Explanation on Reduction…

Estudia: Okay, Phi’, you were about to explain to me the need for reduction based on the fact that knowledge is hierarchical. Go ahead, please.

Philo: Well, think about this. If you always first gained knowledge of things directly by observation and were very clear about those things in reality; then if you moved to a higher level concept while you retained a clear understanding of the lower level, you would be growing your understanding hierarchically. The fact of hierarchy would not be a problem for you. You could not use a higher-level concept without understanding its relationship to perceptual reality. Your new higher-level concepts, ideas and conclusions would be grounded in perceptual reality and hence would never be what we call floating abstractions.

Estudia: If I thought like that, I would have a chain of concepts in my mind that would connect every higher-level concept with the sensory data that was the first link in the conceptualization. Sure, I see that.

Philo: Good. But you must realize that people in general try to use higher-level concepts without understanding completely the intermediate steps.

Estudia: Why do they do that?

Philo: Well, there are several reasons. Impatience, aversion to effort ― they just don’t want to work at understanding the material, or even just simple error. One biggie for many is that they want to use what someone else has come up with or concluded. Other people’s ideas are just used without understanding the chain of concepts that led to the idea. You use a higher-level concept without fully understanding it and consequently you are a little confused, but you build on the idea anyway. You become more and more confused because the chain of knowledge is broken and the concept is not tired to perceptual reality. You are not grounded in your thinking and only accidentally will you wind up producing actual new knowledge or understanding that is factual.

Estudia: So what’s with the ideal of reduction?

Philo: We saw that we have to keep our ideas in context to connect them to reality, right?

Estudia: Right. And I can see that if the context is hierarchical, each level of structure serves as a connecting link. Oh!! That means that in order to keep things in context, we have to identify and remember each connecting link, right?

Philo: Exactly. This is why reduction is required. You have to be able to work in reverse order. From the higher-level concept you should be able go backwards to the step that logically led to the idea from perceptual reality.

Estudia: Ah! So we integrated concepts to move up the chain, and now we disintegrate or rather reduce them to move down the chain.

Philo: Yes. Reduction is the process of identifying the logical sequence of steps that relates a thought to perceptual data. This doesn’t mean you have to retrace the exact steps, but you must retrace the concepts with essentially the same logical structure.. It is the only way to remain objective. Your only direct contact with reality is through the data provided to you by your senses. The sense data is the standard of objectivity and all other concepts, thoughts, ideas, images, i.e. all cognitive material must be grounded in the data of the senses.

Estudia: Can you give me an example?

Philo: That’s your job. Think about this and see if you can take a higher-level concept and reduce it to its perceptual foundation.

Estudia: Hmmm. Okay. Right now?

Philo: No, next time.

Reducing Integration…

Estudia: Okay, Phi’, how are we going to relate the issues of context and hierarchy?

Philo: Well, first remember that knowledge is hierarchical. If you were able to comprehend any and every concept or conclusion just by observation ― by looking at things in reality ― then you wouldn’t have to worry about the order of ideas. Everything would just be observable and some accumulation of primary entities. But things aren’t that simple. Concepts are different from each other in one very important respect.

Estudia: What’s that?

Philo: You tell me. Remember some items can be understood from simple sense perception. Colors, smells, tastes, and so on come immediately to mind. Other things, like furniture or government, can only be understood by understanding a whole host of things. You have to first grasp a continuous chain of concepts from the simplest to more and more complex with each link of the chain dependent on the one before it.

Estudia: Oh, I see what you mean. Concepts differ in how far removed they are from the perceptual level. Some are simple sense experiences but most are more complex.

Philo: Right. In some instances the nature of your senses determines the hierarchy. Like things you can see and observe come before things you can only see through a microscope, or things you can only detect with some measuring instrument.

Estudia: Well that means that knowledge has to follow some order. We have to understand things like “cat”, “dog”, “cow” and more before we can conceptualize “animal”.

Philo: But notice that it doesn’t matter if you used “goat”, “zebra” or “elephant” to form the concept animal. A higher-level concept depends on you grasping a series of simpler concepts; however, the series is not unique. There is no hierarchy when there is an option like this. Hierarchy applies when there is not an option. Hierarchy applies to a concept when the only way to reach that concept is through some understanding of simpler concepts.

Estudia: Kind of like a prerequisite.

Philo: Exactly. Understanding the simpler concepts is a prerequisite to understanding the higher level concept.

Estudia: Certainly applies to most course work in college. You are not going to understand Calculus without some knowledge of arithmetic and geometry.

Philo: Right on. Now this brings us to your original question. We can relate context and hierarchy together. You see, a hierarchy is a kind of context. We discussed the contextual view of knowledge and said that your thinking is relational. You have to keep things in context.

Estudia: Right. So?

Philo: The hierarchical nature of knowledge tells us that our thinking is relational. This hierarchical view tells us that every item or concept has a context that is built in a logical fashion from a foundation of first-level items. Context says that the things we know are a sum of items. Hierarchy says that the way we learned about our concepts was by necessarily starting with the simpler ideas and moving to the more complex.

Estudia: Hmmm. Okay. The idea of context takes the big view. What we know is a sum. The idea of hierarchy takes a look at the way something is learned and concludes that the simple ideas make the more complex ideas possible. So what?

Philo: So what? Well, it makes a big difference. This all says that to gain knowledge you have to integrate ideas into your already existing knowledge. Knowledge we said is contextual. This means you have to integrate new knowledge into your existing knowledge very carefully..

Estudia: That’s pretty obvious to me now. The need for integration is why it is so difficult for me to keep all this in mind. I’m learning all sorts of new concepts and reaching all sorts of conclusions that have to be consistent with what I know or I have to change what I know to fit the new facts. What about the hierarchical nature of knowledge? What does that imply we have to do to gain knowledge?

Philo: Reduction.

Estudia: Reduction? What’s that?

Philo: Let me explain next time we get together.

Estudia: Fine, I need a break. See you later.