Belief and Knowledge - Part Three
In one sense, one cannot escape the fact all knowledge is tautological. After all, the premises which one strings together to describe or characterize a given phenomenon all contain - singly or together (and to the extent they are accurate descriptions or characterizations, at least as far as they go) - the truth of the phenomenon being considered.
An individual may describe, represent, characterize, interpret or individuate experience [and that (i.e., reality) which makes such experience possible] according to an individual's own values, beliefs, assumptions and so on. Nonetheless, one has difficulty avoiding the realization that some part of what one experiences as the "reality" of a given thing or phenomenon is a function, to some extent, of the thing or phenomenon being experienced. In other words, the character of the 'thing' (or phenomenon or whatever) being experienced forms the themes that are the "text" with which one hermeneutically works and that sets the context against which one's under-standing pushes in order to generate congruent conceptualizations or conceptual geometries.
Although there may be problems in attempting to sort out which aspects of an experience are subjectively superimposed on the experience and which aspects of an experience are structured by, or reflections of, the thing or phenomenon being experienced, none of these difficulties should obscure a basic philosophical point. To whatever extent one's understanding is correct or true, this correctness or truth is, inevitably, a function of what the nature of the character of the aspect of reality being experienced is at a given time. Indeed, in order for understanding to be true, the understanding must entail an accurate expression of the congruency relationship between, on the one hand, the character of the epistemic claim being made by an individual, together with, on the other hand, the character of that (whether phenomenological or metaphysical) to which an individual's epistemic claims are making identifying reference.
Understanding does not supply the truth. Understanding, at best, merely recognizes truth. "Connecting insight" consists of a mental recognition, within the context of a given set of data or experiences, in relation to the character of the themes in that context which tie together a set of evidential premises in a way which is accurately reflective of some aspect of the given context. In addition, evidential premises express truth only to the extent that the character of the premises is congruent with the character of the situation under consideration (i.e., the reality, whether phenomenological or metaphysical, to which one is making identifying references in the form of one's characterization or description).
Therefore, unless the premises one used were accurate in that they actually entailed some reflective properties of the character of the aspect of reality under in-vestigation, one's understanding would not be a case of knowledge. This is so because there is no basis for establishing a link between the char-acter of one's understanding and the character of that which makes possible the aspect of the experiential field to which one is attending.
In order to further develop the above line of thinking, consider the following. If one is given a series of numbers and one is asked to give the next number in the series, then, in order to discover the unknown number, one has to try to determine the character of the function which generates each member of the known number sequence.
Once the nature of this function is discerned, one then, knows how to provide the next number in the series. Although the term "mathematical induction" is used to refer to such a discovery process, this process appears to bear many similarities to a deductive context.
The underlying mathematical function in question in any given sequence of numbers produces certain numbers and not others. The number we seek is a determinate and necessary one, and it seems to be implicit in the overall sequence of numbers which are given initially. In other words, there appears to be something inherent in the relationships of the numbers, one to another, which gives expression to a theme that ties the numbers together in a co-ordinate framework of determinate character. The number series entails the mathematical function which gives rise to such numbers, just as the mathematical function entails the numbers to which it gives rise.
Mathematicians do not say they believe that the next number in the series is ‘x’. If they have discovered the nature of the function generating the series, they will correctly produce each succeeding number of the series because they know something which is not present in mere belief.
In many ways, the nature of the issues surrounding problems in mathematical induction are reflected in a variety of other problems in science, history, philosophy and so on. In all of these cases, one often is given a number of particularizations that represent data, information and facts drawn from different dimensions of experience. One, then, attempts to determine the character of the principle(s) that tie(s) the various particularizations together in the form in which they are experientially engaged. One who gains insight into, or sees how, the given data fits together is able to deduce further particularizations from the character of the pattern discerned, just as one who discovers the character of the mathematical function which underlies a series of numbers is able to deduce further particulars in the number sequence.
In each context of deduction, the data embodied in the form of particularizations (either as premises or conclusions) entails the character of the principles or aspects of reality which give rise to them. These particularizations are but abstracted or characterized expressions of such principles or aspects.
In other words, the character of the particularizations is a function of, or shaped by, the character of the reality which gives rise to these particularizations. Indeed, because this is so, one has some hope of using the character of particularizations to form a conceptual context through which one may be able to detect the nature of the character of that which makes particularizations of such character possible.
Thus, this is similar to the case in which one uses the character of the particular numbers of a series to form a conceptual context through which one may be able to detect the character of the function which generates the various numbers of the sequence and, therefore, makes them possible in the form in which they are manifested in the series with which one starts one's investigation of discovery. In both cases, true understanding (i.e., knowledge) is not a matter of jumping to conclusions across an inferential chasm for which no logical or evidential bridge exists.
