Many cosmological arguments (not all) argue that everything that begins to exist must have a cause -- this is basically the principle of causality. But this chain of causality cannot be extended infinitely into the past for two reasons: 1) an infinite amount cannot exist in reality; therefore there must be a first cause that by definition is not the effect of a previous cause itself. 2) We have empirical evidence that the universe itself began to exist (Big Bang cosmology) and is therefore finite; therefore there must be something that exists independently of the universe that brought it into existence. In both cases we end up with something that sounds an awful lot like God.
The objection of some atheists is to ask, "Well then who created God? If everything requires a cause, then God would require a cause too right?"
The response to this should be obvious. Cosmological arguments do not claim that everything that exists requires a cause because there's simply nothing about sheer existence that would require a cause. What philosophers have claimed is that everything that begins to exist requires a cause. It's the "beginning" part that brings causality into play, not the "existing" part. So when we say that "Being does not arise from non-being," the focus is not on the "being" but on the "arising"; it's the latter that necessitates a cause, not the former.
The objection may then be put the other way around: "If God doesn't require a cause, why does the universe? Why couldn't the universe be this first cause?" Again, the response should be obvious: because it began to exist. That's the argument. Of course, you could claim that the argument fails or present an argument of your own that the universe didn't really begin to exist. But to simply say, "Well if God doesn't require a cause, why does the universe?" just ignores the argument that has been presented. It certainly doesn't answer it.
Thus, this objection is a complete straw man. It's a misstatement of the claims being made, a misstatement made in order to raise a bogus objection to certain cosmological arguments. The fact that otherwise brilliant people (such as Bertrand Russell) think this is a good objection only demonstrates that they didn't even hear the argument in the first place.
The reason "Who then created God?" is not a good objection is because the cosmological argument already addresses that issue. The whole point of these arguments is that there must be a cause that is not an effect of a previous cause itself. To ask why this first cause is this way is to ignore the argument that has just been made that this first cause is this way. Of course, showing that something is the case is not the same thing as showing why it is the case. (I would argue that one can answer the "why" question, but that's another issue.) But the atheist is claiming -- at least with this objection -- that unless the argument proves why something is the case, it doesn't prove that it's the case. This is obviously false.
So, for example, I could say that the ratio of a circle's circumference to its diameter equals pi (in Euclidean space). I could then prove this mathematically. The atheist objection would be "Why should this ratio equal pi?" The answer would be, "It does. Here's the proof again." The atheist would then object "Your mathematical proof doesn't explain why this ratio equals pi." And again, the answer would be, "It does equal pi. Here's the proof again." "But why should it be this way?" "It is this way. Here's the proof again." Etc. It reminds me of a Calvin and Hobbes cartoon where Calvin balks at his math homework. You put two numbers together and they magically become some third number. No one can say how or why it happens, you just have to accept it on faith. "As a math atheist, I should be excused from this."
So when an atheist asks why God should be excused from having to have a cause, the answer is simply to repeat the argument, which (allegedly) demonstrates that there must be a first cause that does not have a cause itself. Perhaps the argument fails to demonstrate this, but the objection that God would then require a cause doesn't even address it.
Thursday, October 29, 2009
Monday, October 26, 2009
Pre-Darwinian Evolution
Humphrey has a great post up on creationism and evolution. One of his points is something that I've mentioned on this blog before: the doctrine of rationes seminales. This was a position that apparently originated with the ancient Stoics and was picked up by many Christian writers. The idea, at least as the Christians understood it, is that God created the world in seed-form, or with certain potentialities, which then developed or unfolded accordingly. Obviously this is very similar to evolution. Rationes seminales was accepted by such ancient and medieval Christian writers as Athenagoras, Tertullian, Gregory of Nyssa, Augustine, Bonaventure, Albertus Magnus, and Roger Bacon. Since such Christian luminaries accepted that the world and its elements developed over time, it becomes obvious that evolution is not at all incompatible with Christianity.
Another point I've made before is something C. S. Lewis brings up in his book The Discarded Image and some essays like "The Funeral of a Great Myth." Lewis argues that, prior to Darwin, there was widespread belief in a sort of developmentalism, according to which the universe and life in particular were progressively becoming "better." Wagner's Ring Cycle is an example of this. This view permeated 18th and 19th century culture, so that when the theory of evolution came along, it was perceived by many as proof of it (although, obviously, this view -- as well as that of rationes seminales -- is teleological whereas Darwinian evolution is not). This developmentalism didn't have a specifically Christian connotation to it, as it tended to disparage the ancients and medievals as intellectually inferior. Lewis's point is that evolution wasn't accepted in Western society purely because of the scientific evidence for it, but because it accorded with the already accepted view of progress or improvement. He doesn't intend this to challenge the validity of evolution, but simply to point out that there was more in play than scientific evidence.
Another point I've made before is something C. S. Lewis brings up in his book The Discarded Image and some essays like "The Funeral of a Great Myth." Lewis argues that, prior to Darwin, there was widespread belief in a sort of developmentalism, according to which the universe and life in particular were progressively becoming "better." Wagner's Ring Cycle is an example of this. This view permeated 18th and 19th century culture, so that when the theory of evolution came along, it was perceived by many as proof of it (although, obviously, this view -- as well as that of rationes seminales -- is teleological whereas Darwinian evolution is not). This developmentalism didn't have a specifically Christian connotation to it, as it tended to disparage the ancients and medievals as intellectually inferior. Lewis's point is that evolution wasn't accepted in Western society purely because of the scientific evidence for it, but because it accorded with the already accepted view of progress or improvement. He doesn't intend this to challenge the validity of evolution, but simply to point out that there was more in play than scientific evidence.
Monday, September 21, 2009
Infinite Amounts
Many cosmological arguments, in trying to show that the universe is contingent, argue that an actual infinite amount of something is metaphysically impossible, and so could not occur in reality. As such, there could not have been an infinite regress of events or an infinite chain of cause and effect. There must be a stopping point where a cause is not an effect of a cause itself, but is pure cause, not contingent on anything else. "And this all men call God."
The impossibility of an actual infinite has been defended in the last few decades by William Lane Craig, in his book The Kalām Cosmological Argument, his general apologetics book Reasonable Faith, and numerous philosophical articles, some of which were republished in Theism, Atheism, and Big Bang Cosmology, a book he co-wrote with atheist philosopher Quentin Smith. Most of this post is just paraphrases of Craig’s writings. In Reasonable Faith, Craig points out that there is a distinction between an actual infinite and a potential infinite.
In other words, an infinite amount of defined units is an actual infinite. An “infinitieth” of something is not a defined unit, so this is a potential infinite. An actual infinite is usually signified by aleph-null, but I can’t figure out how to type that in blogger, so I’ll just use ∞ instead, even though it usually represents indefiniteness rather than infinitude.
While actual infinites are used in conceptual mathematics they do not have any corresponding reality.
1. The most famous illustration of this is Hilbert’s Hotel (named after mathematician David Hilbert). Imagine a hotel with two wings that stretch out infinitely in opposite directions and which therefore contain an infinite number of rooms, and imagine that they are all occupied, that is, the hotel is completely full. Somebody shows up and asks for a room. In a finite hotel the proprietor would have to turn him away, but in an infinite hotel the proprietor could just move the person in room 1 to room 2, the person in room 2 to room 3, the person in room 3 to room 4, etc. Now room 1 is open and the person can check in. But the hotel was already full. Each room was occupied. Moreover, the same number of people are in the hotel even though no one has left and there is one more person than before. This is true for any finite number: if a million new people checked in, you could just move the person in room 1 to room 1,000,001, etc.
A friend of mine once suggested that if the hotel is infinite, then there would be no outside for someone to come in from. This is incorrect. We can easily imagine that the hotel extends infinitely in two directions along a street or something. Someone on the other side of the street (perhaps in the infinite restaurant) could then cross the street and check in.
2. But what if an infinite amount of people come to check in? Does the proprietor tell them that the hotel is full and turn them away? No, he just moves the person in room 1 to room 2, the person in room 2 to room 4, the person in room 3 to room 6, etc., moving each person to the room number double their previous number. He thus empties all the odd numbered rooms and the infinite number of new guests can check in. But before they came, each room was occupied. And again, there are the same number of guests as before, even though the proprietor just increased his occupancy by an infinite amount. And he can do this again and again, in fact infinitely many times, and there would never be one more person in the hotel.
