(This essay takes a philosophical approach to "knowledge". It requires a basic undersanding of Epistemology).
Difficult questions can be approached in a number of ways and it is tempting to interpret this question as "has propositional knowledge been defined correctly?" Tempting because this is a relatively easy question to answer. In fact, a 'yes' or 'no' answer could reasonably be argued. Even adding the supplementary question "If not, will it be?" would not prove impossible (given one could extrapolate from the work done in the field since Edmund Gettier's small but perfectly irritating paper of 1963).
My worry, though, is that this reading of the question falls into a trap set by modern Epistemology - a set of assumptions which, I believe, has sent the subject ever deeper into ivory-tower land and leaves the lay-person alienated, confused and perhaps even angry (I speak from experience!). The assumptions include:
I cannot hope to address all these assumptions - I do not have the knowledge or the space - however, I do believe that they should all be addressed if anything like a reasonable examination is to be made of knowledge and its definition. Hence, I shall devote the rest of this essay to an examination of four areas which, though woefully brief, should indicate enormous (perhaps even intractable) difficulties. The four areas are: definitions in general, Epistemological definitions, the concept of 'knowledge' and a survey of proposed definitions of (propositional) knowledge. In doing so I will keep one question in the back of my mind which I hope to answer at the end. It is this: Why, after thirty odd years of trying, has little consensus been reached in defining (propositional) knowledge in the form JTB+? (or TB+, since some definitions include the J in the +).
Firstly, four questions:
Of course, what these questions are really asking is; "Can we define something (especially something as intangible as knowledge) without having a firm grasp on what it is to define something?" Do we then have to start by defining 'define'? Can we, in fact, define 'define'?
Unfortunately, the prospect of falling at the first hurdle stares me in the face. But if we cannot define 'define', how are we to define anything else? Is there a way around this? Or, more appropriately, have we a way around this? Taking my would-be philosopher's hat off for a moment and putting on my would-be psychologist's hat, the course forward looks a little easier. Let me get out of the ivory tower, and find out what people actually do when they define things (the journey may be a waste of time, but it may also be fruitful later on).
Surveying the world, I suspect that what we would find (note, I have not actually left my ivory tower!) is that most people very rarely use definitions, if at all. Let us take a common item such as a stapler. A person does not have to define a stapler in order to use it. They see it in action; they see the result; they have a need; they find/buy one; they use it. This seems fine for at least 99.999% of people's dealings with staplers but there must be some occasions when defining a stapler is necessary.
As good imaginary psychologists we continue our search, and we are rewarded. We find an inventor who has a new way of joining pieces of paper together using small strips of metal. She goes to her nearest patent office and discusses it with an expert. After a while we hear one say "But is it a stapler?", and "Well it depends how one defines a stapler". Bingo. So what do they do? Do they almost immediately get on to "well it depends how one defines define"? Decide that that question is intractable and decide to call it a day? Or do they ring the nearest epistemologist? I doubt it. I suspect a little more pragmatism. I suspect a knowledge of patent practice and a search through the patents on previous paper-joining equipment will give them some sort of answer (It is not unreasonable to assume, however, that the patent clerk's boss when reviewing the patent application, will come to a different decision as to whether this one is a stapler or not. C'est la vie).
Having repeated this investigation with some other things (e.g. sport, soluble, murder, circles, pipes), we return to our tower, and assess our results. We find that people happily use things without defining them, but under certain circumstances (e.g. in patent offices, law courts, maths lessons, art galleries) they need to, and when they do they invariably use their principles and practices; i.e. the cultural legacy that they inherit and occasionally tamper with. So we find in certain cases (e.g. abortion, capital punishment, genetic engineering), where there is a clash of principles/practices or no long-standing (traditional) principles/practices, people dither about and argue and reach very little consensus.
Removing my would-be psychologist's hat, I replace it with my would-be philosopher's one. But, what is this! I've accidentally put on my would-be-mathematician's hat (or is it my would-be logician's hat, they look so similar). The world suddenly looks a different place. It is governed by natural laws. By underlying rules. By definable quantities (lengths, areas, forces, momentum) and by definable operations (add, multiply, integrate, exclusive or).
Replacing my would-be philosopher's hat, I find there are two worlds I can examine. The perfectly ordered world of mathematics (rational and logical) and the all-too-human, imperfect world of real people (often irrational and illogical; crammed with errors of perception, errors of memory, errors of reasoning and errors of language). An idealist's world and a empiricist's world. A priori and a posteriori. The ordered and the chaotic.
To add to this, let me look from another angle. Evolutionary theory teaches us that the fittest life forms are those that survive. To react in an appropriate way to environmental changes is the key to survival and this is what primitive life forms achieve. But the more successful (i.e. more adaptable and flexible) life forms have an added and even greater ability - they are prepared. They have some idea of what is about to happen. They can predict and they can plan. To do this some kind of internal "world model" is required - classifications and relationships. As animals we are built to classify. Even at the level of cells in the retina of the eye, the first step in object identification is taken by detecting the edges between things.
