Thursday, February 17, 2011

axioms of ideas

A while back I thought of this idea that is somewhere between math and philosophy. The goal was to mimic geometry but apply the rules to ideas instead. So, in geometry they have points, I thought in my system I would have ideas like big, small, loud, inside, outside, etc as "points". In geometry the second thing they have is lines made up of points. In my system I have comparisons as "lines". An example line in geometry might be said to be "drawn" between two points. In mine, I "draw" a comparison between two ideas. Like "big is to loud". This compares big and loud. In geometry they have circles, in mine I have concepts. A concept encompasses several ideas, more general concepts include more ideas. The word encompasses is even similar to that in geometry of drawing a circle with a compass to include points on the inside. Also in geometry they have an axiom about parallel lines, remember in mine a line was a comparison like "big is to loud", so a pair of parallel comparisons becomes an analogy... "big is to loud as small is to quiet". If you took the SAT's this might look familiar. An analogy is a correlation between two comparisons... correlation in Latin literally means "running alongside" the way two parallel lines run alongside one another.
So to recap:

1. Ideas = points
2. Comparisons = lines
3. Concepts = circles
4. Analogies = pairs of parallel lines
Now for the more mathematical bit I need to set up the definitions formally the same way they do with geometry.

On Wikipedia it gives these as Euclid's axioms:
Let the following be postulated:
1. to draw a straight line from any point to any point.
2.To produce [extend] a finite straight line continuously in a straight line.
3.To describe a circle with any center and distance [radius].
4.That all right angles are equal to one another.
5.The parallel postulate: That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if                   produced indefinitely, meet on that side on which are the angles less than the two right angles.

And these are the ones I made with the words in bold above instead of the elements of geometry.
let the following be postulated:
1. to draw a comparison from any idea to any other idea
2. to extend a comparison continuously through more and more ideas
3. To describe a concept with any idea as it's center and to the increasingly more general (including more ideas)
4. That all orthogonal comparisons are orthogonal in the same way    (More on this below)
5. For every comparison there is an analogy, the second comparison not including elements of the first

Ok, so I've made a geometry with different words than they used in the original, right?

An extended comparison is comparing even more ideas such as "big is to loud is to bright" (this could go on and on)

A pair of orthogonal comparisons is like "big is to loud" and "big is to wet" They're orthogonal in the sense that they both include the same point: {"big"}, and "loud" and "wet" are as different from one another as they can be without being closer to opposites.  This visual for this is "big is to loud" and "big is to wet" are like perpendicular lines that both start at the word "big".

The notion of parallel relates to analogous comparisons like this one "soft is to hard as inside is to outside" This is an analogy relating opposites, but "inside" might be on the extended comparison "inside is to core is to brain"(things within other things) and "soft" on the extended comparison "soft is to dim is to quiet"(matters of degree) and the two extended comparisons not share any ideas in common.

Upshot

So anyway the idea is that having defined these axioms in the same way as the ones for geometry, any proof in geometry will apply to these axioms of thought as well.

Conclusion:
The cool thing is that I made a system for the words: ideas, comparisons, concepts, and analogies that is exactly the same as the system for geometry using the words: points, lines, circles, and parallel lines, everything that has been proven in geometry over the centuries is instantly known about this new topic as well.

The best part was the funny way the words for the geometrical ideas were always very fitting to the way I had my system worded. Like a comparison is "drawn" between two ideas and a line is "drawn" between two points...every single word I used in mine was like that... Like people were thinking about ideas geometrically already but hadn't put it all together.

Words and People

It seems to me that trying to describe another person with words either in your mind or to another person always amounts to an oversimplification or an over generalization. I feel pretty cynically about the reason people attempt it at all. Also, I'll discuss why I think words are not the tool that philosophy seems convinced that they are.
People are always talking about other people; sometimes in a positive light, sometimes a negative one, but that's not what I'm focusing on today. What I want to talk about is my idea that no matter how many words one uses, even a whole book of words, or how well chosen they are, they are going to fall way short of giving an adequate explanation of any human being. I think it's worthwhile to keep in mind that no matter how much you hear about someone, all that's been said relates to the person the same way that a drawing of the person relates to the person. There are some major differences, the person is flesh and blood the drawing is ink or whatever on paper. Also, it's a special faculty of the mind that enables a person to look at such a drawing and relate it to the person being depicted, and it's also a peculiar faculty of the mind to think that words about a person relate to the person being described. My point is that this faculty relating the abstract to the real works quite a bit too well a lot of times.
I mentioned that I feel cynical about the reason people abstract away from the actual complexity of the person and deal with the abstraction in their mind as if it were the actual person. I think first and foremost people like to operate as if they know enough about things that are unknowable. I think really this is probably practical for the inquisitive human brain not being able to know something would be like an itch that could never be scratched. And also people oversimplify the person they're thinking about's attributes so they can attempt to make informed decisions as to whether they should associate with the other person and social things like that. Which is born of a certain practicality as well, but I feel that except in the most extreme cases the oversimplification of the person doesn't relate to the actual person well enough to be able to make that informed decision that they want to make. It's the best way people have of sorting through and acting on their social life so we can't abandon it, but my point is just that I think people should be aware of how faulty the process is. Some people are very confident in their correct judgement of other people and I think that the best judgement possible is going to be way off.
The next thing is sort of tangentially related is what I see as the folly of philosophy. In the case of philosophy people are arguing about ideas with words. Now as impossible as it is to describe a person with words, a concept is not even something you can interact with in the real world. I mean if there were such a thing as more impossible that would be what philosophy tries to do with words. I love words, but describing ultimate reality with them is like trying to build a bridge out of spaghetti. As great as spaghetti is it's probably not useful in that way. I still think philosophy is fun and interesting just I wish they wouldn't get so upset with each other when they disagree, I mean, realistically, they probably aren't even talking about the same thing! Like if they are discussing transcendental reality or some phrase like that, what happens in each one's brain when they hear those words is likely completely different, and trying to sort that out with words is futile, something that can be fun but shouldn't be taken seriously.