Axioms
A couple of young fresh-faced smiling missionaries knocked on my door the other day, wanting to know if I read the bible. I turned them away – but tried to be nice about it. I’m not sure why, since I actually enjoy having conversations about fundamental issues. Superficially I suppose I thought I was too busy. But I really wasn’t. I was recuperating from a vacation and taking a day off to get over my jet lag. A more plausible reason is that I knew a discussion wouldn’t get us anywhere. Having thought about this sort of stuff (whatever it is) for decades, I’m pretty confident of my basic principles and I suspect so are they – and our agreement on basic assumptions would be pretty small. On the other hand, by having discussions with persons we disagree with, we get the opportunity to probe and refine our own thinking in ways we can’t do well alone, even if nobody’s mind gets changed about anything.
When I talk to such folks I sometimes find that they claim that they take the bible literally. As a theoretical physicist, I have some sympathy for the idea that our thinking can be much improved by not treating life as just a collection of snippets of knowledge we have come to know; that placing some “stakes in the ground” – some organizing principles that we choose to trust under a wide variety of circumstances – helps us to “get things right” more often, not to be led astray by little bits of knowledge that might be more complex and less straightforward than we realize.
But what should we choose as our holdfasts? The principles of physics I was implicitly thinking of in the above paragraph organize limited realms of knowledge – Newton’s laws, the Schrödinger equation, quantum field theory. Further, I’m used to thinking of those principles as both really, really good, but also temporary and local. Newton’s laws of classical physics are not superceded by the laws of quantum physics or relativity, but learning quantum physics and relativity helps us understand the boundaries of applicability of Newton’s laws. We have both a stability in knowing the places where the laws work and to what accuracy, and a flexibility in knowing that new places might be found where new laws have to be generated. These are not our basic principle – our axioms. Axioms are starting points for reasoning: principles we take as true because they are “self-evident” to everybody. Well, we now know better. Even some of Euclid’s axioms about geometry are now known to be (useful) approximations to the physical world rather than exact. Even in the abstract unphysical world of mathematics we know we have a choice of axioms for geometry.
Identifying axioms may help us understand the extent that people have irretrievable philosophical differences and where they might be able to seek out common truths in systems that appear at first to be fundamentally at odds. Let’s explore the nature of our axioms and in particular, let’s contrast the difference in the approach to axioms in the religious and scientific communities.
Religious fundamentalists want to take as an axiom that the bible is literally true – to be taken as the direct word of god. This seems strange and untenable to me. I’ve read at least the Judeo-Christian bible and have even read much of Genesis in the original Hebrew. My reaction is, “that can’t be right.” The first problem occurs right away. We’re all supposed to be descended from Adam and Eve. Cain and Abel didn’t make it to be ancestors, so we all get to descend from Seth, Adam and Eve’s other son. But who was Seth’s wife? If you start from only a single pair there has to be incest to get you started – Eve as mother for a few generations and sisters marrying brothers. That’s creepy and you don’t hear it talked about much by the fundamentalists. But even worse, that assumption makes a firm prediction – one the authors of the bible clearly did not know they were making. If all men are directly descended from Adam we should all have the same Y chromosome. If all women are directly descended from Eve they should all have the same X chromosome – and we should all have identical mitochondria. If we don’t (and we don’t) then there has to have been enough time from Adam and Eve for those genetic patterns to drift a lot – and that would imply a much too rapid rate of evolutionary change. Given what we now know about the human genome, the slow rate of evolutionary change is actually far more problematic for young-earth-bible-literalists than it is for old-earth-scientific-evolutionalists.
The only way I see of getting around this is by inventing lots of creation stuff that is not in the bible. Once you accept the incompleteness (or inconsistency) of the bible as literal truth in one place, it seems to me very hard to identify it as a basic principle.
So if I’m not willing to accept either the bible or Newton’s laws as “basic principles that underlie all knowledge”, what do I have as my epistemological axioms, the things that I accept as being fundamental to deciding what I, as a scientific rationalist, think I know?
Let’s see if I can “open the hood” of my thinking and clarify what goes on.
I suppose my first and simplest axiom is:
Axiom 1: There is a real world that exists independent of human observation.
This one seems to me a very good bet. Especially as we learn more and more about the size and extent of the universe around us. We are a very, very small part of it. It seems to me incredibly arrogant to assume that we are the whole point of the universe. Of course, there could be another universe that has some other point and we could be living in “The Matrix” – a universe constructed just for us – but this seems to me not to be a useful assumption, at least right now. Some scientists think that the laws of quantum physics require “an observer” and therefore we are essential to reality; but given my axiom 1, I find this very hard to take seriously.
So I answer the question, “if a tree falls in the forest does it make a sound?” by “yes it does” without any hesitation. Of course you have to decide what you mean by “sound”; if you mean something that is heard by an observer, then the answer is no. But if you mean something that produces the physical oscillations that we take to be “sound” then I say yes. Why would you tie an observer to sound more tightly than you do to vision? This is like asking, “if no one is there to see a rock is it invisible?” The both seem to me to be silly questions if you accept Axiom 1. (Of course, in philosophy a lot of why you might want to discuss such a question is to question the validity of axiom 1.)