I seemed to have strayed a little from my quest to define "define". Or have I? I do not think so. I think what I have arrived at is the notion that to be human is to try to seek and attain order, since this is what is required to be one of the most successful life forms. Whether one views the quest as to impose order on a chaotic universe, or to extract order from a harmonious universe, the essence is much the same - to classify 'things' and then to find relationships between those 'things'; crucially, hierarchical relationships and associative (e.g. causal) relationships. We put things in boxes; we put labels on those boxes; we have special boxes which hold the relationships between other boxes; and we have mechanisms which judge and sort new items into boxes, and which create new boxes if the old ones are not adequate. From this standpoint, definitions are nothing more than the symbolic tools (usually linguistic &/or logico-mathematic) that aid us in this classifying process.
If part of the human condition is the need to attain order, then the study of Epistemology epitomises this urge. Epistemology can be viewed as sitting between Psychology and Logic, desperately trying to wrestle the often irrational and disordered human mind into the confines of the neat and ordered world of Logic. Like the Freudian Ego, Epistemology's fate is to try to cope with the opposing forces of the Id (Psychology) and the Superego (Logic). The triangular representation shown below shows how Epistemology can be viewed as sitting at the apex of a triangle, the other two apexes being Empirical Science and Pure Mathematics, with Psychology/Sociology and Logic acting as buffers.
Each discipline on the triangle has its own way of defining things. As far as
Epistemology is concerned, its way of defining things sits (as on the triangle)
between those of Psychology and Logic. This is a difficult position. There is
doubt and uncertainty in Psychology, but none in Logic. Psychology employs the
services of imperfect experimental measurements, allied to statistical analysis,
but Logic (and I am thinking here of Propositional and Predicate Logic) contains
no approximations or half-truths. So how does Epistemology resolve its position
between uncertainty and certainty. It does this by concentrating on the realm
of knowledge that is certain, i.e. the world of propositions.
Epistemology is "the theory of knowledge" and Epistemologists bandy the word "knowledge" about as if it covered all types of knowledge. For them, though, it does not. Its use is almost exclusively reserved for propositional knowledge. Why?
The standard reply, I suspect, would be that Epistemology is about ideas, and ideas are best expressed as propositional statements so that they can be scrutinised (for truth - i.e. "consistency") using the rules of Propositional and Predicate Calculus (Note the latter word, indicative of Logic's claim to be part, if not the foundation, of Mathematics).
My question, though, is this: Is it valid to break propositional knowledge off from the rest, or is it merely a theoretical construct in order to make the (calculus) sums easier?
Consider the following three statements:
These are examples of propositional, procedural and acquaintance knowledge, respectively. But are they so different? And are they mutually exclusive? I suggest that in many circumstances they are not. Taking the first two: to know how to do something, must sometimes entail knowledge that certain properties apply to it. For example, for Professor Smith to use e=mc2 entails that he knows that e=mc2. It seems inconceivable that the two statements "Professor Smith knows how to use the principle of relativity to solve certain physical problems" and "Professor Smith does not know that e=mc2" are inconsistent. Similarly, the two statements "Professor Smith knows Einstein's Special Theory of Relativity" and "Professor Smith does not know that e=mc2" are also inconsistent.
Perhaps, then, propositional knowledge is a subset of procedural and acquaintance knowledge. Hence, a piece of procedural (or acquaintance) knowledge is merely a collection of many propositional statements. The logician may desire this, but I doubt if the psychologist would oblige. Many studies of intuition, sub- and pre-conscious perception and reasoning, the effects of emotions and feelings, of habits and automatic behaviour patterns have provided substantial empirical evidence that much of what we do and think cannot be reduced to simple propositions. Again, we are in the realm of uncertainty and approximation.
Propositions are nice and cosy. They make the universe seem a neat and orderly place: h or not-h, and no grey areas. A universe of Platonic absolute truths, and no uncertainties (e.g. Heisenberg's) would make things easy. And it may be true. But no one knows, and it seems a massive assumption to make.
S knows that h iff . . . .
The many and varied definitions of propositional knowledge that fill in the gap after "S knows that h iff . . . " invariably involve the analysis of a number of hypothetical, but nevertheless realisable, situations or scenarios. This analysis usually attempts to achieve two things:
1) Find the relationship between the evidence (E) available to the subject
(S) and the true circumstances of the situation (T)
2) Examine the link between the evidence available to the subject and the proposition
that the subject arrives at (sometimes referred to as p, sometimes as h).
This journey from T to E to p is generally achieved using one of three conceptual
frameworks: logic, causality and truth-tracking.
Definitions, firmly based in logic, contain components such as "reasoning must involve only true premises and lemmas", "nothing can be known which is inferred from a false belief", "S must have conclusive reasons for believing that h", "S must not reason through a false step". Definitions that approach from a causal standpoint stress the idea that the circumstances must appropriately cause the evidence, which must appropriately cause the subject's belief. Hence, they have components such as "p is causally connected in an "appropriate" way with S's believing p".