To whatever extent one can achieve a true understanding, this is because one has been able to entertain ideas or concepts whose combined character provided enough of a demarcated framework or conceptual geometry to permit one to establish congruencies between various aspects of one's experiential field and various aspects of that which helps shape or structure the field's character. These congruencies give expression to, among other things, the character of the conceptual geometry that forms the links of understanding between certain focal facets of the phenomenology of an individual's experiential field and a variety of horizonal considerations which not only evidentially bear upon these focal facets but which form a context upon which one can reflect critically in order to seek to establish a hermeneutical account of why those focal facets have the character they do.
As a result, a true understanding is not simply a matter of linking one's understanding with certain aspects of the phenomenology of one's experiential field. One's understanding also must be able to meet the demands of the interrogative imperative which arises: a) out of the horizonal considerations that surround the focal themes to which one is attending; and, b) in relation to various aspects of the phenomenology of the experiential field to which an individual is attempting to make identifying reference through the individuation or characterization of those aspects.
Furthermore, this interrogative imperative, although it is itself an expression of a certain dimension of the phenomenology of the experiential field. This dimension seeks to determine why any given focal or horizonal facet of the phenomenology of the experiential field has the character it does or what such a structure means or how it can be of value, and so on.
To the extent an aspect of reality is actually knowable, then, some manner of epistemic bridge exists which could link the character of certain facets of the phenomenology of an individual's experiential field with the character of certain facets of that (presumably, some facet of ontology) which makes such a phenomenology of determinate character possible. The epistemic task, then, becomes one of trying to identify the structure of this bridge amidst the experiential entries which appear over time in one's phenomenology or in our collective phenomenologies.
Without a proper identification or recognition of the character of this bridge, there will be a logical/experiential gap. This gap exists in the phenomenology of an individual'e experiential field with respect to the focal/horizonal dialectic of any hermeneutical framework which arises in such phenomenology concerning the character of the reality underlying that phenomenology and to which an individual's is attempting to make an identifying reference through attending to such phenomenology, and this logical and/or experiential gap prevents an individual from claiming that she or he knows the character or structure or nature of the facet of phenomenology (or underlying reality) in which the gap is present And, this remains the case even if an individual's claims concerning the facet in question should turn out to be correct.
The above sense of tautology, which is an unavoidable feature of what true understanding or knowledge entails, in no way implies one must assume one's conclusions in order for one's understanding to be true. The emphasis in the foregoing discussion has been to indicate that whenever knowledge exists, it is functionally dependent on someone’s having recognized or realized the character of the aspect of reality which is contained in, or expressed by, the character of the premises, ideas or concepts one is entertaining as one works toward establishing a "connecting insight" in the proper sense of this term (i.e., that which accurately reflects the character of the link(s) between various aspects of reality).
Differentiating Between Understanding and True Understanding
On the basis of the foregoing considerations, one, now, can return to Malcolm's analysis and understand, to some extent, how Malcolm, perhaps, has created some unnecessary difficulties through his characterization of the issue concerning whether or not an individual actually can distinguish between belief and knowledge within himself. More specifically, Malcolm focuses on cases (4) and (5) (see pages 4-5 of this article) in order to try to establish that an individual has no grounds for being able to claim he or she can differentiate between belief and knowledge.
Thus, in case (4), Malcolm stipulates that an individual: a) claims there is water in the gorge; b) gives a reason for the claim; and, Malcolm also indicates c) water is actually found in the gorge. In case (5), Malcolm says conditions a) and b) of case (4) remain the same, but condition c) is changed such that no water is found in the gorge.
Malcolm's argument appears to run as follows: because the only difference between case (4) and case (5) is the water's presence or absence in the gorge, there is no material on which an individual can reflect that would allow an individual to determine whether his or her claim was a matter of belief or knowledge. Unfortunately, Malcolm has left out all of the important data which would generate the details of an actual three-dimensional (or n-dimensional) epistemological setting.
In this kind of setting, individuals who are making claims would have some ongoing or past facets of the phenomenologies of their respective experiential fields to which they could attend, and in relation to which they would make claims, and on the basis of which they might be able to differentiate between whether or not a given claim was a matter of belief or knowledge. Malcolm has taken the limiting case (i.e., case (5)) in which an individual makes a "knowledge" claim that turns out to be incorrect, and, then, treats this limiting case as being the paradigm which defines the basic characteristics determining the status of all knowledge claims made under all circumstances.
Given the way Malcolm has restricted the context of the gorge example, an individual caught up in a situation like case (5) would not be able to distinguish between belief and knowledge once someone had demonstrated to him or her that no water existed in the gorge. On the other hand, an individual's inability to distinguish between belief and knowledge is tied only to the limiting case as Malcolm describes it. In the instance of case (4), if one's claim is correct and if the understanding on which the claim is based is also correct and if, finally, one believed one's understanding to be correct, then, one would have a basis for distinguishing between belief and knowledge. This basis would be according to the nature of one's present understanding and how that understanding (even if it had not been confirmed, yet, as correct) differed from other contexts of understanding in which the dimension of connecting insight was absent.