Axiom 2: We each live in our own virtual reality, which is an approximation to the real world, not identical with it.
This one also seems incontrovertible. Each of us only has a limited set of information about the real world that we collect through our sensory apparatus – eyes, ears, skin. We assemble that data to create a model of the real world that we live in.
One bit of evidence for this is that through the process of science we have discovered many, many things that are undetectable to us directly through our senses. These can have great importance to our lives and kill us or save us – things ranging from bacteria and asteroids, from UV-light and x-rays to atoms and chemistry. A second bit of evidence is that psychological research has demonstrated very clearly how the brain assembles an internal version the real world – and have created strikingly powerful illusions show how we often get it wrong. Two of my favorites are Ed Adelson’s checkershadow, and Daniel Simon’s Invisible Gorilla.
So Axiom 1 says reality exists, axiom 2 says we can’t know it very well by direct observation. Axiom 3 holds out the hope that we can know it better by working together and trying to figure it out using the best tools we’ve got.
Axiom 3: Science is possible.
What I mean here by “Science” is a community activity addressed at finding out more about reality through observation and attempting to build coherent descriptions of what we see. The nature of this activity is complex and not easily described by a “scientific method” of a few steps. The critical point is that although we may use a theoretical framework to guide our observations and predictions, at base science is fundamentally empirical: built on our observations of what actually happens and our ability to weave an increasingly consistent story about how things are, behave, and work from fewer and fewer principles. I’ll write again later about my view about the nature of scientific activity and the lemmas that tell me when I define something as “science” and when not.
These aren’t so radical. Reality exists; we don’t see it directly; but we can figure it out if we’re careful. Even at this simple level I butt heads against some of the fundamentalists who want to say, “this is not the real world – what’s real is what we will experience after death.” Others will accept my 3 axioms but not the way I think I should apply them. But there is another fundamental difference between me and many religiously-based thinkers. We both believe that we need to develop a broadly accepted code of human behavior. How are we to know right from wrong? Where is the “good”? For them, it must arise from axioms. For me, the axioms are about finding out what “is”. What “should be” must be consistent with what is. IMHO, separating these two is an essential first step
When I talk to such folks I sometimes find that they claim that they take the bible literally. As a theoretical physicist, I have some sympathy for the idea that our thinking can be much improved by not treating life as just a collection of snippets of knowledge we have come to know; that placing some “stakes in the ground” – some organizing principles that we choose to trust under a wide variety of circumstances – helps us to “get things right” more often, not to be led astray by little bits of knowledge that might be more complex and less straightforward than we realize.
But what should we choose as our holdfasts? The principles of physics I was implicitly thinking of in the above paragraph organize limited realms of knowledge – Newton’s laws, the Schrödinger equation, quantum field theory. Further, I’m used to thinking of those principles as both really, really good, but also temporary and local. Newton’s laws of classical physics are not superceded by the laws of quantum physics or relativity, but learning quantum physics and relativity helps us understand the boundaries of applicability of Newton’s laws. We have both a stability in knowing the places where the laws work and to what accuracy, and a flexibility in knowing that new places might be found where new laws have to be generated. These are not our basic principle – our axioms. Axioms are starting points for reasoning: principles we take as true because they are “self-evident” to everybody. Well, we now know better. Even some of Euclid’s axioms about geometry are now known to be (useful) approximations to the physical world rather than exact. Even in the abstract unphysical world of mathematics we know we have a choice of axioms for geometry.
Identifying axioms may help us understand the extent that people have irretrievable philosophical differences and where they might be able to seek out common truths in systems that appear at first to be fundamentally at odds. Let’s explore the nature of our axioms and in particular, let’s contrast the difference in the approach to axioms in the religious and scientific communities.
Religious fundamentalists want to take as an axiom that the bible is literally true – to be taken as the direct word of god. This seems strange and untenable to me. I’ve read at least the Judeo-Christian bible and have even read much of Genesis in the original Hebrew. My reaction is, “that can’t be right.” The first problem occurs right away. We’re all supposed to be descended from Adam and Eve. Cain and Abel didn’t make it to be ancestors, so we all get to descend from Seth, Adam and Eve’s other son. But who was Seth’s wife? If you start from only a single pair there has to be incest to get you started – Eve as mother for a few generations and sisters marrying brothers. That’s creepy and you don’t hear it talked about much by the fundamentalists. But even worse, that assumption makes a firm prediction – one the authors of the bible clearly did not know they were making. If all men are directly descended from Adam we should all have the same Y chromosome. If all women are directly descended from Eve they should all have the same X chromosome – and we should all have identical mitochondria. If we don’t (and we don’t) then there has to have been enough time from Adam and Eve for those genetic patterns to drift a lot – and that would imply a much too rapid rate of evolutionary change. Given what we now know about the human genome, the slow rate of evolutionary change is actually far more problematic for young-earth-bible-literalists than it is for old-earth-scientific-evolutionalists.
