What is knowledge?

I am now at Hong Kong University participating in a knowledge management workshop and offering seminars on educational technology and academic publishing. My contribution to the workshop was a presentation on assessing learning in complex domains – a topic with which I have wrestled for some ten years now. Several other presentations were more directly focused on knowledge building, knowledge management and knowledge visualization. The talks were all excellent and the technologies being developed quite exciting. However, at the end of the workshop, I found myself wondering about this concept called knowledge.

My immediate conclusion was that I was in a state of confusion. My first impulse was to look at how relevant words are used in ordinary language because I suspected some of my confusion was a result of differing uses of key words such as ‘know’ and ‘knowledge’. These remarks are a summary of where I have arrived after a few hours of deliberation – not very far from where I started, I regret to report.

In recalling several of the presentations, the words on which I focused were ‘believe’, ‘belief’, ‘know’, and ‘knowledge’. In each of these pairs there is a verb and a noun. The English language is full of verb-noun pairs, as are many other languages. An interesting exercise is to try to find a verb or noun for which there is no corresponding counterpart. Perhaps not so interesting after all, as nothing comes to mind – at least not to my limited mind. I expect a linguist to interject a comment at this point, but alas I am alone without a linguist to consult.

The next step is to notice that one can associate one and the same person with the noun and the verb, as in these phrases: “I believe that Columbus sailed the ocean blue in 1492,” “My belief is that Columbus sailed the ocean blue in 1492,” “I know that the cube root of 64 is 4” and “my knowledge includes the fact that the cube root of 64 is 4.” This line of reasoning led me to wonder about a number of things. First, is there always a subject associated with a verb – a believer to go with believing and a knower to go with knowing? Second, is there some essential difference in the objects associated with believing and knowing? I realize these are not particularly novel questions, and I have previously wondered about these matters myself, only to leave this logical landscape in pursuit of other seemingly more compelling matters.

I then tackled what I believed to be the simpler of these two questions – whether there was always a subject associated with a verb.  This is different than simply looking for a noun that pairs up with the verb; in this case I am looking for someone who performs or is associated with the action indicated by the verb. For example, consider the noun-verb pair rain-raining. Of course there is rain and when it is present we say it is raining. But is there someone who does the raining? Oops. Be careful not to slip on the wet pavement caused by all that rain.

With believing and knowing, however, we readily identify a subject: ‘I believe’ or ‘I know or perhaps he or she believes or knows something. Surely you believe and know many things. Individuals believe and know things. That analysis surely fits well with ordinary discourse.

Then I realized that the word ‘knowledge’ is used not only to refer to what an individual knows but to what a group of people know. This is more akin to its use in the phrase ‘knowledge management’. Many instances of such use can be found and are evident in such phrases as ‘scientific knowledge’, ‘common sense knowledge’, and ‘contribution to the knowledge base’. This dual use of knowledge to refer to individuals and to groups of individuals has the potential to introduce ambiguity and possibly confusion in discussions about learning, instruction and performance. While one can find uses of ‘belief’ associated with groups of people, this is much more rare than the ordinary use of ‘belief’ to refer to an individual’s cognitive state of affirmation with regard to a particular proposition or claim.

What ambiguity or confusion might result from the use of ‘knowledge’? Shall I step off this precipice? I shall. Constructivism is widely accepted by philosophers, psychologists, educational researchers and instructional technologists. The kernel idea in constructivism is that individuals actively construct and interpret experience. Constructivism can be traced at least as far back as the 18^th century and Immanuel Kant’s Critique of Pure Reason in which Kant postulates certain categories of the mind that a person brings to all experience – namely, the categories of space, time and causality. We structure our experiences according to those categories; part of the interpretation of experience involves space, time and causality. In subsequent centuries, much has been added to the notion of individual construction and interpretation of experience. In the 20^th century, Wittgenstein takes the notion much further. In the Tractatus Logico-Philosophicus, Wittgenstein observes that we picture facts to ourselves – we create internal representations of things we experience. Wittgenstein fails to mention that we also have the ability to picture things that are not facts to ourselves, but let us put that aside for the moment. In Philosophical Investigations, published after his death, Wittgenstein introduces the notion of language games, which involve a community sharing these internal representations with each other, implicitly following a set of conventions governing their discourse. Taken together, Wittgenstein’s two notions comprise what is often referred to as ‘socio-constructivism’. We create internal representations of things we experience – this is a descriptive claim about what people do in the process of making sense of their experiences and in coming to know about and understand things they experience. This ability to create internal representations is a remarkable aspect of cognition in and of itself – so remarkable that we hardly notice it at all. In addition, humans talk to each other about these internal representations – an equally remarkable ability that again goes largely unnoticed. Okay … enough history of philosophy already … I have now stepped off the precipice.