The third conceptual framework could loosely be called "truth-tracking". This is here components of the definition refer to S's altered (or unaltered) beliefs depending on slight tweaks in the circumstances of the situation: i.e. how p alters (flips from true to false, or vice versa) as T and E alter. This view is appealing since it concentrates on the one aspect that is particularly crucial to the logical and causal approaches. That is, the conceptual relationship symbolised as p*q. Using words, the logician would describe this as "if p then q" or "p implies q". Proponents of the causal view (including, I suspect, most scientists) would describe this as "p causes q". Nozick's Conditional definition exploits this crucial relationship, by doing away with any reference to justification and replacing it with two conditionals: "If it were the case that p then S would believe p" and "If it were the case that not-p then S would believe not-p".
The problem with the Conditional account, though, is that it requires somewhat of an externalist view. In other words, S may know p, but can never be sure of this since the evidence that S does know p lies outside S's evidence. This may be theoretically fine, but does not make this definition very practical, except in fuelling the sceptic's arguments. On the other hand, the internalist view is just as shoddy, since it quickly leads to the problem of infinite regress. Ways around the latter problem have been proposed, such as the idea that there are basic beliefs that do not require justifying (Foundationalism), and that the group of beliefs constituting E can be self-consistent and complete (Coherence theories).
I do not want to dive into a great debate about the pros and cons of the various approaches and definitions; this essay is not about that, it is about the assumptions which underlie many of these debates, and how they may be flawed. So I shall end with a brief look at the assumptions that are often made when theorists criticise their fellow theorist's definitions. The review is sketchy, but I hope reveals the extent to which theorists presume that people have some beliefs which do not rest upon uncertainties, approximations and half-truths. This, I suggest, is not necessarily the case.
1) Infinite regress. An apparently strong criticism. As mentioned above, it can be avoided with certain assumptions (basic beliefs, coherent beliefs), but these seem very shaky since they assume certainty in areas where uncertainty may abound. It is possible, however, that infinite regress is not the major problem it at first seems, if notions of partial certainty and probability are used (e.g. ideas linked to Baye's Theorem).
2) Vagueness. A seemingly good criticism, but one which could be levelled at virtually all definitions, since the terms theorists use in their definitions are rarely themselves defined. Unfortunately, the defining of terms in definitions leads us back to the infinite regress problem.
3) Impossibility. An interesting criticism that plays with, but does not state, the inherent problems of the theoretical and the practical. For example, "S knows that p iff S knows everything" seems logically reasonable, but practically impossible (hence, presumably, useless).
4) Leads to Scepticism. Definers of knowledge seem to detest Scepticism, as if it put their very livelihoods at risk. They, therefore, refute any definition that leads to sceptical views, which assumes that Scepticism is not true. Which no one knows (and, I suggest, will never know).
5) Questionable examples. At the fuzzy areas that inevitable lie at the borders of (non-logicomathematic) definitions, there is always debate as to whether this or that example or counterexample does or does not constitute a case of S knowing that h. To the bemused onlooker, this can often seem like the modern equivalent of arguments about how many angels can fit on a pin head. Unfortunately for Epistemology, common-sense is not very precise.
6) Using "non-epistemic notions". Similar to the vagueness criticism. For example, a definition that included "there is no relevant coincidence involved in S's believing p", would probably be criticised as poor since it includes the non-epistemic term "coincidence". (NB Some believe "causes" to be a non-epistemic term).
7) Too local (i.e. not global). For example, causal definitions are viewed by many as not applying to such areas as Ethics, Pure Mathematics and, even, immediate sense-data.
In summary, most of the criticisms used to shoot down definitions of propositional knowledge are flawed if one does not assume that propositional knowledge is a good way of representing the way the human mind "models" the "real" (and possibly uncertain) world in certain terms. I believe it is the gap between how the mind really works and the way the logician would like it to work that is at the heart of the problem of definitions of propositional knowledge, and has led to little consensus over the past thirty-odd years. The human mind may operate mechanistically and be reduced to a series of equations. If so, then a definition of knowledge may be possible. But if it can be shown that the microscopic uncertainties, that Quantum Physics teaches us about, rise up to make macroscopic uncertainties, then a perfect definition of knowledge (with no fuzzy edges) seems unlikely.
Clark, M., (1963). Knowledge and Grounds: a comment on Mr. Gettier's paper, Analysis, 24.2, p46-48.
Dancy, J., (1985). An Introduction to Contemporary Epistemology. Oxford: Blackman.
Gettier, E. L., (1963). Is justified true belief knowledge?, Analysis, 23.6, p121-123.
Goldman, A. I., (1967). A causal theory of knowing, The Journal of Philosophy, 12, p357-372.
Nozick, R., (1981). Philosophical Explanations. Oxford: Oxford University Press.
Pappas, G. S. & Swain. M., (1978). Essays on Knowledge and Justification. Ithaca, N.Y.: Cornhill University Press.
Sturgeon, S., (1993). 'The Gettier Problem', Analysis, 53.3. p156-164.