On Categories of Knowledge

It seems to me that there are many different things we can mean when we say that a person knows something. Allow me to illustrate with a hypothetical:

Let us say that I am taking a geography test, the subject of which is “The Countries of the World.” Consider two scenarios:

  • In the first scenario, I am given a list of words. The words contain two subsets: countries of the world, and non-countries. For example, “Zambia, Washington, Thailand, Candyland.” I am tasked with circling the countries of the world in the list, without circling any of the non-countries.
  • In the second scenario, I am prompted to write down the name of every country of the world.

Someone who successfully completes either of these tasks will be said to “know the countries of the world.” However, I believe most of us would agree that the second task is much more difficult than the first. For example, in scenario one, when presented with such abstruse examples as “Dominica,” “Timor-Leste,” or “Brunei,” it is possible that I will be prompted to remember that these are indeed countries, perhaps because I remember reading newspaper articles about them. However, without the prompt, I may not remember to include them in my list of the countries of the world.

In case you were wondering










If the degree of difficulty is so different, how can the same verb be used to describe the mental process that occurs in each of these examples? And if the mental process is different, how so? If I cannot recall “Timor-Leste” is a country until I am prompted–but can correctly identify it when asked, “is Timor-Leste a country?”–then do I know Timor-Leste is a country?

In the first case, you are presented with a prompt. You apprehend a mental object. You are looking for countries. In other words, you are trying to determine whether a mental object fits into a mental category. In order to see how this is done, let’s consider how this works with other objects and categories. If I present you with a fruit and ask you, “is this an orange?” you will compare the object in front of you with your memories of prior objects categorized as “orange.” In most instances, you will proceed by “cluster definition, which can be described mathematically. Let us say an orange is made up by various parameters, such that it can be described as a linear combination. For an orange (y), these parameters might be size (x1), color (x2), and texture (x3), each of which has an a-value. For example, a1 for size might approach 0 as size shrinks. Thus, you can think of an orange as:

y = a1x1 + a2x2 + a3x3

More importantly for our purposes, you can find the range of a-values for each parameter for the set of all known oranges. (For example, color might vary from yellow-green to deep orange, quantified, of course.) All subsequent items whose parameters each fall within the range for the known set of oranges will be identified as oranges.

There is an obvious problem with this theory; it adequately describes how we identify whether newly apprehended items belong to a class we already have information about, but it does not describe at all how we describe the process by which we establish that two items initially belong to the same set. It also fails to account for the obvious possibility that we may encounter a bigger orange than we have ever seen before (or smaller, or more orange, or smoother, etc). Clearly we have set ourselves a difficult task, because it is in the growth of novel categories that we acquire the most of our knowledge, and that is the sector we have just admitted our theory cannot account for.

That is where I will leave off for now.





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