3. Another illustration would be a bookcase with an infinite number of books. If you took seven books off the shelf there would be an empty space where they had been. But there’s still an infinite amount of books left, so therefore the bookshelf is still completely full with no empty spaces.
4. Conversely, if you took out all of the books but seven, you would have taken an infinite amount of books off the shelf. However, if you took an infinite amount of books off the shelf, it would be completely empty; but it’s not, there are seven left.
5. Now what if you took out every other book? That would leave a space between each remaining book. Although you took away an infinite number of books, there’s still an infinite number of books remaining, since there’s an infinite amount of odd numbers and an infinite amount of even numbers. The absurdity of this last example can be realized by imagining that you take the first book and push it up against the third book, so there isn’t a space between them any more. Then push these two books up against the fifth, and all of these against the next one, etc. Then there will be an infinite amount of empty space on the bookshelf (from the infinite number of books taken off it), so it’s necessarily empty. But there are still an infinite number of books left on the shelf. As such, it’s necessarily full. But if the bookshelf is full, the first book would be where it’s always been, even though you just moved it. The bookcase is simultaneously completely empty and completely full. When you look at this bookcase, what would you see?
Obviously, Hilbert’s Hotel and a bookcase like this could not exist in reality. Yet, if an actual infinite amount could exist, they could exist as well. Arguments 1-5 can be reduced to the following mathematical equations (where X and Y are actual amounts, that is, any number greater than zero):
Note also that 4 and 5 contradict each other: infinity minus itself equals both infinity and an actual amount.
A friend of mine once complained about these arguments by saying that when I add to or subtract from infinity I was treating it like an amount, and this is invalid. That is precisely the point: an amount, by definition, can be added to or subtracted from. Since we cannot do this with infinity, there cannot be an actual infinite amount of defined units. These arguments simply demonstrate this. As Craig writes,
Some might object that God is often referred to as infinite. Doesn’t this disprove God’s existence since an actual infinite can’t exist? It does not for the following reason: what makes an actual infinite impossible is that it consists of an infinite amount of units or members (like books or hotel rooms). God is not “made up” of any amount of units. In saying that God is infinite, we are saying he is unlimited by anything. Since God does not consist of a bunch of units, the argument against an actual infinite amount of units existing does not apply to him.
The impossibility of an actual infinite has been defended in the last few decades by William Lane Craig, in his book The Kalām Cosmological Argument, his general apologetics book Reasonable Faith, and numerous philosophical articles, some of which were republished in Theism, Atheism, and Big Bang Cosmology, a book he co-wrote with atheist philosopher Quentin Smith. Most of this post is just paraphrases of Craig’s writings. In Reasonable Faith, Craig points out that there is a distinction between an actual infinite and a potential infinite.
A potential infinite is a collection that is increasing toward infinity as a limit but never gets there. Such a collection is really indefinite, not infinite. For example, any finite distance can be subdivided into potentially infinitely many parts. You can just keep on dividing parts in half forever, but you will never arrive at an actual ‘infinitieth’ division or come up with an actually infinite number of parts. By contrast, an actual infinite is a collection in which the number of members really is infinite. The collection is not growing toward infinity; it is infinite, it is ‘complete.’
In other words, an infinite amount of defined units is an actual infinite. An “infinitieth” of something is not a defined unit, so this is a potential infinite. An actual infinite is usually signified by aleph-null, but I can’t figure out how to type that in blogger, so I’ll just use ∞ instead, even though it usually represents indefiniteness rather than infinitude.
While actual infinites are used in conceptual mathematics they do not have any corresponding reality.
1. The most famous illustration of this is Hilbert’s Hotel (named after mathematician David Hilbert). Imagine a hotel with two wings that stretch out infinitely in opposite directions and which therefore contain an infinite number of rooms, and imagine that they are all occupied, that is, the hotel is completely full. Somebody shows up and asks for a room. In a finite hotel the proprietor would have to turn him away, but in an infinite hotel the proprietor could just move the person in room 1 to room 2, the person in room 2 to room 3, the person in room 3 to room 4, etc. Now room 1 is open and the person can check in. But the hotel was already full. Each room was occupied. Moreover, the same number of people are in the hotel even though no one has left and there is one more person than before. This is true for any finite number: if a million new people checked in, you could just move the person in room 1 to room 1,000,001, etc.
A friend of mine once suggested that if the hotel is infinite, then there would be no outside for someone to come in from. This is incorrect. We can easily imagine that the hotel extends infinitely in two directions along a street or something. Someone on the other side of the street (perhaps in the infinite restaurant) could then cross the street and check in.
2. But what if an infinite amount of people come to check in? Does the proprietor tell them that the hotel is full and turn them away? No, he just moves the person in room 1 to room 2, the person in room 2 to room 4, the person in room 3 to room 6, etc., moving each person to the room number double their previous number. He thus empties all the odd numbered rooms and the infinite number of new guests can check in. But before they came, each room was occupied. And again, there are the same number of guests as before, even though the proprietor just increased his occupancy by an infinite amount. And he can do this again and again, in fact infinitely many times, and there would never be one more person in the hotel.
3. Another illustration would be a bookcase with an infinite number of books. If you took seven books off the shelf there would be an empty space where they had been. But there’s still an infinite amount of books left, so therefore the bookshelf is still completely full with no empty spaces.
4. Conversely, if you took out all of the books but seven, you would have taken an infinite amount of books off the shelf. However, if you took an infinite amount of books off the shelf, it would be completely empty; but it’s not, there are seven left.
5. Now what if you took out every other book? That would leave a space between each remaining book. Although you took away an infinite number of books, there’s still an infinite number of books remaining, since there’s an infinite amount of odd numbers and an infinite amount of even numbers. The absurdity of this last example can be realized by imagining that you take the first book and push it up against the third book, so there isn’t a space between them any more. Then push these two books up against the fifth, and all of these against the next one, etc. Then there will be an infinite amount of empty space on the bookshelf (from the infinite number of books taken off it), so it’s necessarily empty. But there are still an infinite number of books left on the shelf. As such, it’s necessarily full. But if the bookshelf is full, the first book would be where it’s always been, even though you just moved it. The bookcase is simultaneously completely empty and completely full. When you look at this bookcase, what would you see?
Obviously, Hilbert’s Hotel and a bookcase like this could not exist in reality. Yet, if an actual infinite amount could exist, they could exist as well. Arguments 1-5 can be reduced to the following mathematical equations (where X and Y are actual amounts, that is, any number greater than zero):
1. X + Y ≠ X but ∞ + Y = ∞
2. X + X ≠ X but ∞ + ∞ = ∞
3. X - Y ≠ X but ∞ - Y = ∞
4. X - X = 0 but ∞ - ∞ = Y
5. X - X ≠ X but ∞ - ∞ = ∞
Note also that 4 and 5 contradict each other: infinity minus itself equals both infinity and an actual amount.
A friend of mine once complained about these arguments by saying that when I add to or subtract from infinity I was treating it like an amount, and this is invalid. That is precisely the point: an amount, by definition, can be added to or subtracted from. Since we cannot do this with infinity, there cannot be an actual infinite amount of defined units. These arguments simply demonstrate this. As Craig writes,
There is simply no way to avoid these absurdities once we admit the possibility of the existence of an actual infinite. Students sometimes react to such absurdities as Hilbert’s Hotel by saying that we really don’t understand the nature of infinity and, hence, these absurdities result. But this attitude is simply mistaken. Infinite set theory is a highly developed and well-understood branch of mathematics, so that these absurdities result precisely because we do understand the notion of a collection with an actually infinite number of members.
Some might object that God is often referred to as infinite. Doesn’t this disprove God’s existence since an actual infinite can’t exist? It does not for the following reason: what makes an actual infinite impossible is that it consists of an infinite amount of units or members (like books or hotel rooms). God is not “made up” of any amount of units. In saying that God is infinite, we are saying he is unlimited by anything. Since God does not consist of a bunch of units, the argument against an actual infinite amount of units existing does not apply to him.
