Coursework Title 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?

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THEORY OF KNOWLEDGE

"ONLY SEEING GENERAL PATTERNS CAN GIVE US KNOWLEDGE. O NLY SEEING PARTICULAR

EXAMPLES CAN GIVE US UNDERSTANDING." TO WHAT EXTENT DO YOU AGREE WITH THESE

ASSERTIONS?

May 2013

Theory of Knowledge Essay - Question Number 2

Word Count: 1571

Open any textbook. Chances are whether explaining Pythagoras' theorem, investigating

genetic inheritance or introducing the effects of the business cycle on unemployment and

inflation the author will provide a general rule or pattern (to be learned) followed by specific

examples (to help explain and understand). What can we learn from general rules and what

can we learn from examples? It is said that "Only seeing general patterns can give us

knowledge. Only seeing particular examples can give us understanding." It is important to

distinguish the meanings and implications of two key words: 'knowledge' and

'understanding' (because the statement impties the two concepts bold different values) in

different areas of knowledge such as Mathematics, human sciences (particularly Economics)

and natural sciences (particularly Biology). How do ideas of patterns and examples tie in to

ideas of reason and perception in the search of knowledge and understanding? Patterns may

give us knowledge and examples may help us understand but more importantly neither

knowledge nor understanding exist in isolation.

A knower will find the claim wrought with issues when attempting simply to define the words

and differences between 'knowledge ' and 'understanding'. The most famous definition of

knowledge is certainly Plato's idea of a 'justified, true belief' (Steup, 2012). Let us say, for

the purpose of this essay, that knowledge is an ensemble of information with which the

knower is acquainted and that he deems to be true on the basis of some or other f01m of

justification. Such information is obtained through education and experiences and can teach

us useful skills in the acquisition and use of facts. What is interesting about the knowledge

clain1 here, is that it makes a clear distinction between Knowledge and Understanding not

only in their nature but also in how a knower comes by them. N emirow ( 1995) raises some

interesting questions as to the relationship between knowing and understanding. He outlines

three possibilities when he asks, "Is understanding related to knowing? Is understanding itself

?

a kind of knowing? Is it a precondition of knowing?" (P. 28). If the two concepts are related,

as I will argue they are, this makes it very difficult to isolate the two completely as has been

attempted through the repetition of the word 'only' in the original claim. Nemirow continues

to give a defmition of understanding as "to be able to implement or apply a rule." (P. 28).

This definition would seem to comply with the suggestion that understanding relates to

specific examples (those instances for which the rule is applied) but rules relate to knowledge

in general. Nevertheless we seem to be dealing with two concepts that are related. An idea

also picked up on by Downie (1962) who writes that if a person understands, " It is plausible

to claim that this is because he has been given information which enables him to connect the

matter with his existing knowledge." (P. 237). Downie and Nemirow both suggest that

understanding is to do with relating a piece of infonnation, or a single application of a rule to

a general pattern in the knower's existing knowledge. As of yet, the terms 'knowledge' and

'understanding' do remain distinct from one another, but let us continue to analyse their

relationship in terms of some concrete examples from my own education.

Let us begin by discussing how our argument applies in the domain of Mathematics.

Mathematics is often suggested to be an area of knowledge dominated by reason as a way of

justifying a knower's claims. It also aims to be a domain free from the uncertainties

encountered in other areas of knowledge. From the point of view of our discussion,

Mathematics is interesting because it works abundantly with the discussion of general patterns

and makes them into theorems, or rules. Knowledge of such rules should, then, allow a

knower to solve problems through the application of general rules to specific examples. Our

knowledge claim would suggest that these examples are what gives the mathematician

understanding of the rules in use. Skemp (1976) however suggests that understanding in

Mathematics is more complicated than that. He argues that there are two kinds of

mathematical understanding: instrumental and relational. A, basic, instrumental understanding

allows the learner to apply rules and get correct answers but does not require a true insight

into the process behind or reason for doing so. A fuller, relational understanding requires the

knower to be able to explain the purpose for doing so as well as the theory behind the rules.

As such, in Skemp's view, it is impossible to fully understand (at least in a relational way)

through individual examples without a full grasp of the general, underlying pattern. This

suggests that it simply is not possible to isolate the effects of ' only seeing specific examples'

or 'only seeing general patterns ' . This impossibility represents a significant issue with the

knowledge claim.

