A complete theory of knowledge - if one can be found - a device that, given a person and a proposition, conclusively selects either the “does know” or the “does not know” option, is an extremely complex project; one that has to handle a broad range of seemingly unrelated cases covered by the common-sense understanding of knowledge as a feeling of certainty about a fact. In the below discussion I argue against a well-defined concept of knowledge as an attribute, presenting a vaguely externalist picture of a imprecise although objective knowledge as a bundle of relations between the rational beings and their external world.
Very few people keep a record of their birth date; I myself have never consulted my birth certificate to secure the knowledge of my exact age. Nor do I recall the moment at which the mystery has been revealed to me by a reliable testimony of my parents. Nevertheless, one's date of birth is as good an example of knowledge as one can present. It is one of the many small facts unconsciously learnt in childhood that remain in our memory even though the recording events, if we were ever conscious of them, have been forgotten.
This and similar examples are often used by externalists in support of their theories. Even though an internalist may respond in at least the two ways examined below, he is at any rate forced to resort to technicalities for a case that should be a simple everyday example of trivial knowledge.
The only obvious internalist evidence in the discussed example is a memory of the fact. However, an attempt to quote memory as evidence is probably the most unsound analysis of the birthday puzzle. Memories are potentially misleading and should not be allowed into evidence unless also justified (by a “justified memory” I understand a memory that one is justified in distinguishing from similar memories of dreams or otherwise unreal events.) However, any justification we may attempt to present for the memories of our dates of birth cannot use the undoubtedly actual but forgotten process of learning, as such justification would, by the construction of our example, be necessarily of an externalist flavour, referring to facts outside of available evidence. An internalist cannot afford to infer an existence of important evidence from the assumption of knowledge as that would weaken her insistence on evidence as central to the theory of knowledge. She would be assuming her theory without verification. Of course, an internalist is free to call on a range of memory types and accept only suitably-qualified memory as valid evidence. It is however difficult to see how such analysis of memory can be performed without falling back to the external world reference.
Because I am unable to conceive of a justification that would not involve memory in the discussed example, I will assume that, for an internalist, my beliefs as to the day of my birth are justified by some kind of qualified memory evidence. On another hand, an externalist's analysis would treat the memory factor as part of the link between the knower and the justifying facts such as the forgotten learning process, part of a causal link as proposed by Alvin Goldman in his essay A Causal Theory of Knowing or a variable in the “law-like connection” between the beliefs and the world as suggested by D. M. Armstrong in his discussion of non-inferential knowledge from Belief Truth and Knowledge (Cambridge, 1973). Usually, an externalist would not discard the subject's memories as incidental, although he rarely considers them of crucial importance. Such treatment removes any but mere syntactic distinction between externalist and internalist justification of the same knowledge claim, both acknowledging that memory supported by some other belief-forming circumstances is essential. Because reliance on memory is in no case sufficient for knowledge, “the other factor” necessarily external to the knower (a trivial assumption if memory is her only link to the facts) dominates the analysis. The internalist analysis of the birthday puzzle is hence reduced to an elaboration on the explicitly externalist one.
In an alternative approach, an internalist will discard the whole experiment as an example of a practical “knowledge-how” instead of classifying it as a propositional knowledge subject to the sought-after definition. This may be done by noting that there is no clear distinction between knowing one's birth date and one's native language. Hence, in the same way in which one may attempt to reduce “knowing English” to a long list of “knowing how to say X in English”, knowing one's date of birth may be reinterpreted as an ability to quote it. As part of that approach, an internalist will constrain herself to discussing only conscious knowledge of facts, leaving practical knowledge as an ability to perform a task outside of the domain of definition. She will then proceed to state that all cases in which the process of acquiring information to serve as evidence could be considered unconscious do not deserve the label of knowing, but, instead, should be treated as a semi-instinctive ability to quote or otherwise use the information in question.
While we may choose to follow the above path when pursuing an externalist theory, we are not restricted to outright rejection of the resulting “practical” knowledge. Instead, in principle at least, we may still be able to say something about such knowledge, as the problematic lack of access to the evidence is not critical to our analysis.
It should now become clear why internalism is the more restrictive approach. Because of the important role that a single factor (evidence) plays in all internalist theories, knowledge as seen by internalists is necessarily a narrower concept than the equivalent one proposed by the more generous of the externalist theories. Although this restriction in itself does not have to constitute an objection to internalism, I will shortly argue that, for the above reason, internalist theories cannot provide an understanding of knowledge sufficiently complete to give justice to the subject.
In the remainder of this essay, I will assume that the primary epistemic goal is to arrive at a definition of knowledge that will serve as both the summary of our understanding and a metric to be used to test individual cases of claimed knowledge. Although such metric may not be fully practical or infallible for any but an omniscient observer, as a minimum we should be able to use it to approximate the ideal categorisation reasonably well. I expect that, by furthering our understanding of knowledge, a good definition will allow us to make an educated and usually correct guess when classifying a given case as knowledge or otherwise.