Tuesday, August 11, 2009
Size Doesn't Matter (thank God), part 3
(See also part 1 and part 2)
In this series I am contesting the claim that the unimaginable vastness of the universe, revealed to us in modern astronomy, makes it absurd to ascribe any significance to the earth and its inhabitants. In part 1 I addressed the science side of this claim and in part 2 I addressed the historical side. Ignoring the issues already discussed, this claim assumes that the relative sizes of the earth and the universe demonstrate that the former must be, somehow, insignificant or unimportant. Apparently, on some level, we instinctively equate size with value or significance. The original meaning of the word "great" is "very large", a phenomenon that occurs in many languages. "Bigger" just means "better."
But to take this as an ontological statement about something's actual importance is incredibly naïve. Just because bigger sometimes seems better, it's absurd to think that there is a significant correlation between size and value. What exactly is it about size that would bestow value anyway? Why would a smaller thing automatically be less important than a bigger thing? While it's true that the immense size of the universe can make us feel insignificant, this is a psychological fact about us, not a scientific fact about the universe. For people who accuse others of simple-mindedness, those who argue that the universe's size demonstrates our unimportance are remarkably simple minded themselves.
C. S. Lewis puts this so much better than I ever could that I'll just refer you to the 7th chapter of Miracles:
It reminds me of Jodie Foster's comment at the end of Contact (I don't know if it's present in the novel by Carl Sagan): if we're the only living creatures in the universe, it seems like an awful waste of space. But as Victor Reppert writes, "It is not as if energy or time [or space] is a scarce resource for God and we have to ask him, if he seems to be ‘wasting’ it, why he isn't putting it to better use. ‘Waste’ is an issue only where there is scarcity."
A similar objection that I mentioned in part 1 needs further comment. I pointed out that the universe's mass density -- the amount of matter in the universe -- must be extremely fine-tuned. Otherwise, the universe's expansion would have precluded the possibility of life existing anywhere at any time in the universe's history. In other words, the universe must be the particular size it is in order for us to exist. However, one could point out that while this matter may have been necessary at the universe's inception, it seems gratuitous for it to still be here. To insist that this vast universe is all there for our sake seems absurd. Every piece of matter may have had some relevance to the universe's initial expansion billions of years ago, but there is no obvious connection between distant pieces of matter and the human race's present existence. There are plenty of galaxies billions of light years away, which have plenty of planets orbiting plenty of suns. What does a particular rock on one of these planets have to do with life on earth now? The absence of such a connection makes humanity appear irrelevant to the universe.
Ignoring my previous response, this objection assumes that life or the human race is the only possible reason why the Judeo-Christian God would have created the universe. But just because all this matter has no relevance to humanity's existence today, it does not mean that God does not delight in it for some other reason, and so sustains it in existence. Again, this point is made best by C. S. Lewis:
A final point: in order to assert that the premoderns thought that the earth's size somehow rendered its inhabitants significant, it would require us to believe (at least) that they thought the earth and its inhabitants significant. In order for the statement, "they believed X because of Y" to be true, it has to be true that "they believed X." The argument that they thought the earth's size bequeathed significance on humanity can't even get off the ground unless they thought humanity had significance.
But this is not the case. We've already mentioned one criterion: brightness. The earth was thought to be less important and valuable than the celestial objects because they were bright while the earth was not. Another criterion that's often misunderstood is the earth's location at the center of the universe. This is usually twisted to imply that the center was the place of prestige, but the exact opposite is the case. They thought Earth was located at the bottom of the universe, which, in their view, was the least prestigious place therein. And the further down you went, the worse it was; this is why hell was thought to be at the center of the earth, and Satan at the center of hell. Arthur Lovejoy, in The Great Chain of Being, wrote that the medieval model is better described as "diabolocentric" than "geocentric." See the essays by Dennis Danielson on this.
However, one might object that Christianity conceives human beings as being so significant that God chose to be incarnated as one to die on their behalf. But this misunderstands exactly what the Christian claim is.
In other words, whatever significance or value human beings have is derivative. The moral law tells us that people do have an inherent value; the reason murder is wrong, for example, is because each individual is of infinite worth. But the reason each individual is of infinite worth is because he/she is created in God's image. And the reason God loves us is not because we are lovely or lovable, but because he is loving; indeed, the claim is that God is love itself.
In this series I am contesting the claim that the unimaginable vastness of the universe, revealed to us in modern astronomy, makes it absurd to ascribe any significance to the earth and its inhabitants. In part 1 I addressed the science side of this claim and in part 2 I addressed the historical side. Ignoring the issues already discussed, this claim assumes that the relative sizes of the earth and the universe demonstrate that the former must be, somehow, insignificant or unimportant. Apparently, on some level, we instinctively equate size with value or significance. The original meaning of the word "great" is "very large", a phenomenon that occurs in many languages. "Bigger" just means "better."
But to take this as an ontological statement about something's actual importance is incredibly naïve. Just because bigger sometimes seems better, it's absurd to think that there is a significant correlation between size and value. What exactly is it about size that would bestow value anyway? Why would a smaller thing automatically be less important than a bigger thing? While it's true that the immense size of the universe can make us feel insignificant, this is a psychological fact about us, not a scientific fact about the universe. For people who accuse others of simple-mindedness, those who argue that the universe's size demonstrates our unimportance are remarkably simple minded themselves.
C. S. Lewis puts this so much better than I ever could that I'll just refer you to the 7th chapter of Miracles:
There is no doubt that we all feel the incongruity of supposing, say, that the planet Earth might be more important than the Great Nebula in Andromeda. On the other hand, we are all equally certain that only a lunatic would think a man six-feet high necessarily more important than a man five-feet high, or a horse necessarily more important than a man, or a man's legs than his brain. In other words this supposed ratio of size to importance feels plausible only when one of the sizes involved is very great. And that betrays the true basis of this type of thought. When a relation is perceived by Reason, it is perceived to hold good universally. If our Reason told us that size was proportional to importance, the small differences in size would be accompanied by small differences in importance just as surely as great differences in size were accompanied by great differences in importance. Your six-foot man would have to be slightly more valuable than the man of five feet, and your leg slightly more important than your brain -- which everyone knows to be nonsense. The conclusion is inevitable: the importance we attach to great differences of size is an affair not of reason but of emotion -- of that peculiar emotion which superiorities in size begin to produce in us only after a certain point of absolute size has been reached.
We are inveterate poets. When a quantity is very great we cease to regard it as a mere quantity. Our imaginations awake. Instead of mere quantity, we now have a quality -- the Sublime. But for this, the merely arithmetical greatness of the Galaxy would be no more impressive than the figures in an account book. To a mind which did not share our emotions and lacked our imaginative energies, the argument against Christianity from the size of the universe would be simply unintelligible. It is therefore from ourselves that the material universe derives its power to overawe us. Men of sensibility look up on the night sky with awe: brutal and stupid men do not. When the silence of the eternal spaces terrified Pascal, it was Pascal's own greatness that enabled them to do so; to be frightened by the bigness of the nebulæ is, almost literally, to be frightened at our own shadow. For light years and geological periods are mere arithmetic until the shadow of man, the poet, the maker of myths, falls upon them. As a Christian I do not say we are wrong to tremble at that shadow, for I believe it to be the shadow of an image of God. But if the vastness of Nature ever threatens to overcrow our spirits, we must remember that it is only Nature spiritualised by human imagination which does so. This suggests a possible answer to the question raised a few pages ago -- why the size of the universe, known for centuries, should first in modern times become an argument against Christianity. Has it perhaps done so because in modern times the imagination has become more sensitive to bigness? From this point of view the argument from size might almost be regarded as a by-product of the Romantic Movement in poetry. In addition to the absolute increase of imaginative vitality on this topic, there has pretty certainly been a decline on others. Any reader of old poetry can see that brightness appealed to ancient and medieval man more than bigness, and more than it does to us. Medieval thinkers believed that the stars must be somehow superior to the Earth because they looked bright and it did not. Moderns think that the Galaxy ought to be more important than the Earth because it is bigger. Both states of mind can produce good poetry. Both can supply mental pictures which rouse very respectable emotions -- emotions of awe, humility, or exhiliration. But taken as serious philosophical argument both are ridiculous.
It reminds me of Jodie Foster's comment at the end of Contact (I don't know if it's present in the novel by Carl Sagan): if we're the only living creatures in the universe, it seems like an awful waste of space. But as Victor Reppert writes, "It is not as if energy or time [or space] is a scarce resource for God and we have to ask him, if he seems to be ‘wasting’ it, why he isn't putting it to better use. ‘Waste’ is an issue only where there is scarcity."
