A Short Critique of Bradley Monton's Paper
by BilboBradley Monton, an atheist professor of philosophy at the University of Colorado at Boulder (his blog), is much maligned by Intelligent Design critics, though I'm not sure why. He has written a paper, "Design Inferences in an Infinite Universe," criticizing design inferences from the origin of life and irreducible complexity. I would think that would place him squarely in the ID critics' camp. But I'm not interested in psychologizing the critics. I'm interested in his paper.
He bases his argument on empirical evidence that the universe is infinite:
The mainstream view of contemporary cosmologists is that the evidence suggests that space is infinite. Specifically, the evidence suggests that on a large scale space is not curved. For example, the Wilkinson Microwave Anisotropy Probe (WMAP) was recently used to measure the Cosmic Microwave Background radiation. The temperature fluctuations in the radiation suggest that space is flat, and hence infinite. (p.3)
He develops this evidence into a premise:
Let's suppose that the universe is in fact spatially infinite, and that matter elsewhere in the universe is similar to matter here, and that there was randomness in the initial conditions for different regions of the universe. (p.4)
After considering the improbability of life arising spontaneously in a finite universe, he asks,
…how probable is it that life would spontaneously arise from non-life on a particular planet? (p.5)
And his answer is,
As long as the probability is not zero, then if the universe is spatially infinite we should expect life to arise somewhere in the infinite universe….In fact, we can draw a much stronger conclusion. We should expect life to arise an infinite number of places in the universe…. (p.5-6)
Therefore,
My conclusion is that one shouldn't use the development of life from non-life, or the existence of irreducibly complex biological systems, to argue for design. (p.6)
Monton provides a replacement model for inferring design, or inferring that God is the designer. Essentially, he thinks that the occurrence of miracles — such as a man walking on water — would allow for valid inferences to God. Why?
As a final topic, it's worth making explicit why we can infer design in the seeming miracle case, but not in the origin of life case or the irreducible complexity case. After all, one might think that the cases are analogous — in each case, there's the possibility that God did it, and the (highly improbable) possibility that it happened due to chancy naturalistic processes. So since we could infer design if a seeming miracle were to occur, why not already infer design based on the existence of irreducibly complex life?
Here is one key difference. In explaining why one can infer design on the basis of the seeming miracle, I pointed out that the seeming miracle would be more likely to occur under the supposition that God exists than it would under the supposition that there is no designer. This is what leads to the probability shift in favor of the designer hypothesis. In the existence of life case, though, it would be reasonable to think that there would be no more life in the universe under the supposition that God exists than under the supposition that there is no God. After all, even under the supposition that there is no God, we would expect there to be life in an infinite number of places in the universe. I see nothing in Christian theology, for example, which suggests that the density of life in the spatially infinite universe would be greater than it would be if there were no God. (p.16)
My very brief critique of Monton's argument is this: He has this argument exactly backwards. Let us take, as an example, the existence of toaster ovens. In an infinite universe, we should expect to find toaster ovens in an infinite number of places. However, toaster ovens are more likely to be found under the supposition that toaster oven designers exist than under the supposition that toaster oven designers do not exist. Likewise, given the extreme improbability of life spontaneously arising (which Monton grants), life is more likely to be found under the supposition that designers of life exist, than under the supposition that designers of life do not exist. Having found life, it is therefore more likely that designers of life exist than that they do not.
March 29th, 2009 at 9:43 pm
Bilbo wrote:
Bilbo, the mathematical concept of infinity requires careful consideration. Mathematicians realized that in the 19 century and devised strict rules for working with infinite quantities. Both you and Monton handle infinities in completely arbitrary ways, so it's no wonder that you get different answers.
Monton makes other bloopers.
This does not compute. In mathematics, the flatness of a space does not necessarily imply its infinite extent. The former is a local property, while the latter is a global one. To relate the former to the latter, one needs to know the topology of the space (how it is connected). A simple example of a flat but finite space is a square with periodic boundary conditions. It is realized in the classic arcade game Asteroids: a ship moving beyond the right edge of the field emerges on the left side of the screen.
