Responses 005 (2008) (Redux)
About seven months ago, I posted a response to a specific question about the nature of knowledge. Since then, the question has come back to life, and I've been asked whether that was my entire response.
Well, looking at it again, I still haven't found an area of knowledge that defines itself, in the strict sense of the term (but read through to the end of this post). Some people have said, well, what about set theory? Aren't some sets obviously self-defining? For example, certain numbers have certain properties (like being a prime number). Then the set of all prime numbers can be defined, and it is obviously a set of knowledge points. Prime numbers are THERE, they just need to be found.
Actually, that's true in some sort of way. Number properties, such as the inability to be divided exactly by any other number (except 1), are pre-existent in some sense. It's also true that some people have no concept of number in the first place. Is the concept of 'number' invented or discovered? This one's a hard thing to call, especially bearing in mind that the idea of 'nothing' is obviously pre-existent, and so is the idea of 'one thing' — after that, the concept of number is just adding onto that.
What about art? Are some things already beautiful (well, 'aesthetically pleasing' might be better) and waiting to be discovered as such? But the problem is, the set of things that are beautiful is not automatically and completely self-defining. There is always a bit of uncertainty at the edges, unlike with prime numbers. This means that an area of knowledge such as art or literature requires humans to define it, and hence is not pre-existent. It cannot be discovered, it can only be invented.
Some people say physics is like math and pre-existent. But the thing is that we create constructs to explain effects, and we work out formulae, but those formulae are our descriptions of replicable events, that's all. In fact, there are NO such things as replicable events in the sciences, although we try very hard to make them so because that would be ideal science. Science, therefore, consists of 'best guess' collation of results with an acceptable uncertainty built in. Because we like round numbers, if x is proportional to y^1.9999546, we would probably assume that it is actually y^2 and leave it at that. Science is a pure construct; it claims to discover, but it actually describes and explains in human terms.
Consider the discovery of penicillin as opposed to the invention of the telephone. The penicillium organism existed before we found it and used it; the telephone did not until we made one. But the decision to study the organism in certain ways and describe its behaviour in certain ways is an invention, not a discovery. So knowledge can be discovered, but an area of knowledge (in this case, antibiotics) must be invented.
Actually, the whole idea of 'discovering' an area of knowledge still seems spurious to me. It's like stumbling upon a layout for knowledge relationships that is automatic and complete without any human agency being involved. Even in biology (the area of knowledge concerning all living things), where you can argue that 'life' is a pre-existent defining focus, the point still remains that someone has to stand up and say, "Come, let's define an area of knowledge concerning all living things and call it 'biology'."
However, I've realised something. When we invent a machine, we do indeed discover an area of knowledge that is automatically implied by the existence of that machine. For example, you can't have computer science without computers. (And yes, you can't have zymurgy without having discovered brewer's yeast first.) But once you invent a computer, you automatically begin to discover the things a computer can do, the theories that govern information structuring and transfer based on the idea of digital computation and logic, and so on. The area is indeed self-defining even though the machine was invented...
Oooh. I have to go and think this through again...
Well, looking at it again, I still haven't found an area of knowledge that defines itself, in the strict sense of the term (but read through to the end of this post). Some people have said, well, what about set theory? Aren't some sets obviously self-defining? For example, certain numbers have certain properties (like being a prime number). Then the set of all prime numbers can be defined, and it is obviously a set of knowledge points. Prime numbers are THERE, they just need to be found.
Actually, that's true in some sort of way. Number properties, such as the inability to be divided exactly by any other number (except 1), are pre-existent in some sense. It's also true that some people have no concept of number in the first place. Is the concept of 'number' invented or discovered? This one's a hard thing to call, especially bearing in mind that the idea of 'nothing' is obviously pre-existent, and so is the idea of 'one thing' — after that, the concept of number is just adding onto that.
What about art? Are some things already beautiful (well, 'aesthetically pleasing' might be better) and waiting to be discovered as such? But the problem is, the set of things that are beautiful is not automatically and completely self-defining. There is always a bit of uncertainty at the edges, unlike with prime numbers. This means that an area of knowledge such as art or literature requires humans to define it, and hence is not pre-existent. It cannot be discovered, it can only be invented.
Some people say physics is like math and pre-existent. But the thing is that we create constructs to explain effects, and we work out formulae, but those formulae are our descriptions of replicable events, that's all. In fact, there are NO such things as replicable events in the sciences, although we try very hard to make them so because that would be ideal science. Science, therefore, consists of 'best guess' collation of results with an acceptable uncertainty built in. Because we like round numbers, if x is proportional to y^1.9999546, we would probably assume that it is actually y^2 and leave it at that. Science is a pure construct; it claims to discover, but it actually describes and explains in human terms.
Consider the discovery of penicillin as opposed to the invention of the telephone. The penicillium organism existed before we found it and used it; the telephone did not until we made one. But the decision to study the organism in certain ways and describe its behaviour in certain ways is an invention, not a discovery. So knowledge can be discovered, but an area of knowledge (in this case, antibiotics) must be invented.
Actually, the whole idea of 'discovering' an area of knowledge still seems spurious to me. It's like stumbling upon a layout for knowledge relationships that is automatic and complete without any human agency being involved. Even in biology (the area of knowledge concerning all living things), where you can argue that 'life' is a pre-existent defining focus, the point still remains that someone has to stand up and say, "Come, let's define an area of knowledge concerning all living things and call it 'biology'."
However, I've realised something. When we invent a machine, we do indeed discover an area of knowledge that is automatically implied by the existence of that machine. For example, you can't have computer science without computers. (And yes, you can't have zymurgy without having discovered brewer's yeast first.) But once you invent a computer, you automatically begin to discover the things a computer can do, the theories that govern information structuring and transfer based on the idea of digital computation and logic, and so on. The area is indeed self-defining even though the machine was invented...
Oooh. I have to go and think this through again...
Labels: Discovery, Epistemology, Invention, Knowledge
etched with acid at 8:29:00 pm
2 Comments:
Would Godel's Incompleteness Theorem have any impact on this? Since you raised the question of sets... Or would the AOK exclude those undefinable statements or something (or just take it in stride and kind of gloss it over, i dunno o.O)
Hmm. Interesting question; but to apply Gödel's Incompleteness Theorem you'd have to think about how it applies by analogy to any area of knowledge that invokes discrete elements.
You can't, of course, apply it to things like art and history, except by straining the analogy into some sort of outré metaphor.
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