A similar objection that I mentioned in part 1 needs further comment. I pointed out that the universe's mass density -- the amount of matter in the universe -- must be extremely fine-tuned. Otherwise, the universe's expansion would have precluded the possibility of life existing anywhere at any time in the universe's history. In other words, the universe must be the particular size it is in order for us to exist. However, one could point out that while this matter may have been necessary at the universe's inception, it seems gratuitous for it to still be here. To insist that this vast universe is all there for our sake seems absurd. Every piece of matter may have had some relevance to the universe's initial expansion billions of years ago, but there is no obvious connection between distant pieces of matter and the human race's present existence. There are plenty of galaxies billions of light years away, which have plenty of planets orbiting plenty of suns. What does a particular rock on one of these planets have to do with life on earth now? The absence of such a connection makes humanity appear irrelevant to the universe.
Ignoring my previous response, this objection assumes that life or the human race is the only possible reason why the Judeo-Christian God would have created the universe. But just because all this matter has no relevance to humanity's existence today, it does not mean that God does not delight in it for some other reason, and so sustains it in existence. Again, this point is made best by C. S. Lewis:
There is no question of religious people fancying that all exists for man and scientific people discovering that it does not. Whether the ultimate and inexplicable being -- that which simply is -- turns out to be God or "the whole show," of course it does not exist for us. On either view we are faced with something which existed before the human race appeared and will exist after the Earth has become uninhabitable; which is utterly independent of us though we are totally dependent on it; and which, through vast ranges of its being, has no relevance to our own hopes and fears. For no man was, I suppose, ever so mad as to think that man, or all creation, filled the Divine Mind; if we are a small thing to space and time, space and time are a much smaller thing to God. It is a profound mistake to imagine that Christianity ever intended to dissipate the bewilderment and even the terror, the sense of our own nothingness, which come upon us when we think about the nature of things. It comes to intensify them. Without such sensations there is no religion.
A final point: in order to assert that the premoderns thought that the earth's size somehow rendered its inhabitants significant, it would require us to believe (at least) that they thought the earth and its inhabitants significant. In order for the statement, "they believed X because of Y" to be true, it has to be true that "they believed X." The argument that they thought the earth's size bequeathed significance on humanity can't even get off the ground unless they thought humanity had significance.
But this is not the case. We've already mentioned one criterion: brightness. The earth was thought to be less important and valuable than the celestial objects because they were bright while the earth was not. Another criterion that's often misunderstood is the earth's location at the center of the universe. This is usually twisted to imply that the center was the place of prestige, but the exact opposite is the case. They thought Earth was located at the bottom of the universe, which, in their view, was the least prestigious place therein. And the further down you went, the worse it was; this is why hell was thought to be at the center of the earth, and Satan at the center of hell. Arthur Lovejoy, in The Great Chain of Being, wrote that the medieval model is better described as "diabolocentric" than "geocentric." See the essays by Dennis Danielson on this.
However, one might object that Christianity conceives human beings as being so significant that God chose to be incarnated as one to die on their behalf. But this misunderstands exactly what the Christian claim is.
Christianity does not involve the belief that all things were made for man. It does involve the belief that God loves man and for his sake became man and died. I have not yet succeeded in seeing how what we know (and have known since the days of Ptolemy) about the size of the universe affects the credibility of this doctrine one way or the other. ... If it is maintained that anything so small as the Earth must, in any event, be too unimportant to merit the love of the Creator, we reply that no Christian ever supposed we did merit it. Christ did not die for men because they were intrinsically worth dying for, but because He is intrinsically love, and therefore loves infinitely.
In other words, whatever significance or value human beings have is derivative. The moral law tells us that people do have an inherent value; the reason murder is wrong, for example, is because each individual is of infinite worth. But the reason each individual is of infinite worth is because he/she is created in God's image. And the reason God loves us is not because we are lovely or lovable, but because he is loving; indeed, the claim is that God is love itself.
Thursday, July 9, 2009
Neo-geocentrism
A big part of the claim that Christianity is at war with science is geocentrism, the belief that the earth is at the center of the universe. As readers of this blog are aware, this issue is almost entirely misunderstood: in the ancient/medieval cosmology, the closer you were to the center of the universe, the less privileged and esteemed you were. This is precisely why hell is even closer to the center of the universe than the surface of the earth, and why Dante placed Satan at the exact center of hell (and thus of the entire universe), immobilized in a field of ice.
The misunderstanding is that since the premoderns thought the earth was at the literal center of the universe, they must also have thought it was the metaphorical center as well. It confuses geocentrism with anthropocentrism. But this can only be maintained by completely ignoring their Aristotelian cosmology, according to which the universe was arranged in concentric spheres, with God on the outside as the prime mover. The furthest place in the universe from God, therefore -- the furthest place in a sphere from what is outside the sphere --, is at its center. Of course, this ignores the fact that in Christian theology God is not merely transcendent to the universe but omnipresent within it as well; nevertheless, the premoderns maintained that the closer you were to the center, the less valuable you were. This has been amply demonstrated by Dennis Danielson in his essays "Copernicus and the Tale of the Pale Blue Dot", "The Great Copernican Cliché", and chapter 6 in Galileo Goes to Jail and Other Myths About Science and Religion; Humphrey wrote an enlightening post on this issue as well.
But I find it interesting that when Christians are told that their worldview requires a belief that conflicts with science, some respond by embracing the belief in question. Thus, there are geocentric ministries today which argue that being a Christian requires belief in a geocentric universe -- although they prefer the term "geocentricity" as it doesn't have as much historical baggage. The Geocentricity website is the official site of the Association for Biblical Astronomy, "biblical astronomy" meaning Aristotelian/Ptolemaic astronomy. The second link takes you to a collection of the publications of their journal.
There's another site that bothers me more. When I was in (Protestant) seminary, my favorite theology professor used a book for one of his classes written by a Protestant-turned-Catholic entitled, Not by Faith Alone. I didn't take that class, but I did plan to someday study this book, maybe together with Alister McGrath's Iustitia Dei, and see where I came out. However, the author of Not by Faith Alone has also published a two volume work entitled Galileo Was Wrong: The Church Was Right, volume 1 of which deals with "the scientific case for geocentrism", thus absolving me of any requirement to take him seriously. (Update: Just to be clear, I'm not tying the Catholic doctrine of justification to geocentrism. I'm only saying that particular author is not credible.)
The Geocentric Bible is essentially an online book arguing for geocentrism; he says he first heard of this view from a young-earth creationist ministry. This leads to another point: most young-earth ministries have embraced a neo-geocentrism in order to account for the problem of starlight travel time. They argue that the universe we know is actually a white hole -- a black hole so crunched that light begins to escape via quantum tunnelling -- with our galaxy (the Milky Way) at its center. They call it "galacto-centrism" since the earth is only approximately at the universe's center. For now I'd just like to point out that in arguing for this view, they appeal to the idea that if we're important to God, we should expect to find ourselves at the center of the universe. In other words, they accept the conflation of geocentrism with anthropocentrism, a conflation which is not only unhistorical, but which was invented in order to mock and ridicule Christianity. This strikes me as an extremely unwise concession: when fighting the spirit of the age, you shouldn't let it define the terms of the debate. Moreover, the fact that they have to appeal to geocentrism in order to defend their belief in a young earth makes the latter even less plausible than it already was.
The misunderstanding is that since the premoderns thought the earth was at the literal center of the universe, they must also have thought it was the metaphorical center as well. It confuses geocentrism with anthropocentrism. But this can only be maintained by completely ignoring their Aristotelian cosmology, according to which the universe was arranged in concentric spheres, with God on the outside as the prime mover. The furthest place in the universe from God, therefore -- the furthest place in a sphere from what is outside the sphere --, is at its center. Of course, this ignores the fact that in Christian theology God is not merely transcendent to the universe but omnipresent within it as well; nevertheless, the premoderns maintained that the closer you were to the center, the less valuable you were. This has been amply demonstrated by Dennis Danielson in his essays "Copernicus and the Tale of the Pale Blue Dot", "The Great Copernican Cliché", and chapter 6 in Galileo Goes to Jail and Other Myths About Science and Religion; Humphrey wrote an enlightening post on this issue as well.
