Is it ever reasonable to infer impossibility from high improbability?

Question

For context, please refer to the section Biological Information: Beyond the Reach of Chance (pages 10-12) in DNA by Design: An Inference to the Best Explanation for the Origin of Biological Information by Stephen C. Meyer.

I’ll quote two brief excerpts from this section (you can read the rest at the link above):

While many outside origin-of-life biology may still invoke “chance” as a causal explanation for the origin of biological information, few serious researchers still do.33 Since molecular biologists began to appreciate the sequence specificity of proteins and nucleic acids in the 1950s and 1960s, many calculations have been made to determine the probability of formulating functional proteins and nucleic acids at random. Various methods of calculating probabilities have been offered by Morowitz, Hoyle, Cairns-Smith, Prigogine, Yockey, and more recently, Robert Sauer.34 For the sake of argument, these calculations have generally assumed extremely favorable prebiotic conditions (whether realistic or not), much more time than was actually available on early Earth, and theoretically maximal reaction rates among the constituent monomers (i.e., the constituent parts of the proteins, DNA, and RNA). Such calculations have invariably shown that the probability of obtaining functionally sequenced biomacromolecules at random is, in Prigogine’s words, “vanishingly small . . . even on the scale of . . . billions of years.”35 As CairnsSmith wrote in 1971:

Blind chance . . . is very limited. Low-levels of cooperation he [blind chance] can produce exceedingly easily (the equivalent of letters and small words), but he becomes very quickly incompetent as the amount of organization increases. Very soon indeed long waiting periods and massive material resources become irrelevant. 36

More realistic calculations (taking into account the probable presence of nonproteineous amino acids, the need for specific functional proteins of considerable length, and the need for multiple proteins functioning in coordination) only reinforce these results. For example, recent theoretical and experimental work on the so-called “minimal complexity” required to sustain the simplest possible living organism suggests a lower bound of some 250 to 400 genes and their corresponding proteins.41 The nucleotide sequence space corresponding to such a system of proteins exceeds 4³⁰⁰⁰⁰⁰. The improbability corresponding to this measure of molecular complexity vastly exceeds the most conservative estimates of the so-called “universal probability bound” of 1 chance in 10¹⁵⁰, the point at which appeals to chance become absurd given the “probabilistic resources” of the entire universe.42 Thus, when one considers the full complement of functional biomolecules required to maintain minimal cell function and vitality, one can see why chance-based theories of the origin of life have been abandoned. What Mora said in 1963 still holds:

Statistical considerations, probability, complexity, etc., followed to their logical implications suggest that the origin and continuance of life is not controlled by such principles. An admission of this is the use of a period of practically infinite time to obtain the derived result. Using such logic, however, we can prove anything.43

The main conclusion in this section is that, even under the most optimistic conditions, the probability of life originating by chance is so low that we can confidently infer chance was not the cause.

In other words, the argument moves from extreme improbability estimates to inferring impossibility.

Is this kind of inference ever justified, either in this specific context or in any other context?

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NOTE: This is follow-up discussion to Are there any fallacies in arguments for design from DNA?

Answer 1

For the word to be useful in everyday life, the word "impossible" must colloquially mean nothing but very improbable. Because we can never rule anything out with perfect certainty.

In quantum mechanics there is a nonzero chance for any particle to be found anywhere. Thus, there is a nonzero chance all the particles in your body could quantum tunnel to the Moon in the next five seconds. There is a nonzero chance for practically any sequence of events; entropy could by chance decrease, water could flow uphill, your cat could spontaneously turn into a chicken (quantum tunneling again). But we say these things are impossible because the probability is so small. If we refused to say these kinds of things are impossible, then we would be unable to use the word "impossible" usefully at all.

The argument against evolution you quote hinges on whether the probability really is as low as they claim. Typically, creationist calculations of extreme improbability assume that the organism needs to get all the pieces right at once to be viable, and neglects intermediate forms. The argument you quote claims the simplest possible organism has 250 genes and 40 proteins, but prions have properties similar to life and are just single proteins with no genes. Descriptions of the origins of life usually involve, first, naked self-replicating molecules (like prions) - no DNA, no genes. Then some of the molecules encased themselves in lipids, forming a primitive cell membrane. RNA probably came after that, and DNA after RNA.

