6:36 - What is truth?
Many people think that truth is a single entity: everything can be compared with the single truth, and verified.
I disagree. Not only do I assume that truth is a multitude, I assume that different situations measures of truth can give different answers of whether something is true.
(Please note: I strongly believe that truth -- or truths -- exist. I just do not believe that when we talk about truth, we always mean the same system.)
Here's three examples of what I mean:
Mathematical Truth:
Truth in mathematics means that if a person accepts axioms A, B, and C , then they will accept theorems X, Y, and Z, they will reject theorems X', Y', and Z', and they will have nothing to say about theorem W.
The catch is the axioms. If you agree with them, then you can use the theorems. If you disagree with the axioms, then that branch of mathematics has nothing to say about truth. You have to decide whether the axioms apply.
(Hard) Science Truth:
Truth in science means that if every time that a specific situation occurs, then specific results will happen. The results might be probabilistic ("A 1g mass of uranium placed in front of a detector for x milliseconds has a 50% chance of setting off the detector") or descriptive ("When I put food in front of my dog, she eats 90% of the time.").
The catch is that the situation must be testable: it must be possible to re-witness the same situation.
Historical Truth:
Truth in history means that something happened.
The catch is that historical truth is difficult to prove. One can read records, ask people who were there, or examine physical evidence -- but very few historical events can be proven to have taken place.
These three kinds of truth are not the same.
Mathematical but not Scientific or Historical:
Many abstract forms of mathematics aren't related to science; they're studied for their own beauty. The situations never happen in reality, so they can't be observed even once.
Scientific but not Mathematical:
Some science is observational, not mathematical. Biology has many instances of this: mapping genes to their effects uses deep algorithms, but the resulting map hardly uses mathematics. (If you want the real difference between science and mathematics, learn the difference between inductive and deductive logic.)
Historical but not Scientific or Mathematical:
Any event that happens only once in history -- the crowning of a particular monarch, a battle of a war -- cannot be repeated. Therefore, it's not scientific. (And I have no idea how to link the Battle of Waterloo with axioms or theorems.)
Here's where I get controversial: I don't believe that I've listed all of the forms of truth.
Fiction, even fantasy, has its own truth. If the setting isn't consistent, if the characters don't act believably, then it rings false.
Music, also, has its own truth. Only a few patterns of sounds are music to our ears -- the rest is noise.
Finally, religion has its own truth. It has the power to move people to do great works, and to die for their beliefs. Denying its truth is to deny a large dimension of many people's lives.
What do you think? Take care, all.
This essay first appeared in Fluorescent Dreams Wax Cylinders. You may copy this essay, provided you also copy the link back to the original source. Fnord!
Music.. I'm not so sure. A pattern being appreciated is likely the result of physiology or upbringing. I happen to like clocks: does that make clocks into their own form of truth?
If the clock consistently gives the correct time, it does...
Being less flippant -- some forms of music seem to have more power than others. Why has the melody Greensleeves lasted for hundreds of years, while almost all others of that time period fallen away? Why does the music of Bach live on, while few of his contemporaries still are played?
some forms of music seem to have more power than others
Very much so. Some tunes cause shivers to run up and down my body. Does that make them a form of truth, though, or merely extremely pleasant and inspiring? Sensations need not be truths: I like red a lot, but red is not true.
(It is indeed an interesting question why certain pieces are carefully preserved by future generations; I'm just not convinced it has to do with any concept of truth.)
I'm sorry, but there is no way I can see "the stories religion tells people" as "truth." They're nice stories, but there's no reality to them. I find it sad when people choose to die for a story.
The human brain is wired for stories. Stories are immensely powerful things and it's not just cultural - words have great impact. To dismiss this is to ignore the underlying reasons for *why* people choose to die for a story.
I'd be inclined to divide the space up rather differently, according to where the truth comes from:
* mathematical proof
* observation and experiment (hard science, but only experimental results, not theory. Also historical information as obtained from archeology.)
* authority (most history and religion. Tends to be unreliable unless it can be cross-checked.)
* introspection (psychological truth -- you don't get to dispute my feelings, because I'm the only one who can observe them. This also covers the personal part of religion: prayer, meditation, and so on.)
* mapping (the correspondence between theory and observation, or between a description and our perceptions)
A lot of trouble is caused by using the same word to cover parts of two different categories.
I have trouble with this being called "truth." It's too fuzzy and unpredictable. In my opinion, that which we call "truth" should be reasonably predictable.
"Music, also, has its own truth. Only a few patterns of sounds are music to our ears -- the rest is noise."
That also varies from person to person. I find what others regard as street noise to have a beautiful quality of music. I also regard human speech as music. Every language has its own melody and rhythm. To me, that is a truth, albeit a subjective truth.
What you're describing as 'mathematical truth' is really 'logical truth' and specifically, you're describing a classic mistake a lot of people make: that being logically true makes something factually true. As you note, you can take any set of axioms and construct a valid logically sound statement - yet if the axioms are faulty, the conclusion is no less faulty for having been arrived at by logical process.
The difference between intuitive and intellectual is also very important. The scientific view tends to discount intuitive over intellectual because intuition can often leap over steps - it's often hard to describe logically. Yet as we're starting to learn, a lot of what we think is intellectual in actually intuitive first, then rationalised into something that is more intellectual.
Neural networks don't work by discrete logic.
An apple doesn't have truth. Saying, "The apple is red" is a statement of truth. If the apple is green, it's a statement of untruth. Music, religion, and fiction are imagination based on opinions of simple concepts such as sound, history, and ink on pages which only have truth at that level, or less, and only if we talk about them.
That being said, I made a related post in regards to this article not too long ago.
Edited at 2008-05-06 11:21 pm (UTC)
(Her neighbors have been complaining about that lately.)
well done
Some parts of music are purely social. For example, the twelve-tone scale is social: other cultures use different scales with different expressiveness. Our chord progressions define Western music -- many musical cultures have different ways to organize their music.
Other parts are ingrained to humanity and physics. I would be shocked if a musical culture did not use the octave as a consonance. I would be surprised if a musical culture didn't use drums, didn't use some kind of string, didn't use some kind of blown instrument, or didn't use voice.
Finally, some parts have aspects of both social and ingrained elements. 4/4 music is common throughout the world -- because it's simple. However, much music is written in other time signatures or even without time signatures.
Does that make sense?
You may be right about the octave. There just may some functions of acoustics and physics that are undeniable. But I would say they are a truth of sound rather than a truth about music. Do all cultures make use of the octave musically?
I'd be surprised -- creating a stringed instrument is so easy. (Making a GOOD stringed instrument and keeping it in tune is hard, but the basic idea of plucking a vine held taut is easy.) On the other hand, I am not an ethno-musicologist.
But I would say they are a truth of sound rather than a truth about music.
I think that music is a combination of the physical and the social. For example, making something vibrate at frequency x usually causes it to vibrate overtones at pitch 2x, 3x, and so forth.[*] That's a physical requirement.
Because overtones are inherent in most natural instruments[**], we accept them -- and build music from those overtones. For that reason, I would be surprised if a culture didn't make use of the octave (the first overtone).
Again, I'm not an ethno-musicologist. I was part of a musical group that heavily used the harmonic series to make instruments -- that's why I'm comfortable talking about this stuff.
Thanks for the great discussion!
[*] Closed pipes have overtones at 3x, 5x, and so forth. And two-dimensional vibrations -- like certain drums -- have other overtones.
[**] Wikipedia says that whistling, tuning forks, and rubbing your finger along the top of a crystal glass are nearly-pure sound waves without overtones.