But I find it interesting that when Christians are told that their worldview requires a belief that conflicts with science, some respond by embracing the belief in question. Thus, there are geocentric ministries today which argue that being a Christian requires belief in a geocentric universe -- although they prefer the term "geocentricity" as it doesn't have as much historical baggage. The Geocentricity website is the official site of the Association for Biblical Astronomy, "biblical astronomy" meaning Aristotelian/Ptolemaic astronomy. The second link takes you to a collection of the publications of their journal.
There's another site that bothers me more. When I was in (Protestant) seminary, my favorite theology professor used a book for one of his classes written by a Protestant-turned-Catholic entitled, Not by Faith Alone. I didn't take that class, but I did plan to someday study this book, maybe together with Alister McGrath's Iustitia Dei, and see where I came out. However, the author of Not by Faith Alone has also published a two volume work entitled Galileo Was Wrong: The Church Was Right, volume 1 of which deals with "the scientific case for geocentrism", thus absolving me of any requirement to take him seriously. (Update: Just to be clear, I'm not tying the Catholic doctrine of justification to geocentrism. I'm only saying that particular author is not credible.)
The Geocentric Bible is essentially an online book arguing for geocentrism; he says he first heard of this view from a young-earth creationist ministry. This leads to another point: most young-earth ministries have embraced a neo-geocentrism in order to account for the problem of starlight travel time. They argue that the universe we know is actually a white hole -- a black hole so crunched that light begins to escape via quantum tunnelling -- with our galaxy (the Milky Way) at its center. They call it "galacto-centrism" since the earth is only approximately at the universe's center. For now I'd just like to point out that in arguing for this view, they appeal to the idea that if we're important to God, we should expect to find ourselves at the center of the universe. In other words, they accept the conflation of geocentrism with anthropocentrism, a conflation which is not only unhistorical, but which was invented in order to mock and ridicule Christianity. This strikes me as an extremely unwise concession: when fighting the spirit of the age, you shouldn't let it define the terms of the debate. Moreover, the fact that they have to appeal to geocentrism in order to defend their belief in a young earth makes the latter even less plausible than it already was.
Thursday, April 16, 2009
Size Doesn't Matter (thank God), part 2
July 13, 2013: I have temporarily removed the content of this post because it has some similarities with an article I wrote that is being published in an academic journal. Even though a blogpost probably doesn't count as having previously published the material, I'm taking the content of this post offline in order to avoid the appearance of impropriety. I'll put it back online in a year or so.
Monday, March 23, 2009
Size Doesn't Matter (thank God), part 1
Contemporary western culture is dominated by the "conflict thesis", the claim that science and religion are at war, and that religion (or at least Christianity) is losing. The latter claims that human beings are the pinnacle of creation, but science has revealed that we are merely animals evolved from simpler forms of life, which in turn were just the product of matter and energy acting upon each other, all of which occupies an insignificant dot in an insignificant location in an infinite universe. Nietzsche illustrates this perspective well with the parable with which he opens his brilliant essay "On Truth and Lies in a Nonmoral Sense":
To think we have any significance or value in light of this is essentially to stick your fingers in your ears, shake your head, and say, "La la la la, I can't hear you!"
One of the elements in this metanarrative is the incomprehensible vastness of the universe, only discovered in the modern scientific era, and the infinitesimal size of the earth in comparison. This renders absurd any suggestion that human beings, occupying only a speck of dust in a cosmic sandstorm, are special, showing (once again) that contemporary science has refuted Christianity. Or so the story goes.
This view is expressed well by Douglas Adams' Total Perspective Vortex and Monty Python's Galaxy Song. I was going to embed the latter, but since there are some, shall we say, improprieties therein, I decided to go with a different song that expresses this sentiment in a more family-friendly fashion.
Unfortunately (at least for some), there are multiple problems with the conflict thesis in general, and with the claim regarding the spatial insignificance of the earth in particular. Regarding the latter, everyone, of course, feels a sense of insignificance when faced with the vastness of the cosmos. This is universal, although some ages and cultures feel it more intensely than others. But before it can made into an argument against Christianity, several further questions must be answered. For example, why would something's value or importance be connected to its size? Does Christianity actually teach that humanity is the most important thing in the universe? If so, does it tie this to a belief that the universe is small and the earth the largest thing in it? Is it really only with modern science that we've discovered the universe's immensity, and thus the disparity between it and ourselves? In the remainder of this post I'll be addressing this last question from the side of science.
-- The impression that the universe dwarfs us is based on a sort of common sense view of measurement. But a couple of years ago James made a very important point about this issue. He compared human beings to the smallest and largest things in the universe; that is, he used the exponential scale which is precisely the standard of measurement which physicists employ. When this is done, it reveals that human beings are actually closer to the larger end of the scale than the smaller end. The smallest is the Planck length at 10-35 meters, and the largest is the universe itself, at about 1025 meters. "So comparing our absolute size to the smallest and biggest possible things in the universe, we are about three fifths of the way up the scale. In other words, we are of medium to large size using the exponential scale, the only scale that makes any sense in physics."
Of course, one could simply reject this standard of measurement as having any relevance to the issue. If one does, however, then one would have to reject the argument under discussion as well: for it depends on the claim that modern science has demonstrated our spatial insignificance. You cannot make this claim while rejecting the very method of measurement actually used by the sciences in question.
-- Another scientific point involves the Anthropic Principle. One of the characteristics I mentioned in this post is that the universe's mass density must be precisely what it is in order for life to be possible anywhere at any time in the universe's history. The mass density is the amount of matter in the universe. The velocity with which the matter and energy created in the Big Bang burst outward was precisely governed by the universe’s mass density, since the more mass there is, the more gravity would slow down the expansion, matter being what gravity acts upon. If the universe's mass density were different by one part in 1060, life could never exist at any place and at any time in the universe's history. In other words, if the universe was just a trillionth of a trillionth of a trillionth of a trillionth of a trillionth smaller or larger than it is -- an amount equal to "about a tenth part of a dime" according to the link above -- the universe’s velocity would either have overpowered gravity, or it would have been overpowered by gravity. The first case would have prevented the matter from being collected into stars and galaxies. The second case would have resulted in the universe collapsing back in on itself. Either way, life would have been impossible anywhere at any time in the universe. So in order for life to be possible on our dust speck of a planet, the universe must be precisely the size that it is.
Of course, some people will insist that this is not enough. Just because every piece of matter had some relevance to the universe's initial expansion, it does not have any connection to our existence now -- and this calls into question any view that sets up the earth and humanity as significant. In other words, unless every rock, planet, star, and galaxy in the universe is always and only there for our benefit, Christianity (somehow) cannot be true.
But what exactly is being asked here? Given the necessary fine-tuning of the universe's mass density, the matter making up these rocks, planets, stars, and galaxies had to be there. To ask why they're still there is to ask why God didn't destroy them once they served their initial purpose. In other words, it is to expect God to destroy the evidence of what he has done. This is problematic on several levels, not least of which is that if God did do this, the same people who raise this objection would obviously be pointing to the lack of evidence for God. So it seems that no matter what he does -- whether he keeps the matter there as a testimony to his actions or whether he destroys it once it has served this purpose -- they will use it as an argument against his existence. I may come back to this in future installments.
-- Alexandre Koyré argues in From the Closed World to the Infinite Universe that there is an element to modern cosmology that is lacking in its ancient and medieval counterparts. Regardless of how big they thought the universe to be, they clearly believed it to be finite. But modern science has, according to Koyré, demonstrated that the universe is infinite. The reason this is significant is because moving from one finite size to another is not the same as moving from a finite size to an infinite one. Regardless of how large the ancients and medievals conceived the universe to be, there is a difference in kind involved here, and this is the significant aspect of modern cosmology that refutes the ancient and medieval cosmology. "Let us not forget, moreover, that, by comparison with the infinite, the world of Copernicus is by no means greater than that of mediaeval astronomy; they are both as nothing, because inter finitum et infinitum non est proportio. We do not approach the infinite universe by increasing the dimension of our world. We may make it as large as we want: that does not bring us any nearer to it."
I will not contest here Koyré's claim that an infinite universe is a different type of thing than a finite one, and as such, would represent a complete change of our view of the cosmos as well as ourselves. On this score, C. S. Lewis agrees: in The Discarded Image (a text to which I'll be returning) he argues that there is a radical difference between believing in a distant horizon and believing in no horizon at all.