There are two distinct approaches we may take in order to achieve the above goal. On one hand, we may see knowledge as a potentially definable metaphysical attribute of the knower, parallelling that of the truths of propositions. As part of this approach, an epistemologist assumes existence of one correct definition (or, as an insignificant variation, a set of equivalent definitions), and focuses her efforts on discovering that definition. Because this approach is essentially identical to the methods of conventional science, the only reasonable way to succeed in it is by a direct application of the scientific method to a range of thought experiments. Therefore, an epistemologist proposes a hypothesis and tests it against the largest possible class of cases. As part of achieving her goal, she presumably attains a complete understanding of the concept of knowledge, or, equivalently, she must demonstrate such an understanding in order to claim success. Obviously, because the process of testing is never completed (a theory of knowledge is essentially empirical in nature, and therefore synthetic), the goal is never reached. However, as the number of successfully handled cases grows, so does our confidence in the theory, until a single counterexample is found, at which time the theory must be either amended or rejected.
Alternatively, an epistemologist may obtain insight into the problem of knowledge purely by pursuing the definition itself. She notes that, because the process of verification is in principle infinite, it constitutes a sufficiently challenging objective by itself. As part of this approach, she does not concern herself with the completeness of the definition, but merely with its applicability to some subset of all possible cases, which it should analyse completely and accurately. Even though this approach may be less ambitious than the methodical one sketched previously, it does fulfil the epistemic goal in that it both furthers our understanding of (some class of) knowledge and provides a required metric for the subset.
The approach essentially recasts the guiding question of “what is knowledge?” into a more manageable, yet arguably more interesting “what is involved in knowing something?”. For the birthday example, we would satisfy ourselves with the analysis of the case as a true belief justified by memories formed through a legitimate learning process, where the concept of the legitimacy of a learning process is assumed to be sufficiently well understood and outside of the strict scope of the analysis. Unlike traditional epistemology, we do not trouble ourselves with the clearly limited applicability of this analysis.
A feature of the approach is an inversion of the traditional “hypothesis followed by the test cases” structure of analysis based on “empirical” evidence of the thought experiments. Instead, if generalisation is not a goal, research typically focuses on the thought experiment in order to build the hypothesis. Such analytical approach is more natural in that, unlike the “experimental” alternative, it favours detail and does not confuse potentially unrelated or only weakly related cases. When universality ceases to be an issue, we may spend more time developing our hypothesis out of a single test case. After all, it seems unreasonable to allow the problem of the first Gettier case to affect the quite unrelated research into the issues involved with knowing one's date of birth, when the only connection between the two is the customary use of the common label of “knowledge”.
An instructive application of the selective definition approach is the thermometer model proposed by D. M. Armstrong in his discussion of the non-inferential knowledge from Belief Truth and Knowledge (Cambridge, 1973). Because the definition requires a substantial amount of background notation to introduce, I will not repeat it in this essay. Armstrong's treatment of non-inferential knowledge is stated in a formal, precise language that precludes all ambiguities. Although rather strict, the definition forms a consistently conclusive metric when applied within its scope. When tracing development of the definition throughout the above-mentioned essay, one cannot help but notice that Armstrong, by progressively amending the initially simple case to eliminate all originally identified problems, does not merely articulate a convenient formalism. More than a method, each amendment captures the reasons why the corresponding issue poses no problem to our intuitive notion of knowledge that is the subject of the research.
The thermometer model is an example of the typically-externalist reliabilism. Before challenging the model, it would be appropriate to ask whether all similarly compact theories must exhibit externalist features. Although I will leave this question open, I suggest that, because internalism, by definition, relies on the notoriously difficult to analyse knower's state of mind for justification, and because the intrinsic concept of availability of evidence is of a pragmatic nature, it is unlikely that an internalist theory offering the same level of abstraction as in the thermometer model may be presented.
The main problem with the thermometer model is its narrow applicability. As the author himself notes, it is difficult to see how the theory could be extended to cover anything beyond the discussed non-inferential knowledge. Because the theory seems to work well for one class of cases, it suggests that singling that class out in the unified definition is a very plausible approach. Indeed, it shows that, instead of discarding a model on grounds of limited scope, in keeping with the goal of furthering our understanding of knowledge, we should introduce and defend such specialised definitions. The thermometer model suggests that knowledge is best approached with the selective definition model: as a heterogeneous concept, with a range of theorems that handle a small number of cases well. At any rate, it is a counterexample to the assumption of the existence of a single concept of knowledge.
An alternative to narrowing the scope of a theorem is to include some open-ended list of cases in the definition. An interesting view that utilises this approach is the causal theorem proposed by Alvin I. Goldman in A Causal Theory of Knowledge from Knowing, Essays in the Analysis of Knowledge (edited by Michael Roth and Leon Galais). Goldman explains the Gettier cases by defining knowledge as “S knows that P if and only if the fact P is causally connected in an “appropriate” way with S's believing P.” He proceeds to supply an open-ended list of appropriate knowledge-producing causal processes. The author acknowledges in the essay that the theorem is more of a definition than an insight into the issue, and, indeed, I will risk the generalisation that theorems aimed at understanding favour either generality or alternatively a limited domain of definition.