I *heart* philosophers.
Comment by olegt — March 29, 2009 @ 9:43 pm
March 29th, 2009 at 10:40 pm
Well, olegt, you stole my thunder, but here's something else about this assertion:
From what I can tell, his whole paper relies on this inference. But on the nasa site that talks about the WMAP's findings, and the 1% flatness specifically (item no. 3), there is no inference drawn about the universe being infinite. On the contrary, looking at the other items on the list, the results seem to infer a finite universe, since they deal with its size (items 4, 5, 6, for example) or its beginning (item 8, for example).
WMAP page
The whole paper falls apart on the weakness of this assumption. He should have referred to a collaborating source, if there is one.
Comment by AnaxagorasRules — March 29, 2009 @ 10:40 pm
March 29th, 2009 at 11:19 pm
"…how probable is it that life would spontaneously arise from non-life on a particular planet? (p.5) As long as the probability is not zero, then if the universe is spatially infinite we should expect life to arise somewhere in the infinite universe"
When he or anyone else demonstrates that the probability of life spontaneously arising from non-life is not zero, then wake me up.
Comment by kornbelt888 — March 29, 2009 @ 11:19 pm
March 29th, 2009 at 11:24 pm
Olegt:
Olegt, it is my understanding that our universe, while unimaginably vast, is nonetheless finite. Is this not so?
Comment by Bradford — March 29, 2009 @ 11:24 pm
March 30th, 2009 at 12:06 am
**To Bilbo: Thanks for writing about my paper! I address your concern a bit in the last footnote:
"What if one’s preferred theology is such that God would be expected to create much more life than would exist in a naturalistic universe – would our existence provide evidence for the existence of God? Or what if one’s preferred theology is such that God would be expected to create life only on one planet – would our existence provide evidence against the existence of God? To address these questions would get us into controversial issues"…
…and I'm avoiding talking about such controversial issues in the paper. In the situation where God would create more life than there would be if there weren't a God, I'm not convinced that finding that we exist provides evidence for the existence of God, but I'm also not convinced that it wouldn't.
**To olegt: I'm glad you *heart* philosophers, but if so then you should read our footnotes! From footnote 1:
"It is mathematically possible for the universe to be spatially flat and yet finite (as explained by for example Heckmann and Schücking (1962, 441-2)), but such non-standard topologies are usually rejected by physicists."
**To AnaxagorasRules: You say that my paper falls apart because I haven't adequately supported my claim that the universe is spatially infinite, but in fact I don't need to support that claim at all for my paper; I'm just arguing about what the consequences would be if it were spatially infinite. See the start of Section 2:
"While this isn’t strictly speaking necessary for my argument, it’s worth pointing out that the best current evidence from physics suggests that the universe is spatially infinite."
Comment by bradleymonton — March 30, 2009 @ 12:06 am
March 30th, 2009 at 4:36 am
Kind of following on from Bradford, how can you arrive at an infinite universe from the Big Bang (when it had finite size, given a finite amount of time)?
Comment by The Pixie Again — March 30, 2009 @ 4:36 am
March 30th, 2009 at 11:24 am
I flagged up my doubts about apparently an earlier version of this paper two years ago:
http://exilefromgroggs.blogspot.com/2006/03/suspect-weak-paper-against-dembski.html
Same general thesis – that the universe is infinite (questionable premise anyway – certainly the fact that the universe is "flat" would contradict that it has infinite mass => infinite resources for evolution to work on – if it had infinite mass, it would be very, very closed), therefore anything can happen. Same targetting in the paper of Dembski's design inference. If that constitutes the core body of Monton's work for two years ….
Comment by Exile From Groggs — March 30, 2009 @ 11:24 am
March 30th, 2009 at 12:10 pm
Dembski calculated this value and showed that it was, indeed, not zero. That's why all the specific complexity work includes that "so unlikely as to be considered impossible" value, something like 1 in 10^500 as I recall.