It also depends on how many times there was a chance for evolution to start on different planets. Evolution didn't have to happen on Earth specifically; perhaps there are trillions of planets in the habitable zone, so if the chance of it happening on a particular planet is one in a trillion, then there are better than even odds it would happen somewhere.

There's also the possibility that evolution could have gotten started with many different chemical bases. So even if the chance it started on Earth with our particular chemistry is low, that doesn't mean the chance it started on Earth is low, because you have to sum for each possible chemistry, of which there might be a large number.

Answer 2

Imagine that you had a fair die with 10²⁰⁰ sides (I don't know if a die with exactly that many sides could be fair, but presumably there are possible fair dice of that order of magnitude). When you roll this die, and it lands on, say, 1,678,223, then there was a 1/(10²⁰⁰) chance of it landing on that specific side. Same if it landed on 744, or 3,330, or whatever. Does this make it impossible for the die to have landed on the side that it did? Or why would we infer that the die was unfair (that there was an intelligent gambler, so to say, who designed the die to land on some specific side) from its landing on some side?

On an even more technical level, there are versions of probability theory where even a probability of 0 is not grounds for impossibility:

... many applications of probability require what are known as continuous distributions (such as the uniform/rectangular, normal, and beta distributions), and thus require a restriction to countable additivity. In a continuous distribution, there are uncountably many states, usually named by real numbers. Each individual state has probability 0, even though events containing uncountably many states often have non-zero probability. (This violates full additivity.) However, in the common continuous distributions, there is usually a way to define a probability density for each state, such that the probability of any event is the integral of the density over the states that make it up. In finite and discrete distributions, it is standard to treat events of probability 0 as if they do not happen, while in continuous distributions there is always some event of probability 0 that occurs.

Answer 3

In this specific context, it is absolutely not justified to give a actual number to what an upper bound is.

Meyers references the "universal probability bound" proposed by Dembski. Dembski estimates this based on the available matter, reaction rate, and time elapsed in the observable universe. Such a limit makes no sense in this context.

There is no reason to have the limit as the observable universe, because the universe doesn't have to be in our observable sphere for life to arise. That's getting causality backwards.

Such a reaction only had to take place anywhere in the entire universe, and then the observable universe becomes the sphere where those living beings have access to information (due to age of the universe and speed of light). We only know the size of the observable universe, not the entire universe, so Dembski's numbers are based off the wrong size values, and thus mean nothing.

Answer 4

If you are using "infer" and "impossible" in their strict sense, then no: low, non-zero probability does not allow one to infer impossibility.

Even some zero-probability events are not impossible.

If you are using either "infer" or "impossible" more loosely, then sure, as causative says. Although I disagree that "we can never rule anything out with perfect certainty." We can: rolling an 8 on a six-sided die with the outcomes {1,2,3,4,5,6} is impossible.

Answer 5

The main conclusion in this section is that, even under the most optimistic conditions, the probability of life originating by chance is so low that we can confidently infer chance was not the cause.

My counter-argument is:

The chances that these researchers, even under the most optimistic conditions, have an absolute and complete understanding of how life originated in every part of the universe is so low, that I can confidently infer that they are wrong.

The content provided contains a potential logical fallacy known as an "Argument from Ignorance" or "Argumentum ad Ignorantiam." This type of fallacy occurs when it is asserted that a proposition is true because it has not been proven false or vice versa.

In the given statement, the conclusion is that because the probability of life originating by chance is so low, we can confidently infer that chance was not the cause. This statement assumes that because one explanation (chance) seems improbable, it must therefore be incorrect. However, just because something is improbable does not necessarily mean it did not or could not occur. Furthermore, without considering other potential explanations or evidence, the conclusion drawn may be based on incomplete reasoning.

Additionally, the fallacy could also be considered an "Appeal to Probability," where it is assumed that because something is possible, or improbable, it must necessarily happen or not happen. The statement implies a certainty ("confidently infer") based solely on probability, which doesn't account for other contributing factors or evidence that could affect the outcome.

Therefore, the logical error lies in drawing a definitive conclusion based solely on the improbability of one scenario without considering other possibilities or evidence.

Answer 6

In a quantum world, anything that actually happens has a very low chance of happening. So no, improbable doesn't mean "impossible". On the contrary, it means "possible".

The following response was prepared for your previous question on DNA, which is now closed. Hope it helps.

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These arguments are primarily based on our ignorance about the origins of life on earth, or in the universe for that matter. We're presented with a "god-of-the-gap" here.

