Monday, January 05, 2009
Try to make a website/journal/document collection with all of my knowledge. Arrange it so I can find the connections and missing pieces.
This is about my search for certainty. I need certainty and it is driving me to attempt to understand “reality” as well as I possibly can.
A human’s ability to understand, have certainty, or to know, is limited by:
1. Our sensory organs (the input devices)
2. Our capacity for calculation–we cannot know the entire universe unless we are the size and age of the universe
3. Our ability to measure–We might have the ability to sense something or calculate something, but we might not be in a position to measure it. Is it too far away? Is it too difficult to separate the thing we want to measure from the background noise? Also, the uncertainty principle.
Is thinking a form of sensory input like smell or taste?
All human knowledge must be imperfect (or said differently, it lacks perfect precision) because of the limitations above. To be “certain” of some idea is not to precisely understand the entire idea–because this is impossible. Instead, “certainty” is about the proper degree of imprecision or about the proper expression of probability. When one says, “I am certain that I exist,” for example, it is properly imprecise: the statement does not try to define “I” or “existence” in a precise way. Those two ideas are vaguely expressed–because we are not certain of the precise parameters of “I” nor of “existence.
The original statement “I am certain that I exist” is true because some of the terms in the statement (“I” and “existence”) lack precision. The second way to be certain about an idea is to express it in probabilistic terms. Most probabilistic expressions are implied in the statement. One can be certain in the statement “The sun will rise tomorrow” not because it is certain that the earth will continue to rotate on its axis and orbit the sun. Within the statement “The sun will rise tomorrow” are many implied caveats: the sun will rise tomorrow unless the earth explodes; the sun will rise tomorrow unless an alien life form uses its technology to completely stop the fusion reactions of the sun. One cannot be 100% certain that the sun will rise tomorrow, but one can be certain that the most likely occurrence tomorrow is that the sun will rise–and implicitly express the probabilities that it will not rise. Take another example, “I will go to your house tomorrow.” One can be certain of the statement because there are many implied caveats. There is a 99% chance I will go to your house tomorrow because it is unlikely something will prevent me from going to your house. Because the statement is probabilistic, we can be certain of the statement.
Arrangement of the knowledge
It is not a hierarchy because there are likely multiple axioms. And even if there are not multiple axioms, some derived statements will combine to produce other derived statements. Expression of non-hierarchical and non-linear knowledge is difficult, however, because writing is linear (it must follow the time dimension). I think it might be useful to arrange the knowledge as a numbered list anyway. If there is more than one axiom (I observe myself thinking, therefore I am and there must be something called existence), then level zero could contain the axiomatic statements. The remaining numbered levels could be divided into convenient sections that only draw on ideas already derived (or proved).
Descartes implies that all knowledge must come from reason. I am not sure this is true. The axiom, I observe myself thinking therefore I exist and there is an existence, is not purely the result of reason. It is largely the result of observation.
Is it possible to have certainty that is founded on uncertain knowledge? For example, we are not certain of the fabric of the universe–is it quarks, energy, strings, or something else?–but we seem to be certain that gold is gold and that water is made of hydrogen and oxygen. If we construct a set of rules that we are not certain about (e.g., rules of chemistry and physics) make a prediction based on the rules, and then verify that our prediction is true, can we be certain of something? Either the rules or the outcome? So, if we say that putting salt in water will lower the temperature at which the water freezes, and then we experiment and measure and observe, are we “certain” of any part of this knowledge? We don’t really know what salt is, or water, or a solid, or time, or temperature: but can we say that we know for certain that salt water has a lower freezing temperature than water alone? Yes, because certainty is expressed in imprecise or probabilistic terms. When we say that salt water has a different freezing point, we are saying that it is 99.99% likely to be true. Even if we don’t understand all of the rules that affect the result, we have observed the result enough times to achieve some certainty. This suggests that most certainty comes from a reason-based induction from observation–and not from a deductive process from a small set of axioms.
1. I observe myself thinking therefore I exist and there is an existence
2. This can only be true if existence and non-existence are mutually exclusive, therefore some rules of logic must be true
3. Rules of logic are true independent of my existence (is that true?), therefore something exists besides myself
4. The act of observing (myself thinking) validated my existence, therefore observing (also called sensing) is sometimes a valid method to obtain knowledge and certainty
5. Combine logic and observation to validate most of our derived knowledge (also called scientific knowledge)