Apparently it's because he's wrong. So let's consider why you think it's unexpected for ID critics to criticize someone that's wrong. It's almost as if you think ID critics are taking sides rather than evaluating arguments impartially. Is that because you support anyone on your side?
Comment by don provan — March 30, 2009 @ 12:10 pm
March 30th, 2009 at 12:17 pm
Too funny. How would Bilbo ever get that idea?
Comment by Bradford — March 30, 2009 @ 12:17 pm
March 30th, 2009 at 12:20 pm
Bradley Monton:
Have I been under the misimpression that the universe is finite? Where are our lurking cosmologists?
Comment by Bradford — March 30, 2009 @ 12:20 pm
March 30th, 2009 at 12:52 pm
Bradford:
Well, I’m not a lurking cosmologist, but I do think the multiverse scenario is one possible solution. The multiverse scenario posits that, while our “island” universe is indeed limited and finite, there are infinite other universes out there. One idea is that these other island universes exist in a kind of super space. This super space would then be spatially infinite and temporally eternal. In other words, it would be the true universe. But, how would you ever empirically prove such and idea? How does one prove that anything is infinite?
Comment by JOHN_A_DESIGNER — March 30, 2009 @ 12:52 pm
March 30th, 2009 at 1:00 pm
I've posted more thoughts in reply to this discussion of my paper here:
http://bradleymonton.wordpress.com/2009/03/30/big-bang-infinite/
Comment by bradleymonton — March 30, 2009 @ 1:00 pm
March 30th, 2009 at 1:06 pm
Bradley,
I have read a preprint of the paper on the philsci archive. It does not seem to have footnotes. Glad you're aware of the topology issue. Not sure where you got the idea that "such non-standard topologies are usually rejected by physicists." We don't know the topology of the Universe at this point, so nothing is off the table.
At any rate, that is just one problem that I had with the paper. The other, more severe problem is your careless handling of infinities. That way one can get any answer that one desires, as is illustrated by the Riemann series theorem. You could arrive at completely different answers, as Bilbo pointed out in the opening post.
Comment by olegt — March 30, 2009 @ 1:06 pm
March 30th, 2009 at 4:06 pm
Do you agree with his calculation?
Comment by kornbelt888 — March 30, 2009 @ 4:06 pm
March 30th, 2009 at 6:49 pm
Bilbo:
Actually, we have no idea how improbable spontaneous arising of life is. We also have no idea whether the hypothetical designers of life wanted to concentrate life on one planet or to spread it all over the universe. Hence we have no way of knowing – given that life exists – that designers are more likely than not. There is simply not enough information to decide this, no matter how much you would like your favorite designer to have poofed us into existence. Sorry.
Comment by Raevmo — March 30, 2009 @ 6:49 pm
March 30th, 2009 at 6:56 pm
I also thought the finite age of the known universe (assuming the big bang) and the finite (even constant) speed of light would prevent the universe to be infinite in size. Is this really controversial?
Comment by Raevmo — March 30, 2009 @ 6:56 pm
March 30th, 2009 at 7:27 pm
Raevmo
I agree, in order to decide conclusively we would need some fantastic event like the designer showing up and verifying his credentials with some amazing feat like a resurrection.
Peace
Comment by fifth monarchy man — March 30, 2009 @ 7:27 pm
March 30th, 2009 at 7:47 pm
Hi, Bradley,
In the update to your blog, this paper which you link to, regarding the possibility of an infinite universe, actually points to the opposite as being the case. Namely a universe that may expand forever, necessarily implying a finite universe. Perhaps one could infer an infinite spatial context in which the universe can expand, but that is a leap that is not addressed specifically in that short article.
Back to the statement that I questioned:
That conclusion is not in the form of a conditional, but in the form of a deduction:
A flat universe is infinite. (Your unstated premise)
WMAP shows a universe that is within 1% of being flat.
This is so close to being flat that we can say the universe is infinite.
This conclusion is the jumping off point for the remainder of the paper. But this argument is a poor one, not valid because the conclusion does not necessarily follow from the premises. If you are using a different argument, it is not apparent.
