted assumptions. For example, the sceptic's mentioning of the possibility concerning purple men from Pluto is essentially an un-rooted assumption. This is so since outside of some entirely arbitrary mathematical estimates on the possibility of the existence of life on other planets in the universe, there really is no evidence to indicate life exists on other planets (although subsequent evidence to the contrary may be uncovered). Moreover, there is even less evidence which is capable of indicating that there are beings from Pluto who are purple and have the technological capability to put a space craft on Mr. Thoreau's dam site, as well as who would take the trouble, for whatever reason, to close or open the water gates at the dam site.
On the other hand, a geologist who had lived in the vicinity of the gorge and was thoroughly familiar with both the behavior of groundwater near the gorge and with the behavior of Mr. Thoreau and who made the "assumption" - on the basis of what he or she knew - that water was in the gorge or that Mr. Thoreau had done what he said he had done would be basing his or her judgement on a set of rooted assumptions or assumptions. Such assumptions are capable of being logically tied, to some degree, to a certain amount of data which could be, or had been, substantiated somewhat.
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