After Darwin, a philosopher announced the death of one of them, but there are still a few around. I can count at least three gaps in our current scientific understanding of the universe, each currently occupied by a god-of-the-gap (GOTG):

1. Why does the universe exist, and why so gigantic and amazing?
2. How did life emerge from inanimate matter?
3. How did thoughts, reason, logic and art emerge from life? This is also known as the mind-body problem.

I mention these three gaps because they connect to one another in interesting ways (which gives some folks reason to believe that the GOTGs behind those 3 gaps are one and the same). I believe that gap 3 (origin of consciousness) will be easier to solve than gap 2 (origin of life) because life is already a bit like language. Life is information bossing matter around. If the dinosaurs had had the opportunity to live and multiply a little longer, one day a dino smarter than the others would have appeared, almost by necessity. It was bound to happen IMO.

Gap 1 may never be solved by science, it's the biggest question one could ask. We will answer it the last, if we ever make it that far. So there will always be at least one GOTG around. Gap 1 connects with gap 2 through the panspermia hypothesis: life may not have appeared on earth; it may have come from elsewhere in the universe.

Gap 2 looks like an impossible gap to breach scientifically right now, hence there are many GOTG arguments here, including the ones you mentioned. So let's review them (first article only):

Origin of Information: The properties of matter alone do not explain the origin of biological information, and blind chance becomes inadequate due to the immense improbability of specific arrangements, like in functional DNA or proteins. [...]

Information is universal, because there is no matter without form, and form is information. Life did not invent it but built on it. What life brings is not form, not even complex form, but forms that can replicate themselves. What I call form bossing matter around. And that takes complexity to a whole new level, where "things", e.g. complex of proteins and cells, appears to behave in a goal-oriented manner.

What life brings, is teleology. And the response of believers is to say, Well there's no problem at all, life did not create teleology, because teleology was there all along, before life, in god(s). IOW they say that teleology created life on earth, not vice-versa. Or if you prefer: the universe was already alive with god(s), before they created life on earth. It's a bit facile I think because the next question is obviously: Where do those gods come from?

Similar objections apply to panpsychism.

I.e. we're left with the same question: whence teleology? The hypothesis of gods does not really help. It is a bit the same with panspermia: sure, life on earth could have come from space either by some civilization spreading the seed (the gods) or accidentally. But we're left with the same gap #2: how did life originally spring from inert matter, on earth, in gods, or anywhere else?

Scientific Laws and Self-Organization: Proposed naturalistic models like scientific laws or self-organization [...] fail to account for the origin of biological complexity [...]

This is true at time T, it may become false tomorrow. FYI the current leading hypothesis is being developed under the concept of RNA world. It's a very exciting set of ideas which posits a prior stage to life, before DNA, before cells even, when an RNA "soup" was progressively complexifying, mutating and replicating.

The RNA world hypothesis helps solve the chicken and egg question of DNA and proteins, evoked in your OP: Who was first, the DNA that codes for proteins, or the proteins that help store, currate and read DNA? In our own cells, RNA is positioned between DNA and proteins in the transcription process: it transmits the genetic code from chromosomes (DNA) to ribosomes 1, sorts of immensely complex nano mechanisms made mainly of RNA themselves, that translate the genetic code into the specific protein each gene codes for. The point is that RNA is at the heart of information management in our cells, and in more ways than one as the latest Nobel for medicine illustrates. RNA is the heart of life, NOT DNA, which is only a storage device. So the hypothesis of a pre-DNA version of life is attractive. The idea is that RNA multiplied, it domesticated proteins, and then used DNA as its backup storage. Et voilà!

Intelligence as a Cause: High-[...] Experience in various fields (e.g., archaeology, SETI) suggests that information-intensive systems originate from intelligent agents.

Whence these intelligent agents, then? Where do they come from? Once again that's only kicking the can down the road.

Inferences to Design: [...]The presence of high information content in a system, exceeding 500 bits (as calculated by Dembski), strongly implies intelligent design due to the inadequacy of chance or naturalistic explanations.

Same as above: just because we don't have one yet, doesn't mean we will never find a good naturalistic explanation. We're far from one but we're making progress.

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1 Just to give an idea of the level of complexity we're talking about, here is a bird-eye, simplified map of bacterial and eukaryotic ribosomes (made of RNA):