I have a lot of sympathy for people who take an independent stand based on their research, and the last thing I want to do is 'Velikovsky' you, but your point of departure, where you start speculating what happens in an infinite universe, branches off from a passage that, on the face of it, seems to decieve. If you meant that passage as a conditional dealing with possibilities, then I think you should have been more explicit in stating it.
Comment by AnaxagorasRules — March 30, 2009 @ 7:47 pm
March 30th, 2009 at 8:10 pm
Prof. Monton, that would be a good place to leave our disagreement, but I've been doing some thinking since I posted this thread, yesterday, and I suspect that Olegt is correct: We've been handling infinities in arbitrary ways. It's not clear to me that in a spatially infinite universe we could reasonably conclude anything about God or a designer, based on miracles or improbabilities of life.
A man walks on water. But we expect this to happen an infinite amount of times in a spatially infinite universe. Why suspect that God caused this to happen? Why is it more likely to happen under the supposition that God exists, than under the supposition that God doesn't exist?
Now let's suppose that numerous miracles occur: the same man walking on water, stilling the storm, curing the sick, multiplying loaves of bread, raising the dead. But in a spatially infinite universe, we would expect this (a person doing all of this) to happen an infinite amount of times. Why is it more likely to happen under the supposition that God exists, than under the supposition that God doesn't exists?
My design inference suffers the same fate: We find that life on this planet has arisen spontaneously. But in a spatially infinite universe, we would expect the spontaneous appearance of life an infinite number of times. Why would it be more likely to happen under the supposition that a designer exists, than under the supposition that a designer doesn't exist?
Now suppose that we find that life has arisen, not only on this planet, but on every planet in our solar system. But in a spatially infinite universe, we would expect the spontaneous appearance of life on neighboring planets to happen an infinite number of times. Why would it be more likely to happen under the supposition that a designer exists, than under the supposition that a designer doesn't exist?
It looks like being in a spatially infinite universe makes it difficult (if not impossible) to reason from either miracles or improbabilities of life to God or a designer.
Getting back to WMAP: Does it show that the universe was infinite before the Big Bang? Or that the universe will expand infinitely? Or something else?
Comment by Bilbo — March 30, 2009 @ 8:10 pm
March 30th, 2009 at 8:15 pm
Is it?
Are they?
Ask Dembski that.
Comment by Bilbo — March 30, 2009 @ 8:15 pm
March 30th, 2009 at 8:18 pm
Even if we knew that it was true, that the universe is finite, does it mean life is?… Isn’t that the IDers thesis, Prof. Monton? IDers?
Comment by Rock — March 30, 2009 @ 8:18 pm
March 30th, 2009 at 8:26 pm
Because that's how he approaches arguments.
Comment by don provan — March 30, 2009 @ 8:26 pm
March 30th, 2009 at 8:29 pm
Bilbo:
You still don't understand. In a spatially infinite universe where walking on water is impossible we expect this to happen zero times.
Comment by Raevmo — March 30, 2009 @ 8:29 pm
March 30th, 2009 at 8:29 pm
Of course not. Dembski's "calculation" is completely bogus. But the point is that even Dembski couldn't make the probability zero, even with a bogus calculation.
Comment by don provan — March 30, 2009 @ 8:29 pm
March 30th, 2009 at 8:33 pm
And, of course, even that's granting the designers exist. If you consider what we know about the probability of the designers themselves existing — i.e., absolutely nothing — then even these possible avenues of confirming a hypothetical designer evaporate.
Comment by don provan — March 30, 2009 @ 8:33 pm
March 30th, 2009 at 8:35 pm
Given what we know (so far) about nature, I wouldn't expect that to happen anywhere in this universe.
Comment by kornbelt888 — March 30, 2009 @ 8:35 pm
March 30th, 2009 at 8:37 pm
Bilbo wrote:
The short answer is the Universe is flat or close to that. We don't know whether it is finite. The Universe did not exist "before the Big Bang."