Perhaps, then, one could argue that since an infinite universe presents us with an object in which the mind cannot rest, this sense of "agoraphobia" that it produces entails a greater sense of insignificance than any finite universe could convey; and hence a greater assault on humanity's dignity. However, Lewis argues to the contrary: an infinite universe would have no absolute standard of measurement, only relative standards. But a finite universe would have both absolute and relative standards of measurement.
Koyré argues that modern science requires a complete overhaul of our view of the cosmos and our place in it because we have discovered that the universe is infinite. The irony is that, even before Koyré wrote this, Einstein's relativity equations and Edwin Hubble's observations of the expansion of the universe indicated something different. Today Big Bang cosmology has established that the universe is spatially and temporally finite. It began to exist a particular time ago, and has a finite size. In this sense at least, the ancient/medieval cosmology has been exonerated. Whether Lewis is right to describe it as "unimaginably large" will be the subject of the next installment.
Once upon a time, in some out of the way corner of that universe which is dispersed into numberless twinkling solar systems, there was a star upon which clever beasts invented knowing. That was the most arrogant and mendacious minute of "world history," but nevertheless, it was only a minute. After nature had drawn a few breaths, the star cooled and congealed, and the clever beasts had to die.
To think we have any significance or value in light of this is essentially to stick your fingers in your ears, shake your head, and say, "La la la la, I can't hear you!"
One of the elements in this metanarrative is the incomprehensible vastness of the universe, only discovered in the modern scientific era, and the infinitesimal size of the earth in comparison. This renders absurd any suggestion that human beings, occupying only a speck of dust in a cosmic sandstorm, are special, showing (once again) that contemporary science has refuted Christianity. Or so the story goes.
This view is expressed well by Douglas Adams' Total Perspective Vortex and Monty Python's Galaxy Song. I was going to embed the latter, but since there are some, shall we say, improprieties therein, I decided to go with a different song that expresses this sentiment in a more family-friendly fashion.
Unfortunately (at least for some), there are multiple problems with the conflict thesis in general, and with the claim regarding the spatial insignificance of the earth in particular. Regarding the latter, everyone, of course, feels a sense of insignificance when faced with the vastness of the cosmos. This is universal, although some ages and cultures feel it more intensely than others. But before it can made into an argument against Christianity, several further questions must be answered. For example, why would something's value or importance be connected to its size? Does Christianity actually teach that humanity is the most important thing in the universe? If so, does it tie this to a belief that the universe is small and the earth the largest thing in it? Is it really only with modern science that we've discovered the universe's immensity, and thus the disparity between it and ourselves? In the remainder of this post I'll be addressing this last question from the side of science.
-- The impression that the universe dwarfs us is based on a sort of common sense view of measurement. But a couple of years ago James made a very important point about this issue. He compared human beings to the smallest and largest things in the universe; that is, he used the exponential scale which is precisely the standard of measurement which physicists employ. When this is done, it reveals that human beings are actually closer to the larger end of the scale than the smaller end. The smallest is the Planck length at 10-35 meters, and the largest is the universe itself, at about 1025 meters. "So comparing our absolute size to the smallest and biggest possible things in the universe, we are about three fifths of the way up the scale. In other words, we are of medium to large size using the exponential scale, the only scale that makes any sense in physics."
Of course, one could simply reject this standard of measurement as having any relevance to the issue. If one does, however, then one would have to reject the argument under discussion as well: for it depends on the claim that modern science has demonstrated our spatial insignificance. You cannot make this claim while rejecting the very method of measurement actually used by the sciences in question.
-- Another scientific point involves the Anthropic Principle. One of the characteristics I mentioned in this post is that the universe's mass density must be precisely what it is in order for life to be possible anywhere at any time in the universe's history. The mass density is the amount of matter in the universe. The velocity with which the matter and energy created in the Big Bang burst outward was precisely governed by the universe’s mass density, since the more mass there is, the more gravity would slow down the expansion, matter being what gravity acts upon. If the universe's mass density were different by one part in 1060, life could never exist at any place and at any time in the universe's history. In other words, if the universe was just a trillionth of a trillionth of a trillionth of a trillionth of a trillionth smaller or larger than it is -- an amount equal to "about a tenth part of a dime" according to the link above -- the universe’s velocity would either have overpowered gravity, or it would have been overpowered by gravity. The first case would have prevented the matter from being collected into stars and galaxies. The second case would have resulted in the universe collapsing back in on itself. Either way, life would have been impossible anywhere at any time in the universe. So in order for life to be possible on our dust speck of a planet, the universe must be precisely the size that it is.
Of course, some people will insist that this is not enough. Just because every piece of matter had some relevance to the universe's initial expansion, it does not have any connection to our existence now -- and this calls into question any view that sets up the earth and humanity as significant. In other words, unless every rock, planet, star, and galaxy in the universe is always and only there for our benefit, Christianity (somehow) cannot be true.
But what exactly is being asked here? Given the necessary fine-tuning of the universe's mass density, the matter making up these rocks, planets, stars, and galaxies had to be there. To ask why they're still there is to ask why God didn't destroy them once they served their initial purpose. In other words, it is to expect God to destroy the evidence of what he has done. This is problematic on several levels, not least of which is that if God did do this, the same people who raise this objection would obviously be pointing to the lack of evidence for God. So it seems that no matter what he does -- whether he keeps the matter there as a testimony to his actions or whether he destroys it once it has served this purpose -- they will use it as an argument against his existence. I may come back to this in future installments.
-- Alexandre Koyré argues in From the Closed World to the Infinite Universe that there is an element to modern cosmology that is lacking in its ancient and medieval counterparts. Regardless of how big they thought the universe to be, they clearly believed it to be finite. But modern science has, according to Koyré, demonstrated that the universe is infinite. The reason this is significant is because moving from one finite size to another is not the same as moving from a finite size to an infinite one. Regardless of how large the ancients and medievals conceived the universe to be, there is a difference in kind involved here, and this is the significant aspect of modern cosmology that refutes the ancient and medieval cosmology. "Let us not forget, moreover, that, by comparison with the infinite, the world of Copernicus is by no means greater than that of mediaeval astronomy; they are both as nothing, because inter finitum et infinitum non est proportio. We do not approach the infinite universe by increasing the dimension of our world. We may make it as large as we want: that does not bring us any nearer to it."
I will not contest here Koyré's claim that an infinite universe is a different type of thing than a finite one, and as such, would represent a complete change of our view of the cosmos as well as ourselves. On this score, C. S. Lewis agrees: in The Discarded Image (a text to which I'll be returning) he argues that there is a radical difference between believing in a distant horizon and believing in no horizon at all.
Hence to look out on the night sky with modern eyes is like looking out over a sea that fades away into mist, or looking about one in a trackless forest -- trees forever and no horizon. To look up at the towering medieval universe is much more like looking at a great building. The 'space' of modern astronomy may arouse terror, or bewilderment or vague reverie; the spheres of the old present us with an object in which the mind can rest, overwhelming in its greatness but satisfying in its harmony. That is the sense in which our universe is romantic, and theirs was classical.
This explains why all sense of the pathless, the baffling, and the utterly alien -- all agoraphobia -- is so markedly absent from medieval poetry when it leads us, as so often, into the sky. Dante, whose theme might have been expected to invite it, never strikes that note. The meanest modern writer of science-fiction can, in that department, do more for you than he. Pascal's terror at le silence éternel de ces espaces infinis never entered his mind. He is like a man being conducted through an immense cathedral, not like one lost in a shoreless sea.
Perhaps, then, one could argue that since an infinite universe presents us with an object in which the mind cannot rest, this sense of "agoraphobia" that it produces entails a greater sense of insignificance than any finite universe could convey; and hence a greater assault on humanity's dignity. However, Lewis argues to the contrary: an infinite universe would have no absolute standard of measurement, only relative standards. But a finite universe would have both absolute and relative standards of measurement.
The really important difference is that the medieval universe, while unimaginably large, was also unambiguously finite. And one unexpected result of this is to make the smallness of Earth more vividly felt. In our [infinite] universe she is small, no doubt; but so are the galaxies, so is everything -- and so what? But in theirs there was an absolute standard of comparison. ... The word 'small' as applied to Earth thus takes on a far more absolute significance.