As we move away from pure Mathematics into the realm of sciences, the 'general patterns '

that we encounter will become increasingly challenged by uncertainty. Reason alone is no

longer the source of our knowledge. Perception of experiments gives us results from which

we draw conclusions. This means that we derive general patterns from an investigation of

specific examples. In the natural sciences, patterns are often problematic as they become

unsure whether they are modelling our perception of how things really work, or how reason

dictates they should work in some fictional, ideal scenario. Despite such rules being derived

from and proved by examples, as a student of natural sciences, I have had the experience of

seeing such patterns, and understanding the claims they are making without needing to see the

examples they were derived from. When I first learned about the Pmmett Square in Genetics,

an abstract diagram using only the letters A and B, to represent any possible characteristic,

was enough for me to understand how to apply this to any particular example. Through one

general pattern, I was able to understand, as well as know, one of the dominating theorems of

genetic inheritance. Let us go back to Skemp's (1976) theory of types of understanding

Mathematics and see how it applies here. Although one general pattern gave me a sufficient

understanding of how to use Punnett Squares to answer exam questions, simply looking at

this general rule hasn' t given me the kind of relational understanding that means I could fully

describe the science behind Genetics. Nemirow (1995) draws a link between "the abilities

required for understanding" and the knower' s "insights into the essence of things" (P. 30). In

this example then, it would seem that I knew the rule from only seeing a general pattern but

that I might have needed specific examples to gain a relational understanding. However I may

believe the rule, the mle may even be true, but I will argue that is was not fully justified if I

did not have the relational understanding to justify it (I took the knowledge on authority

alone). This would suggest again, that knowledge and understanding come together, and that

neither will be complete only seeing rules or only seeing examples.

Now let us take a step further into uncertainty, movmg from the natural to the human

sciences. As the common Economics witticism goes "if all economists were laid end to end,

they would not reach a conclusion" (George Bernard Shaw, in Baumol, 2005, P. 169). In this

area of knowledge it is even harder to purely rationalize perception of events into one

provable theorem. As a result, the general patterns observed in human sciences tend to be split

theorists in multiple directions. We get conflicting claims about patterns, each catering to

different specific events. What is interesting about this is that a longstanding general pattern,

often one that had come to be accepted as a mle, can be challenged by a single specific event,

which stands out. Keynes observed a pattern known as the Business Cycle (Ramirez, 1990),

which dictated fluctuations in inflation and employment as the GDP grows. A pattern like this

just makes sense to me, I considered myself to know and understand without the need for

examples. However, what is interesting about the Business Cycle is that is was called into

question by Stagflation in the 1970s where a pattern of low growth and inflation emerged

which was unexplained by Keynesian theory. (Blanchard, 2000). Although it seemed that a

pattern alone was enough to gtve both knowledge and understanding it only took one

abnormal example in changing our understanding or even calling the knowledge claim into

question. Failure to take into account such an important example would have led economists

to believe a justified fallacy, and the knowledge they drew from a pattern alone would be

false.

In conclusion, having acquaintance with a pattern or rule, whether or not this is fully

understood, is often enough to make valid knowledge claims. Similarly, observing specific

examples can help us understand these claims in a fully ' relational' way. However, my issue

with the claim that "Only seeing general patterns can give us knowledge. Only seeing

particular examples can give us understanding." essentially comes from the word 'only' .

Observations of the relationship between my own knowledge and understanding in

Mathematics, human sciences and natural sciences, would suggest that it is not valuable to

treat knowledge or understanding in isolation. However a knower goes about acquiring

knowledge/understanding (be it through patterns or examples) is unimportant if the

coexistence of these characteristics is ignored.

Works Cited:

Baumol, W (2005) Errors: Consequences of Big Mistakes in the Natural and Social Sciences. Social Research. Vol. 72, No. l. PP. 169-194.

Blanchard (2000) Macroeconomics. Pearson: London.

Downie, D . (1962) Knowledge and Understanding. Mind, New Series, Vol. 71 , No. 282. PP. 237-240.

Nemirow, L. (1995) Understanding Rules. The Journal ofPhilosophy, Vol. 92, No.1. PP. 28-43.

Ramirez, M (1990) Keynes, Marx and the Business Cycle. Eastern Economic Journal. Vol. 16, No.2. PP. 159-167.

Skemp, R. (l976)Relational Understanding and Instrumental Understanding Mathematics Teaching. Vol. 7, No.7. PP. 20-22.

Steup, M. (2012) Epistemology, The Stanford Encyclopedia of Philosophy. Zalta, E (eds). http://plato.stanford.edu/archives/fall20 12/entries/epistemology (Dec 20 12).

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