A quick summary of WMAP findings is available on the experiment's web site. A short dictionary of the Big Bang cosmology can be found here. You will find there the following passage linking the (local) curvature and (global) geometry of the Universe:
The statement is qualified:
Comment by olegt — March 30, 2009 @ 8:37 pm
March 30th, 2009 at 10:45 pm
You know, you never answered my question way back when: how many popular religions contemporary to Jesus had a leader who was: the son of god and a human woman, died, was buried in a rock tomb, rose from the dead, after three days, and was discovered by women. If ancient texts describing these things can be trusted then I guess people were rising from the dead all the time back then, or perhaps it was simply a common myth.
Comment by Todd Berkebile — March 30, 2009 @ 10:45 pm
March 31st, 2009 at 12:10 am
Todd:
This has been gone over many times at TT. It's not a matter of interpretation either. You don't have to believe in the resurrection to know the rest of the story is historically well documented. The life of Christ, his crucifixion and burial have been written about by non-Christian first century sources in addition to the New Testament writers. Mythologies form well after alleged events and leave no eyewitnesses or historic documents in their wake.
Comment by Bradford — March 31, 2009 @ 12:10 am
March 31st, 2009 at 12:23 am
Hi, Todd,
If you are alluding to the Romans or the Greeks, whose lineages went back to Zeus or Apollo or some other ancient diety, keep this reading from Genesis in mind:
(KJV) 14 And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: 15 And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so.
26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. 27 So God created man in his own image, in the image of God created he him; male and female created he them.
In contrast to many religions of antiquity, the ancient Hebrews did not believe that the stars and moons were gods (as the Cannanites or Sumerians did, for example), but were products of the one God, who put the sun, stars, and moon in the heavens for the convenience of humanity. Also, man was created in God's image.
I'm somewhat familiar with the ancient 'pagan' religions and their myths, but I've never heard of a Hebrew myth of a resurrection other than with Jesus, and believe the one involving him to be singular with respect to the ancient Hebrews (or primeval Christians, I suppose). Are you familiar with another resurrection story?
Comment by AnaxagorasRules — March 31, 2009 @ 12:23 am
March 31st, 2009 at 6:01 am
Bradley Monton has posted this from his book in response to comments on this thread:
It was my understanding that the expansion of the universe since the Big Bang was the expansion of space, rather than the expansion of the universe into a pre-existing space, but I am not a physicist, so I will assume either Monton is correct, or that this is not known either way. In the paper he says:
Monton moves here from a spacially infinite universe, to a universe with infinite planets (and so presumably infinite stars, galaxies, etc.), and therefore infinite mass. Does this imply a Big Bang event that produces a singularity with infinite mass, and that an infinite number of stars rapidly expands out into the universe? Or was there an infinite number of Big Bangs, each producing a finite number of stars within a spacially infinite universe?
Furthermore, if the Big Bang occurs within already extant and spacially infinite universe, then that would suggest that the Big Bang had a specific spacial location within that universe. We would expect all the galaxies produced in that event to be distributed in a sphere around that point, and I would guess that distribution would be a function of the distance from the Big Bang point. As far as I am aware, no one has proposed any such distribution of the galaxies.
Comment by The Pixie Again — March 31, 2009 @ 6:01 am
March 31st, 2009 at 8:10 am
Pixie:
The nature of the universe is a point of interest to many of us and I note on this thread that Pixie and others have expressed surprise at the notion of an infinite universe. The surprise crosses the usual ID/non-ID divide. Also unusual is that noone has waded in with an expert opinion which usually occurs on matters like this. I'm used to someone posting a comment explaining and referencing the explanation with linked studies. Strange.
Comment by Bradford — March 31, 2009 @ 8:10 am
March 31st, 2009 at 8:21 am
Bradford,
I am not an expert in cosmology, but I did post a comment with links.
Comment by olegt — March 31, 2009 @ 8:21 am
March 31st, 2009 at 8:50 am
Olegt:
Thanks for that Olegt. That is a good website which I'll go back to. I just have one point to make which probably reflects my lack of knowledge. The site states that the BB model is based on two theoretical pillars- General Relativity and the Cosmological Principle. Years ago when I read about Hubble's work and red shifts and an expanding universe I thought that an argument for the BB was that if you went back in time and were able to observe a less and less expanded universe you would eventually reach a point of matter condensing back into the white whole it emerged from if that is even the correct terminology. Is that not a valid argument for the BB?
