Faith, certainty, and reason
Sep. 15th, 2008 09:55 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mirrorshardThis is something I've had percolating for awhile, sparked off originally by a reader's letter in the Metro, which was (of course) batshit insane. It argued, as far as I can recall, that scientists were right in being more certain and dogmatic than religious leaders. (It isn't a matter of right or wrong; it's down to understanding where certainty comes from and why being certain about anything complicated makes you look like an idiot.)
Since then, I've had a few conversations which have brought new viewpoints to it, most of which ended up with an agreement that the axiom mismatch meant we weren't getting anywhere.
Of course, acknowledging that an axiom mismatch exists is the first important thing. One point which is commonly overlooked is that any system of thought is an artificial structure, erected within the extremely complicated perceptual universe that exists (FSVO, &c.) around us. It depends on context and axioms - the fundamental truths you need to take for granted in order for your system of thought to work. (Ref. Godel.) If you're going to shore up your belief system (your tools for understanding the universe) with hard-edged logic, then Godel's theorem applies; the mathematics are inexorable.
This structure (or scaffold) can be viewed two ways. The first is that it's a good and accurate tool, across the entire domain where the axioms are true. The classical example here is Newton's Laws of Motion. They are completely and exactly accurate for macroscopic objects; they break down and do not apply at very small scales. The problem is that your axioms may fail unexpectedly; the corollary of that is that any system of thought is i) only as strong as its weakest axiom, and ii) strong in inverse proportion to the number of axioms it requires.
The other way to look at it is as a model. (The money quote from there is from Eykhoff: a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form. The map is not the territory; the map is a simplified version of the territory that we can understand and manipulate.) Modelling is a really useful way to deal with the universe, but two things must be remembered: i) no model is complete, and ii) models fail by not taking things into account. So when a model attempts to predict things that are affected by a factor it doesn't consider, the results can become wildly divergent from reality just a short distance in phase space from places where they are effectively exact.
One interesting corollary of the model viewpoint is that you can tell how useful a given model is (ie. how close it is to reality) by looking at its complexity. A complex model of a complex system may not necessarily be accurate, since it might be built wrongly; but a simple model of a complex system will always be wrong.
If you believe that either your axioms are always and forever true, or that your model is complete, then you are no longer using any form of logic known to science and I don't really have anything to say on the subject; your belief is not disprovable. It's not even wrong.
This is one reason that scientists can come across as overly certain and dogmatic; it's because, given the boundaries of the domain they're working in, there is no other possible answer. It's like saying that 2 + 2 = 4; the way the question is phrased requires that there is only one answer. For scientists, the axioms and assumptions are implicit. If you find the arrogance offputting, try mentally appending "assuming the Earth doesn't turn into a very large haddock" to anything that looks like a flat statement of dogmatic certainty. Generally, a competent scientist or engineer will be very careful about their assumptions: 2 + 2 = 4 given nonweird mathematics, and "this bridge will not fall down within 25 years under normal load conditions".
There is, of course, a difference between those two statements; the first is interesting in some contexts, but is otherwise intellectual wankery. The second, if incorrect, kills people. If you bring out your assumptions in the open, and invite people to test them (to try and disprove them) then you reduce the chances people will be killed.
Religious statements about the nature of the universe and our relationship to it are sort of analogous, except that they generally try to hide the axioms & assumptions, and often get terribly upset when those are brought into question.
This is one reason I try and avoid making statements on religious grounds, or trying to affirm something religious; I don't have the degree of certainty necessary to make precise statements. It's like the magic image-enhancement software they use on CSI. I know that some actions have more beneficial results than others, and that some activities give me the peaceful, joyous feeling others have described as numinous or (in a Christian context) as indicating the presence of the Holy Spirit. I know that there is a common characteristic of good things and actions, which I'm comfortable terming "God".
Many religions (and non-religious belief systems) have advocated these actions, and described that feeling; I don't know enough to say that one is more accurate or somehow more correct than another. I consider myself Christian because it gives me a comfortable set of metaphors and a cultural vocabulary to talk about these things, and a Quaker partly for familial reasons and partly because the Society of Friends emphasises aspects of Christianity I find important and rejects some aspects I dislike. (I'll happily talk about those at more length another time, if anyone's interested.) I don't in any sense find truth in religion; I find ways to examine and talk about truth.
One of my sidebar quotations is from Niels Bohr - Never express yourself more clearly than you think. This shouldn't be taken as implying that if you don't have crystalline clarity and precision of thought, you are somehow lacking; the universe is not a clear or precise place. Every time we learn something new about it, and about ourselves, it gets less so. We have methods of dealing with chance and human foibles, but mostly things come down to modelling - to reducing the complexity of the physical, psychological, and social universe (at this point you can wave your hands around a bit and throw the word 'fractal' around, if you like) to something we can handle.