It is possible to state a single grand definition of knowledge by using sufficiently generalised wording similar to the classical justified true belief definition. It is however obvious that such approaches give us a very limited understanding of the underlying concept. However, experience shows that elaborating on the generalised definition is far from trivial. On the other hand, a single definition may also be obtained, at the expense of generality, by restricting its applicability. For example, the various infallibilist theories, although of questionable applicability, are certainly intellectually appealing.
It should now become obvious why the a priori constraint assumed by internalist theories on justification as available evidence is no longer legitimate. Although it may well be that many cases of knowledge, such as the well known “sheep in a field” Gettier case, are best explained by typical internalist theories, such as Alvin Goldman's “distinguishability” theorem (Alvin I. Goldman, Discrimination and Perpetual Knowledge), these theories should never be over-generalised. In particular, as already seen, many cases of knowledge, including the birthday puzzle, are best explained using externalist theories. Therefore, externalism, being the more relaxed of the two competitors, is probably the better candidate for generalisations.
Although practically valuable for furthering our understanding of the various cases of claimed knowledge, my approach invites attacks from those who prefer to insist on an existence of knowledge other than as a mere intellectual tool. Because this view is popular amongst epistemologists, and because my analysis, as I hope to demonstrate shortly, does not preclude such interpretation, the possibility is worth pursuing.
The objection can be restated as a worry about the object of the understanding obtained with help of the selective definitions. Clearly, if our understanding is to increase, there must be something that is being understood. However, as I have already alluded to in the above discussion, there is no reason why the collection of definitions cannot be interpreted as a corresponding collection of as many different types of knowledge, either by taking the abstract concept to be equivalent to its articulation in the definition, or by seeing each definition as corresponding to some underlying concept independent of our perceptions. Although we may still consider all knowledge an instance of the single attribute of the knower, in light of an analysis by selective definitions, it seems much more sensible to recognise a possibly infinite number of often overlaping knowledge types. That is, instead of insisting on the convergence of all definitions to a single concept, we recognise the autonomy of each interpretation. Depending on the number of such autonomous approaches that we are willing to recognise as legitimate, the statement “X knows P” may or may not be meaningful on its own. If it is, its truth is equivalent to that of “X knows that P according to one of the accepted definitions.” Otherwise, the informal statement of a knowledge claim should, for the purpose of epistemic analysis, be reinterpreted as “X knows that P in a particular way.” Examples include knowing P non-inferentially, predicting P, knowing P based on memory obtained with a legitimate learning process, and so on.
It is quite possible to describe a single case of a claimed knowledge with two distinct theorems. For example, the causality theorem mentioned above serves as an alternative to the thermometer model. This does not imply that one of the theorems is invalid. Although one may be more appealing when applied to a certain case, none is necessary preferred to the other. Instead, given that each theorem is sound, both should be viewed as different interpretations focusing on different aspects of the same case. Both teach us something about the situation and it seems unjust to reject one simply because another applies to the same noun.
Without dwelling any further into the irrelevant details of any particular theorem, I will now endeavour to interpret the collection of knowledge types as a coherent unified concept. It is possible to bring all of the examples of selective knowledge together in a single picture of a unified knowledge attribute. Experience shows that an attempt to construct such an attribute out of a generalised concept applied to the disjunction of the domains of the various theorems fails by allowing for only an unacceptably restricted amount of knowledge. Instead, we avoid scepticism and remain true to the analytic spirit of the discussed approach by constructing a conjunction of all theorems. Each theorem represents one way in which a knower may be linked to the world with a conscious perception. Knowledge, a single and certainly objective concept, is a multitude of interactions between the knower and the objects of knowledge. As stated in the introduction, it is a loose heterogeneous bundle of concepts describing those interactions.
Note that it is hardly plausible to attempt an alternative, internalist interpretation in presence of the multiple kinds of knowledge, as such interpretation would be immediately reduced to that of multiple sources of evidence. However, because, by assumption, evidence must be reliable, all such sources must be in principle contained by some, possibly complicated judgement of adequacy. Internalist interpretations fail to impress by reducing the multitude of interpretations to a pragmatic choice of the degree of acceptable evidence.
I have argued that, in the light of the introductory birthday puzzle and the multitude of diverse competing theories of knowledge, the only sensible approach is that of treating each theory as an autonomous definition with a selective domain of applicability. Although I do not preclude the existence of a single knowledge attribute, I propose that, for sake of managability of the problem, pursuing a complete definition is an unreasonable thing to do. Instead, epistemological research should maintain a collection of partial definitions, each on its own contributing to the depth of our understanding of the issues involved in a knowledge claim, and, collectively, all giving us a broad picture of the heterogeneous, externalist concept of knowledge.
Patryk Zadarnowski, Sydney 1997