The only way I see of getting around this is by inventing lots of creation stuff that is not in the bible. Once you accept the incompleteness (or inconsistency) of the bible as literal truth in one place, it seems to me very hard to identify it as a basic principle.
So if I’m not willing to accept either the bible or Newton’s laws as “basic principles that underlie all knowledge”, what do I have as my epistemological axioms, the things that I accept as being fundamental to deciding what I, as a scientific rationalist, think I know?
Let’s see if I can “open the hood” of my thinking and clarify what goes on.
I suppose my first and simplest axiom is:
Axiom 1: There is a real world that exists independent of human observation.
This one seems to me a very good bet. Especially as we learn more and more about the size and extent of the universe around us. We are a very, very small part of it. It seems to me incredibly arrogant to assume that we are the whole point of the universe. Of course, there could be another universe that has some other point and we could be living in “The Matrix” – a universe constructed just for us – but this seems to me not to be a useful assumption, at least right now. Some scientists think that the laws of quantum physics require “an observer” and therefore we are essential to reality; but given my axiom 1, I find this very hard to take seriously.
So I answer the question, “if a tree falls in the forest does it make a sound?” by “yes it does” without any hesitation. Of course you have to decide what you mean by “sound”; if you mean something that is heard by an observer, then the answer is no. But if you mean something that produces the physical oscillations that we take to be “sound” then I say yes. Why would you tie an observer to sound more tightly than you do to vision? This is like asking, “if no one is there to see a rock is it invisible?” The both seem to me to be silly questions if you accept Axiom 1. (Of course, in philosophy a lot of why you might want to discuss such a question is to question the validity of axiom 1.)
Axiom 2: We each live in our own virtual reality, which is an approximation to the real world, not identical with it.
This one also seems incontrovertible. Each of us only has a limited set of information about the real world that we collect through our sensory apparatus – eyes, ears, skin. We assemble that data to create a model of the real world that we live in.
One bit of evidence for this is that through the process of science we have discovered many, many things that are undetectable to us directly through our senses. These can have great importance to our lives and kill us or save us – things ranging from bacteria and asteroids, from UV-light and x-rays to atoms and chemistry. A second bit of evidence is that psychological research has demonstrated very clearly how the brain assembles an internal version the real world – and have created strikingly powerful illusions show how we often get it wrong. Two of my favorites are Ed Adelson’s checkershadow, and Daniel Simon’s Invisible Gorilla.
So Axiom 1 says reality exists, axiom 2 says we can’t know it very well by direct observation. Axiom 3 holds out the hope that we can know it better by working together and trying to figure it out using the best tools we’ve got.
Axiom 3: Science is possible.
What I mean here by “Science” is a community activity addressed at finding out more about reality through observation and attempting to build coherent descriptions of what we see. The nature of this activity is complex and not easily described by a “scientific method” of a few steps. The critical point is that although we may use a theoretical framework to guide our observations and predictions, at base science is fundamentally empirical: built on our observations of what actually happens and our ability to weave an increasingly consistent story about how things are, behave, and work from fewer and fewer principles. I’ll write again later about my view about the nature of scientific activity and the lemmas that tell me when I define something as “science” and when not.
These aren’t so radical. Reality exists; we don’t see it directly; but we can figure it out if we’re careful. Even at this simple level I butt heads against some of the fundamentalists who want to say, “this is not the real world – what’s real is what we will experience after death.” Others will accept my 3 axioms but not the way I think I should apply them. But there is another fundamental difference between me and many religiously-based thinkers. We both believe that we need to develop a broadly accepted code of human behavior. How are we to know right from wrong? Where is the “good”? For them, it must arise from axioms. For me, the axioms are about finding out what “is”. What “should be” must be consistent with what is. IMHO, separating these two is an essential first step
posted by An Unabashed Academic at
9:25 AM
2 Comments:
I, too, recently had a visit from a couple of missionaries. I, too, agree that there is no chance that I will change to their world view nor any chance that I will help them see reality.
However, a visit from missionaries as an opportunity to conduct outreach. As a member of a minority religion, I use opportunity to educate the missionaries about my religion and to give them a good taste of Judaism.
Specifically, I wanted the missionaries to walk away with the belief that
1) Jews are friendly,
2) Judaism is fun, and
3) You can come to opposite conclusions from a literal interpretation of the Bible.
To be friendly, it can be nothing more than asking what they would like to drink on a hot day.
To be fun, I asked if they would like to hear the sounds that Joshua made and whether they, too, would like to play a shofar.
To convey the opposite literal Biblical interpretation, I talk about the binding of Isaac. Traditional Judaism teaches that the binding of Isaac is a test of Abraham that Abraham failed. The fact that Abraham was willing to murder his child is proof that Abraham was unworthy of future leadership role and, thus, Abraham disappears from the narrative after this event. Future leadership in the narrative rests with those who are willing to wrestle with or to argue with God and angels.
It is always good to wrestle with difficult ideas.
By
mlf, at 10:44 AM
We would love to hear more posts
(or is it to read more posts)
(or see more posts)
(or experience)
By
Anonymous, at 10:48 AM
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