Since then, I've had a few conversations which have brought new viewpoints to it, most of which ended up with an agreement that the axiom mismatch meant we weren't getting anywhere.
Of course, acknowledging that an axiom mismatch exists is the first important thing. One point which is commonly overlooked is that any system of thought is an artificial structure, erected within the extremely complicated perceptual universe that exists (FSVO, &c.) around us. It depends on context and axioms - the fundamental truths you need to take for granted in order for your system of thought to work. (Ref. Godel.) If you're going to shore up your belief system (your tools for understanding the universe) with hard-edged logic, then Godel's theorem applies; the mathematics are inexorable.
This structure (or scaffold) can be viewed two ways. The first is that it's a good and accurate tool, across the entire domain where the axioms are true. The classical example here is Newton's Laws of Motion. They are completely and exactly accurate for macroscopic objects; they break down and do not apply at very small scales. The problem is that your axioms may fail unexpectedly; the corollary of that is that any system of thought is i) only as strong as its weakest axiom, and ii) strong in inverse proportion to the number of axioms it requires.
The other way to look at it is as a model. (The money quote from there is from Eykhoff: a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form. The map is not the territory; the map is a simplified version of the territory that we can understand and manipulate.) Modelling is a really useful way to deal with the universe, but two things must be remembered: i) no model is complete, and ii) models fail by not taking things into account. So when a model attempts to predict things that are affected by a factor it doesn't consider, the results can become wildly divergent from reality just a short distance in phase space from places where they are effectively exact.
One interesting corollary of the model viewpoint is that you can tell how useful a given model is (ie. how close it is to reality) by looking at its complexity. A complex model of a complex system may not necessarily be accurate, since it might be built wrongly; but a simple model of a complex system will always be wrong.
If you believe that either your axioms are always and forever true, or that your model is complete, then you are no longer using any form of logic known to science and I don't really have anything to say on the subject; your belief is not disprovable. It's not even wrong.
This is one reason that scientists can come across as overly certain and dogmatic; it's because, given the boundaries of the domain they're working in, there is no other possible answer. It's like saying that 2 + 2 = 4; the way the question is phrased requires that there is only one answer. For scientists, the axioms and assumptions are implicit. If you find the arrogance offputting, try mentally appending "assuming the Earth doesn't turn into a very large haddock" to anything that looks like a flat statement of dogmatic certainty. Generally, a competent scientist or engineer will be very careful about their assumptions: 2 + 2 = 4 given nonweird mathematics, and "this bridge will not fall down within 25 years under normal load conditions".
There is, of course, a difference between those two statements; the first is interesting in some contexts, but is otherwise intellectual wankery. The second, if incorrect, kills people. If you bring out your assumptions in the open, and invite people to test them (to try and disprove them) then you reduce the chances people will be killed.
Religious statements about the nature of the universe and our relationship to it are sort of analogous, except that they generally try to hide the axioms & assumptions, and often get terribly upset when those are brought into question.
This is one reason I try and avoid making statements on religious grounds, or trying to affirm something religious; I don't have the degree of certainty necessary to make precise statements. It's like the magic image-enhancement software they use on CSI. I know that some actions have more beneficial results than others, and that some activities give me the peaceful, joyous feeling others have described as numinous or (in a Christian context) as indicating the presence of the Holy Spirit. I know that there is a common characteristic of good things and actions, which I'm comfortable terming "God".
Many religions (and non-religious belief systems) have advocated these actions, and described that feeling; I don't know enough to say that one is more accurate or somehow more correct than another. I consider myself Christian because it gives me a comfortable set of metaphors and a cultural vocabulary to talk about these things, and a Quaker partly for familial reasons and partly because the Society of Friends emphasises aspects of Christianity I find important and rejects some aspects I dislike. (I'll happily talk about those at more length another time, if anyone's interested.) I don't in any sense find truth in religion; I find ways to examine and talk about truth.
One of my sidebar quotations is from Niels Bohr - Never express yourself more clearly than you think. This shouldn't be taken as implying that if you don't have crystalline clarity and precision of thought, you are somehow lacking; the universe is not a clear or precise place. Every time we learn something new about it, and about ourselves, it gets less so. We have methods of dealing with chance and human foibles, but mostly things come down to modelling - to reducing the complexity of the physical, psychological, and social universe (at this point you can wave your hands around a bit and throw the word 'fractal' around, if you like) to something we can handle.