Koyré argues that modern science requires a complete overhaul of our view of the cosmos and our place in it because we have discovered that the universe is infinite. The irony is that, even before Koyré wrote this, Einstein's relativity equations and Edwin Hubble's observations of the expansion of the universe indicated something different. Today Big Bang cosmology has established that the universe is spatially and temporally finite. It began to exist a particular time ago, and has a finite size. In this sense at least, the ancient/medieval cosmology has been exonerated. Whether Lewis is right to describe it as "unimaginably large" will be the subject of the next installment.
Thursday, February 26, 2009
Mathematical Monks and the Multiverse
I recently read a truly excellent SF novel by Neal Stephenson entitled Anathem. It's about an alternate universe that has monks whose interests are more on mathematics rather than theology; and they have an alternate philosophical history that parallels the real one. I highly recommend it to pretty much everyone (especially Elliot at CotC if he hasn't already read it).
Part of my motivation for bringing it up is that at one point the monks discuss the Anthropic Principle, and give an excellent account of it:
However, to get around the theistic repercussions, Anathem appeals to the multiverse hypothesis. Stephenson does this very cleverly: any view that argues that the physical universe isn't all that exists is a sort of multiverse hypothesis. So the Platonic world of forms is positing a multiverse, in which one is a universe of pure forms (in the Anathem alt-history Plato = Protas and Platonist = Protist). Similarly, any theistic explanation of the Anthropic Principle is a multiverse hypothesis, since it holds that there is another world that has some effect in this one. Stephenson's monks conclude from this that, if we have to posit another world in order to account for this one, there can be no reason for limiting the number of other worlds to one.
Of course, in this post I pointed out that there is a reason for limiting the number of worlds to two: Ockham's Razor. The more entities you have to posit, the less likely your theory is correct. The Anthropic Principle shows that we have to posit a world in addition to this one in order to account for the fact that this world has the very specific properties necessary for the existence of life. But unless we have a reason to posit a third or fourth or 173rd world, then to do so simply violates Ockham's Razor.
Ironically, part of Anathem's alternate history includes a parallel to Ockham's Razor, which is frequently referenced by the characters:
So, basically, the multiverse hypothesis violates the Steelyard: the anthropic coincidences make it absurdly implausible that this world is the only one that exists; but unless it is absurdly implausible that only two worlds exist, it is invalid to think there are more than two. Anathem contains the refutation of one of its premises without realizing it.
However, I'm willing to give Stephenson some grace here, since such an acknowledgment would essentially destroy the premise of the entire book. Now go read it.
Part of my motivation for bringing it up is that at one point the monks discuss the Anthropic Principle, and give an excellent account of it:
Paphlagon said, "The cosmogonic processes that lead to the creation of the stuff we are made of -- the creation of protons and other matter, their clumping together to make stars, and the resulting nucleosynthesis -- all seem to depend on the values of certain physical constants. The most familiar example is the speed of light, but there are several others -- about twenty in all. Theors used to spend a lot of time measuring their precise values, back when we were allowed to have the necessary equipment. If these numbers had different values, the cosmos as we know it would not have come into being; it would just be an infinite cloud of cold dark gas or one big black hole or something else quite simple and dull. If you think of these constants of nature as knobs on the control panel of a machine, well, the knobs all have to be set in just the right positions or --"
Again Paphlagon looked to Moyra, who seemed ready: "Suur Demula likened it to a safe with a combination lock, the combination being about twenty numbers long."
"That is right. If you dial twenty numbers at random you never get the safe open; it is nothing more to you than an inert cube of iron. Even if you dial nineteen numbers correctly and get the other one wrong -- nothing. You must get all of them correct. Then the door opens and out spills all of the complexity and beauty of the cosmos."
"Another analogy," Moyra continued, after a sip of water, "was developed by Saunt Conderline, who likened all of the sets of values of those twenty constants that don't produce complexity to an ocean a thousand miles wide and deep. The sets that do, are like an oil sheen, no wider than a leaf, floating on the top of that ocean: an exquisitely thin layer of possibilities that yield solid, stable matter suitable for making universes with living things in them."
However, to get around the theistic repercussions, Anathem appeals to the multiverse hypothesis. Stephenson does this very cleverly: any view that argues that the physical universe isn't all that exists is a sort of multiverse hypothesis. So the Platonic world of forms is positing a multiverse, in which one is a universe of pure forms (in the Anathem alt-history Plato = Protas and Platonist = Protist). Similarly, any theistic explanation of the Anthropic Principle is a multiverse hypothesis, since it holds that there is another world that has some effect in this one. Stephenson's monks conclude from this that, if we have to posit another world in order to account for this one, there can be no reason for limiting the number of other worlds to one.
"It is a legitimate move in metatheorics. You have to be continually asking yourself, 'why are things thus, and not some other way?' And if you apply that test to this diagram, you immediately run into a problem: there are exactly two worlds. Not one, not many, but two. One might draw such a diagram having only one world -- the Arbran Causal Domain -- and zero arrows. That would draw very few objections from metatheoricians (at least, those who are not Protists). One might, on the other hand, assert 'there are lots of worlds' and then set out to make a case for why that is plausible. But to say 'there are two worlds -- and only two!' seems no more supportable than to say 'there are exactly 173 worlds, and all those people who claim that there are only 172 of them are lunatics.'"
Of course, in this post I pointed out that there is a reason for limiting the number of worlds to two: Ockham's Razor. The more entities you have to posit, the less likely your theory is correct. The Anthropic Principle shows that we have to posit a world in addition to this one in order to account for the fact that this world has the very specific properties necessary for the existence of life. But unless we have a reason to posit a third or fourth or 173rd world, then to do so simply violates Ockham's Razor.
Ironically, part of Anathem's alternate history includes a parallel to Ockham's Razor, which is frequently referenced by the characters:
Gardan's Steelyard: A rule of thumb attributed to Fraa Gardan (-1110 to -1063), stating that, when one is comparing two hypotheses, they should be placed on the arms of a metaphorical steelyard (a kind of primitive scale, consisting of an arm free to pivot around a central fulcrum) and preference given to the one that "rises higher," presumably because it weighs less; the upshot being that simpler, more "lightweight" hypotheses are preferable to those that are "heavier," i.e., more complex. Also referred to as Saunt Gardan's Steelyard or simply the Steelyard.
So, basically, the multiverse hypothesis violates the Steelyard: the anthropic coincidences make it absurdly implausible that this world is the only one that exists; but unless it is absurdly implausible that only two worlds exist, it is invalid to think there are more than two. Anathem contains the refutation of one of its premises without realizing it.
However, I'm willing to give Stephenson some grace here, since such an acknowledgment would essentially destroy the premise of the entire book. Now go read it.
Friday, February 13, 2009
The Anthropic Principle for Misanthropes, part 4
(See also part 1, part 2, and part 3)
In this series I have left out a lot regarding the Anthropic Principle, because my focus is on its value as a teleological argument for the existence of God. So, for example, I have not gone over the several types of APs that have been proposed, i.e. the Weak (WAP), Strong (SAP), Participatory (PAP), and Final (FAP) -- the latter of which Martin Gardner cleverly called the Completely Ridiculous Anthropic Principle (CRAP).
Some people think that any teleological argument is invalid in light of Darwin. Such arguments are automatically excluded from consideration, since they also apply to arguments against biological evolution. If some teleological arguments from a particular field are invalid, why doesn't that give us grounds for rejecting those from other fields? My answer is fairly simple: because the arguments against evolution don't work and the arguments from the AP do. It doesn't matter who is presenting the argument or what their motivation is: if it's valid, it's valid; and if it's invalid, it's invalid.
One thing that frustrated me about the AP when I first studied it, however, is that there seem to be examples of fine-tuning that don't serve any purpose. The example that particularly hit home with me was that our location with regards to the sun and the moon make it appear as if they just happen to be the same size in the sky. The AP shows that we have to have a moon a particular size and distance from us, and the earth has to be a particular distance from a particular kind of star during a particular burning phase; but it just seems weird to me that this results in the sun and moon appearing to be the same size in the sky. If someone rigged the game, it looks like they were rigging it to mislead us into thinking that they were the same size. Of course, the ancients were able to study the sun and the moon and determine that they're not even remotely close in terms of size. But it seems like a meaningless coincidence, and this made me suspicious that the examples of alleged fine-tuning that the AP demonstrates were similarly coincidental.