The fact one may have been wrong before when one believed one's understanding had been correct is largely independent of what one believes, now, about one's current understanding, providing one's understanding is correct. The only way in which previous errors might affect the current situation is in the level of confidence one had toward one's present understanding.
That is, one might tend to distrust one's current understanding if one had a habit of making mistakes with sufficient frequency, and, subsequently one developed a certain degree of indecision or uncertainty concerning the accuracy of one's subsequent understandings. But, what one believes about one's understanding must be kept distinct from the understanding itself which is true or false independently of what one believes about it.
In fact, one well might contend that realization of this distinction and the accompanying recognition that one's understanding is correct or not, independently of beliefs about, and attitudes towards, such understanding, is what allows one, to some extent, to come to appreciate the potential difference between a true understanding and a mere "understanding". Over the course of time, one develops a phenomenological sense of the differences between: a) "understandings" which turn out to be incorrect but that one originally thought to be correct; and b) understandings which are true irrespective of what one believed about them originally. Even though this phenomenological sense may not be definitive and clear-cut in all situations, it does provide a background against which differentiations concerning belief and knowledge can be determined in many more cases than Malcolm's analysis would lead one to believe.
According to Malcolm:
"There is only one way that Prichard could defend his position. He would have to say that in case (4) you did not know that there would be water. And it is obvious that he would have said this. But this is false. It is an enormously common usage of language to say, in commenting upon just such an incident as (4), "He knew that the gorge would be dry because he had seen water flowing there that morning." It is a usage that all of us are familiar with. We so employ "know" and "knew" every day of our lives.' We do not think of our usage as being loose or incorrect - and it is not. As philosophers we may be surprised to observe that it can be that the knowledge that ‘p’ is true should differ from the belief that ‘p’ is true only in the respect that in one case ‘p’ is true and in the other false. But that is the fact."(p.60)
Leaving aside the issue of whether Malcolm has correctly assessed what Prichard could and would reply in response to Malcolm's criticisms, when Malcolm's above quote is juxtaposed next to the discussion of the previous 20 pages, Malcolm appears to be wrong in claiming "the knowledge that ‘p’ is true should differ from the belief that ‘p’ is true only in the respect that in one case ‘p’ is true and in the other false." One can agree a claim must be true in order to be considered as a candidate for the status of knowledge. What is also equally necessary is a certain kind of understanding which stands behind or surrounds the epistemic claim.
The understanding associated with mere belief lacks the connecting insight which characterizes the understanding of knowledge. Thus, contrary to what Malcolm seems to maintain, belief can be true and still not be knowledge because it lacks the kind of understanding which provides the necessary connecting insight into the nature of the truth at issue.
Although Malcolm contends that use of the terms "know" and "knew", as described in his quote, is an "enormously common usage of language" and "we do not think of [such] usage as being loose or incorrect", he makes a fundamental mistake in taking the common practice of linguistic usage as the standard or criterion against which truth or correctness may be measured. Whether or not this kind of usage is common or not is beside the point.
This is so because, as it stands (i.e., as Malcolm has described it), this kind of usage can be tremendously elliptical. In other words, it tends to leave out important epistemological dimensions of the concrete or existential situations in which this sort of linguistic usage occurs. As a result, and in contradistinction to Malcolm's position, this usage can be both loose and incorrect if an individual making these claims lacked the necessary connecting insight which could back up his or her claims. Moreover, as stated previously, even if an individual's claim turned out to be correct, he or she would not be entitled, legitimately, to claim knowledge unless an individual understood, in some minimal fashion, the epistemic relationship which necessarily tied the given claim to the object, issue, phenomenon or process about which the claim was made.
Malcolm's Two Senses of Know
Malcolm's errors appear to cause him to adopt a somewhat peculiar and, ultimately, an untenable distinction between two senses of "know". Malcolm refers to these two as the "strong" and "weak" senses of "know". While developing this distinction, Malcolm continues to play off against some ideas of H.A. Prichard.
Prichard had used the idea of proving that the sum of the interior angles of any given triangle is equal to two right angles as an example of how one can differentiate between knowledge and belief, and, therefore, how one cannot mistake what one knows from what one believes. According to Prichard, one does not believe one knows that the sum of the interior angles of a triangle are equal to the sum of the two right angles. Instead, one knows this is the case, and part of what is meant by saying one knows this is the case is an accompanying knowledge that precludes the possibility of there being anything which could be inconsistent with the idea that the sum of the interior angles of a triangle is equal to the sum of two right angles.
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