lvc@cbscd5.UUCP (08/19/83)
Mr. Barzel: This letter was sent to you earlier via mail but I wasn't confident that you received it, so here goes again (slightly reworded). Thank you for taking the time to write about the laws of logic. I apologize for my delay in writing to you. I wanted to take the time necessary to give your letter the attention it merits. First let me say, *wow*! I wasn't aware that light behaved in such an unusual manner. Truth *is* stranger than fiction. 'And' is a word that must be used carefully. In your example, and in one I'll provide in a moment, 'and' is not the correct term one should be using. Here is my example that demonstrates this. Take a plane in 2-space, and three distinct lines A, B, C. Suppose that A and B are perpendicular; B and C are perpendicular. Then one might say incorrectly A and C are perpendicular! The problem is apparent if we instead say A is perpendicular to B, B is perpendic- ular to C. Logic does not force us to say A is perpendicular to C. We must investigate the properties of perpendicularity before any relationship between A and C can be established. Again let me emphasize 'and' is not being used as a logical connective in the first example but instead it establishes the relationship of perpendicularity. In the case of light passing through filters, the same problem appears. I don't know the proper terminology, if any exists, but I think there should be a clearer way to express how light behaves. The only other example of Knowledge I can think of now is mathematics. (lets refer to "Knowledge" as certain knowledge, and "knowledge" as uncertain knowledge for clarity, I also want to mention the terminology was invented by a friend of mine). I view logic in a hierarchy also. At the top are three principles that establish the rest. They are the law of identity, the law of noncon- tradiction, and the law of the excluded middle. These can be derived by considering what the nature of reality is. If one tries to think of alternatives to these it can easily (?) be seen that it is impossible. Logic shouldn't be taken on faith (although I know a lot of people that do). It is how the universe operates. If you would like to discuss the three principles mentioned in the previous paragraph in more detail feel free to write back. Larry Cipriani cbosgd!cbscd5!lvc