The resolution to this leads to a very interesting corollary to the AP. The surface of the earth is the only place in the solar system where an observer could see a total eclipse, in which one body blocks out the sun, but does so just barely, so that the sun's corona can be observed. For millennia, solar eclipses were one of the primary methods by which humankind could study the sun. Such study would only be possible if the sun and the moon appeared to be the same size in the sky. So the same characteristics that make life possible are also the characteristics that allow us to study and investigate the universe around us.
With the advent of the Mars Rovers, there has been a boon in the last several years on Mars studies. Below, on the left, is a series of pictures taken by one of the Rovers of Phobos, one of Mars' moons, crossing between Mars and the sun. The picture on the right is of Mars' other moon Deimos doing the same. Click here to see a very short video (a couple of seconds long) of it.
The point in showing these is that such "eclipses" (they're actually called transits or occultations) would not allow any observers to study the sun's corona.
Here's another example: the AP says that in order for life to be possible, the solar system must reside in a spiral galaxy, and lie in-between spiral arms. In the same way, we have to be between spiral arms in order to see anything beyond our own galaxy. In any other location in any other type of galaxy, the number of nearby stars and the light they produce would prevent us from seeing very far beyond them. So just as it looks like the universe and Earth have been arranged in order to support life, it looks like the universe and Earth have been arranged in order to allow for scientific discovery. Praise God.
In this series I have left out a lot regarding the Anthropic Principle, because my focus is on its value as a teleological argument for the existence of God. So, for example, I have not gone over the several types of APs that have been proposed, i.e. the Weak (WAP), Strong (SAP), Participatory (PAP), and Final (FAP) -- the latter of which Martin Gardner cleverly called the Completely Ridiculous Anthropic Principle (CRAP).
Some people think that any teleological argument is invalid in light of Darwin. Such arguments are automatically excluded from consideration, since they also apply to arguments against biological evolution. If some teleological arguments from a particular field are invalid, why doesn't that give us grounds for rejecting those from other fields? My answer is fairly simple: because the arguments against evolution don't work and the arguments from the AP do. It doesn't matter who is presenting the argument or what their motivation is: if it's valid, it's valid; and if it's invalid, it's invalid.
One thing that frustrated me about the AP when I first studied it, however, is that there seem to be examples of fine-tuning that don't serve any purpose. The example that particularly hit home with me was that our location with regards to the sun and the moon make it appear as if they just happen to be the same size in the sky. The AP shows that we have to have a moon a particular size and distance from us, and the earth has to be a particular distance from a particular kind of star during a particular burning phase; but it just seems weird to me that this results in the sun and moon appearing to be the same size in the sky. If someone rigged the game, it looks like they were rigging it to mislead us into thinking that they were the same size. Of course, the ancients were able to study the sun and the moon and determine that they're not even remotely close in terms of size. But it seems like a meaningless coincidence, and this made me suspicious that the examples of alleged fine-tuning that the AP demonstrates were similarly coincidental.
The resolution to this leads to a very interesting corollary to the AP. The surface of the earth is the only place in the solar system where an observer could see a total eclipse, in which one body blocks out the sun, but does so just barely, so that the sun's corona can be observed. For millennia, solar eclipses were one of the primary methods by which humankind could study the sun. Such study would only be possible if the sun and the moon appeared to be the same size in the sky. So the same characteristics that make life possible are also the characteristics that allow us to study and investigate the universe around us.
With the advent of the Mars Rovers, there has been a boon in the last several years on Mars studies. Below, on the left, is a series of pictures taken by one of the Rovers of Phobos, one of Mars' moons, crossing between Mars and the sun. The picture on the right is of Mars' other moon Deimos doing the same. Click here to see a very short video (a couple of seconds long) of it.
The point in showing these is that such "eclipses" (they're actually called transits or occultations) would not allow any observers to study the sun's corona.
Here's another example: the AP says that in order for life to be possible, the solar system must reside in a spiral galaxy, and lie in-between spiral arms. In the same way, we have to be between spiral arms in order to see anything beyond our own galaxy. In any other location in any other type of galaxy, the number of nearby stars and the light they produce would prevent us from seeing very far beyond them. So just as it looks like the universe and Earth have been arranged in order to support life, it looks like the universe and Earth have been arranged in order to allow for scientific discovery. Praise God.
Saturday, January 24, 2009
An Interesting Reaction
One theistic argument is the moral argument (or axiological argument). It's the idea that in order to say that there are actual moral rights and wrongs, we have to presuppose a sort of metaphysical anchor or ground for these values that transcends individual cultures and epochs, something in fact which looks very much like the Judeo-Christian God. If we reject such a ground, then we are left with pure relativism, where nothing is actually right or wrong. This may be OK when the issue under discussion is whether you should be completely forthcoming on your taxes, but when we point to horrific atrocities, it becomes very difficult to say that there is simply nothing morally wrong going on.
However, rather than defend this argument, I want to point to an interesting reaction to it. Many atheists who hear the moral argument misunderstand it to mean that atheists cannot be moral people or upstanding citizens. If you need to believe in God in order to believe that rape is wrong, then you're essentially arguing that if you don't believe in God, then you must not believe that rape is really wrong. But of course, this isn't the argument. The point, rather, is that the moral judgment "rape is wrong" -- made by theist and atheist alike -- must have a metaphysical ground in order to be valid. Thus, according to the moral argument, the atheist is being inconsistent in affirming that rape is wrong while denying that God exists. But this does not mean that atheists don't know right from wrong.
Now part of the reason I find this reaction interesting is that I could present a parallel argument which almost certainly would not provoke the same reaction. Say, for example, I argued that in order for mathematics to be possible we have to posit a metaphysical foundation for numbers, a Platonic realm of forms, which is best understood as the mind of God (such arguments have been made). So in order to affirm that 2 + 2 = 4, we have to presuppose something like the Judeo-Christian God. How many people would misunderstand such an argument to mean that if you don't believe in God, you don't really believe that 2 + 2 = 4? I suspect very few, if any. Yet this argument is exactly parallel to the moral argument: in order to affirm X we have to presuppose a metaphysical foundation for it that is best understood as God.
So why are some people so liable to misunderstand the moral argument? Again, I suspect (although I could very easily be wrong) it's because our views on morality are inextricably bound up with our views of ourselves: what we do and what we think should be done says a great deal of what kind of person we are. So when someone tells an atheist that her worldview is inconsistent with believing that rape is wrong, she reacts. Instead of realizing that the moral argument is saying something about the relationship between her worldview and moral beliefs, she only sees it as saying something about her moral beliefs, and thus about herself: whether she is a good person.
However, rather than defend this argument, I want to point to an interesting reaction to it. Many atheists who hear the moral argument misunderstand it to mean that atheists cannot be moral people or upstanding citizens. If you need to believe in God in order to believe that rape is wrong, then you're essentially arguing that if you don't believe in God, then you must not believe that rape is really wrong. But of course, this isn't the argument. The point, rather, is that the moral judgment "rape is wrong" -- made by theist and atheist alike -- must have a metaphysical ground in order to be valid. Thus, according to the moral argument, the atheist is being inconsistent in affirming that rape is wrong while denying that God exists. But this does not mean that atheists don't know right from wrong.
Now part of the reason I find this reaction interesting is that I could present a parallel argument which almost certainly would not provoke the same reaction. Say, for example, I argued that in order for mathematics to be possible we have to posit a metaphysical foundation for numbers, a Platonic realm of forms, which is best understood as the mind of God (such arguments have been made). So in order to affirm that 2 + 2 = 4, we have to presuppose something like the Judeo-Christian God. How many people would misunderstand such an argument to mean that if you don't believe in God, you don't really believe that 2 + 2 = 4? I suspect very few, if any. Yet this argument is exactly parallel to the moral argument: in order to affirm X we have to presuppose a metaphysical foundation for it that is best understood as God.
So why are some people so liable to misunderstand the moral argument? Again, I suspect (although I could very easily be wrong) it's because our views on morality are inextricably bound up with our views of ourselves: what we do and what we think should be done says a great deal of what kind of person we are. So when someone tells an atheist that her worldview is inconsistent with believing that rape is wrong, she reacts. Instead of realizing that the moral argument is saying something about the relationship between her worldview and moral beliefs, she only sees it as saying something about her moral beliefs, and thus about herself: whether she is a good person.
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