Comment by Bradford — March 31, 2009 @ 8:50 am
March 31st, 2009 at 9:07 am
From the NASA site olegt linked to:
So it seems the universe can be infinite at the Big Bang. I also found this page helpful (sections III and IV).
Comment by The Pixie Again — March 31, 2009 @ 9:07 am
March 31st, 2009 at 10:01 am
There are Hebrew resurrection myths arising largely from their rebellion against the Romans. There are myths that generals felled in combat against the Romans would be rewarded by god with resurrection after three days. I'd love to discuss this and Bradford's reply more, but it seems off-topic for this thread. Perhaps a topic for the next open thread. I only mentioned it here because FMM used it as evidence that design should be assumed to require a designer.
Comment by Todd Berkebile — March 31, 2009 @ 10:01 am
March 31st, 2009 at 12:42 pm
Pixie quoting the NASA site:
An infinite universe would mean an infinite amount of mass and energy. A finite universe would mean finite matter and energy. Are there means of testing that approach i.e. ways of distinguishing infinite from finite matter? Or is the finite/infinite contrast resolvable even in principle?
Comment by Bradford — March 31, 2009 @ 12:42 pm
March 31st, 2009 at 1:25 pm
Todd,
you did this same thing in another thread in which you were looking for people to engage you on the topic. I responded to the pagan copy cat claim to which you didn't respond.
Comment by GringoRoyale — March 31, 2009 @ 1:25 pm
March 31st, 2009 at 2:24 pm
Raevmo writes:
"You still don't understand. In a spatially infinite universe where walking on water is impossible we expect this to happen zero times."
This confuses physical with logical impossibility. The probability of an event is zero only if it is logically impossible. If it is physically "impossible" there is still a miniscule probability that it could happen and thus, were there an infinity of trials, it should occur an infinity of times.
A second point about Prof. Monton's argument. Even if Prof. Monton's assumption about an infinite universe is correct his argument rests on a second assumption that the rest of the universe is like the observable portion in terms of its material structure. If, however, the unobservable portion of the universe consists solely of a thin distribution of hydrogen gas there's no reason to think that, however vast it is, it would produce life.
Comment by Dick — March 31, 2009 @ 2:24 pm
March 31st, 2009 at 2:54 pm
Dick:
I'm not so sure about that. For example, it certainly depends on whether your set of trials is countably infinite or uncountably infinite (in other words the cardinality of your set of trials). If you sample countably infinitely many times from a normal distribution, you will almost certainly not get the (exact integer) number 1 infinitely many times. Indeed you may never draw the number 1.
Is the probability greater than zero that I will bike to work tomorrow at a speed greater than the speed of light, and survive it?
Comment by Raevmo — March 31, 2009 @ 2:54 pm
March 31st, 2009 at 4:46 pm
Hi Raevmo,
I shortened Monton's argument for convenience. It's clear from his paper that whether or not a man walking on water would have a probability of zero, he's willing to assume that it is greater than zero. From his paper:
I agree that if Monton was arguing that miracles have a probability of zero, then his argument that miracles are good evidence for God, even in a spatially infinite universe, would have been stronger.
I think it depends on whether we can imagine some physical circumstance under which that could happen.
Comment by Bilbo — March 31, 2009 @ 4:46 pm
March 31st, 2009 at 7:15 pm
I apologize, my work schedule means I often cannot keep up with the volume of posts around here.
Comment by Todd Berkebile — March 31, 2009 @ 7:15 pm
March 31st, 2009 at 8:19 pm
Actually, such a fantastic event would prove nothing at all about creation or that designer's role in it. About the best such a designer could do is establish that He's powerful enough that it would be unwise to argue with him about what he claims.
Comment by don provan — March 31, 2009 @ 8:19 pm