Wherein lies the ambiguity or confusion? There was that small matter that we set aside for the moment – namely that we also have the remarkable ability to create internal representations of things that are not factual. We can also picture non-facts to ourselves. By some form of twisted reasoning, I might arrive at the belief that the cube root of 1492 is 64 (of course it isn’t). I have created an internal representation of mathematics such that I am led to that erroneous belief. While this may seem outrageous, one can imagine other cases where a person legitimately creates an internal representation of an experience that is clearly false but also quite understandable (that exercise is left to the reader with an overactive imagination). Obviously people falsely believe things – that is to say, they sometimes sincerely believe things that are clearly not the case. We now arrive at an interesting juncture. Not all beliefs are true, which for now means only that some beliefs held by individuals would not be accepted as factual by a community who generally understand statements relevant to the domain in question. So, while the person holding the belief in question might say that “I know it to be so,” the larger community would not accept that alleged fact as knowledge. An individual belief represents an affirmative state of mind with regard to the matter in question. An individual belief may also be the basis for a knowledge claim on the part of that individual. However, to be considered knowledge, such claims require more than an individual’s affirmative state of mind. Typically, such claims require the affirmative states of mind of many individuals over a reasonably long period of time. While I believe that Columbus sailed the ocean blue in 1492, there are also many others who believe this as well, and their beliefs have been held by many people for a long time. Does that make the claim true? Perhaps not – perhaps he sailed the ocean blue in 1491 and the records of that voyage were off by a year. Perhaps the ocean was green. Perhaps he landed in Greenland instead of the Bahamas (not very likely). Anyway, claims that people have regarded as certainly true and legitimate knowledge have occasionally turned out to be wrong or mistaken. Nonetheless, it makes sense to hold knowledge claims to a higher standard than belief claims (if this is not obvious, then you are destined for a career in politics).

That excursion into the logical landscape surrounding beliefs and knowledge was a result of wondering about the person(s) associated with believing and knowing. While in each case one can associate a particular individual with believing or knowing, it is often the case with knowledge that we are referring to a set of beliefs accepted by a larger community as being particularly well established. All of this is probably obvious to most folks even though it took me a while to struggle to this interim and somewhat tentative conclusion. I am a very slow learner. In any case, I can now say to a person who wonders whether a child constructs knowledge or not, that surely a child does construct knowledge although what is constructed may not add anything to the knowledge base accepted by the relevant knowledge community. People are naturally constructing knowledge (beliefs that they accept as true based on their personal experience) all the time. It is what we do – we picture facts to ourselves and then we talk about those pictures to others. We cannot stop doing it, except perhaps when we are asleep. Creating internal representations of our experiences is a natural and ongoing process.

It is perhaps worth noting that a representation is by its very nature a simplification. Our internal representations do not and could not contain all of the details of the direct experience. Let us call these internal representations mental models. Models always simplify the thing modeled. This is a logical remark and not a factual claim, by the way. Models are simplifications. Mental models are simplifications. We simplify in order to understand. It is in our nature to simplify – it is in our nature to create internal representations of our experiences. On the other hand, when we engage in talking about these simplifications, we are engaging in an expansive enterprise. We are adding nuances and getting feedback and suggestions – in talking about our internal representations, we are adding complexity. Of course, this introduces the possibility for ambiguity and misinterpretation, but it may also enrich the original interpretation (mental model) and add to our understanding.

Well, not having arrived at anything especially insightful in exploring the first question, perhaps I should consider the second: Is there a significant difference in the things that are normally considered the objects of belief versus those that are normally considered the objects of knowledge? The two examples with which I embarked on this journey – ‘Columbus sailed the ocean blue in 1492’ and ‘the cube root of 64 is 4’ – suggest perhaps that there was an essential difference, which is surely the kind of answer that Plato would have provided. Objects of belief are subject to change and might turn out to be false whereas objects of knowledge are not subject to change and are eternally true. However, the first exploration of this territory suggests something different. What a community regards as knowledge are merely those beliefs that are widely held and which have been held for a period of time. I know that is vague and evasive – I should have been a politician. It is the case that claims in some domains lend themselves to being well-established and upheld for long periods of time. Mathematics is one of those domains. Nonetheless, it would seem excessively narrow-minded to restrict knowledge to mathematics and similar domains. From a practical perspective, we are problem solvers. What we seek is knowledge that will enable us to solve problems. Over time, the set of problems we want to solve grows in size and complexity, so we need to be expanding our knowledge base all the time. Otherwise we grow stagnant – or, some might say that we simply become comfortable with our existence as it is. Perhaps the job of an educator is to make one uncomfortable with one’s existence. That is a different path to follow perhaps on another day.