Tuesday, November 13, 2012

Responses 002 (May 2013)

The second question in the list is this:
"Only seeing general patterns can give us knowledge. Only seeing particular examples can give us understanding." To what extent do you agree with these assertions?
It's an odd question, and it hinges a lot on the way we define knowledge and understanding. One way to approach it, therefore, is to begin with such definitions.

Knowledge is plausibly defined as information given a context. This allows us to separate it from understanding, which we can then define as awareness of that context and the significance or usefulness of knowledge within that context.

Here's an example. Consider the mathematical equations of a straight-line graph. They all take the form y = mx + c, and we're taught that m is the gradient of the line and c is the y-coordinate when x = 0 (the y-intercept). We can solve linear equations without seeing a graph at all, and our solutions would be correct; they would be valid and reliable, and people would say we knew how to solve linear equations. However, it would be difficult to explain the concept of a linear equation (why 'linear', for a start) or a gradient (what is a 'slope'?) unless you gave an example, preferably of graphic nature.

Understanding, therefore, includes the ability to explain something. It could also include the ability to make something that can be explained. And it is probably demonstrated best when we manipulate things such that people can figure out what we did, and how we did it, and how we justify what was done.

In a sense, understanding is the outgrowth of knowledge, just as a specific example is the outgrowth of a general pattern. But that's only one side of the argument.

You'll probably recall that this kind of reasoning, from the general to the specific, is called deduction. One of the problems with deduction is that you have to assume that the general rule or pattern is true. If it isn't, then seeing particular examples and linking them to the false general pattern gives us false understanding.

But if we are inductive thinkers, then seeing particular examples gives us knowledge of individual cases, and we can use those to build general patterns. Inductive thinking is the opposite of deductive thinking in that sense — and understanding will come when the general pattern appears from our knowledge of individual cases.

And that's the other side of the argument, for which I shall not provide examples because that would make it too easy for you.

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