Randomness Article in the Latest Issue of the BJPS

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Randomness Is Unpredictability
Antony Eagle
Exeter College and Oxford University, Oxford OX1 3DP, UK

The British Journal for the Philosophy of Science 2005 56(4):749-790; doi:10.1093/bjps/axi138

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid.

1. Randomness in science
1.1 Random systems
1.2 Random behaviour
1.3 Random sampling
1.4 Caprice, arbitrariness and noise

2. Concepts of randomness
2.1 Von Mises/Church/Martin-Löf randomness
2.2 KCS-randomness

3. Randomness is unpredictability: preliminaries
3.1 Process and product randomness
3.2 Randomness is indeterminism?

4. Predictability
4.1 Epistemic constraints on prediction
4.2 Computational constraints on prediction
4.3 Pragmatic constraints on prediction
4.4 Prediction defined

5. Unpredictability

6. Randomness is unpredictability
6.1 Clarification of the definition of randomness
6.2 Randomness and probability
6.3 Subjectivity and context sensitivity of randomness

7. Evaluating the analysis

[R]andomness … is going to be a concept which is relative to our body of knowledge, which will somehow reflect what we know and what we don’t know. Henry E. Kyburg, Jr ([1974], p. 217)

Phenomena that we cannot predict must be judged random. Patrick Suppes ([1984], p. 32)

16 Replies to “Randomness Article in the Latest Issue of the BJPS

  1. 1
    es says:

    Dear William,

    I’ll give it one more try, the previous attempts to get an answer from you were unsuccessful.
    Here are my previous posts in this blog for reference:

    In your Primer on Probability ( )

    you write, “(2) Frequentist approach — probability is a relative
    frequency (i.e., the number of occurrences of an event divided by the number of observed
    oppporutnities for the event to occur; relative frequencies are also called empirical probabilities).”

    Why do you argue against empirical probability (“happen all the time”) when you say that “highly improbable events happen by chance all the time,” “exceedingly improbable things happen all the time,” and on the backcover of your new book – “Just about anything that happens is highly improbable” ???

    I will not post here anymore if you ignore me again this time, but the problem will not go away.

    I am sure by now you understand the problem, why not admit a mistake and make a correction?

  2. 2
    Shane says:

    es – others have already addressed you and explained that this is a semantic issue only. Why can you not accept their responses?

  3. 3
    es says:

    Shane – none of those who responded have addressed the problem that I outlined. Why should I accept opinions of others where there is no logic to their reasoning?

  4. 4

    ES previously wrote: “In view of frequency interpretation of probability “highly improbable events happen by chance all the time” means “Highly infrequent events happen frequently.”

    My reply: Even within the frequency interpretation, frequencies are not exclusively used to assign probabilities. The axioms of probability apply as well as assumptions about probabilistic independence. Frequency establishes that homogeneous rigid disks with distinguishable sides (i.e., coins) land on each side roughly 1/2 of the time. That, in turn, establishes that any particular sequence of N coin tosses will land with probability (1/2)^N. Now toss a coin N times. What is the probability of that event? Do such events happen all the time?

    [By the way, the article summarized at the start of this thread cites my paper “Randomness by Design“]

  5. 5
    es says:

    Shane, with all due respect, the problem is not a ‘semantic issue’, i.e. a arising from the different meanings of words or other symbols.

    If you don’t understand the meaning of ’empirical probability’ as explained by William, perhaps you should not comment here on the subject you don’t comprehend.

    If William is not going to answer – so be it. The problem is not going away.

  6. 6
    es says:

    OK, we are getting somewhere. Glad to see a response from you!

    ” Now toss a coin N times. What is the probability of that event?”


    “Do such events happen all the time?”

    Such events do happen all the time.

    Shall we continue?

    [I’m afraid you would fail an introductory probability course. At any rate, you’ve failed the requirements to continue with this blog. You’re out of here. –WmAD]

  7. 7
    DaveScot says:

    I’ve always understood random to mean unpredictable. The problem I encounter is whether anything is truly unpredictable if you have enough information and computational ability. My gut tells me the universe is deterministic but if you’re omniscient that’s gotta be majorly boring so the omniscient creator of the universe invented beings with non-deterministic free will to shake things up and keep it interesting.

  8. 8

    A question just occurred to me. If everything is under divine providence, hypothetically (although I do believe that), how would you filter that out when you search for design? In other words, if everything is a product of intelligence and nothing is random, how would we look for special cases? I’m not expressing myself clearly, but I think I got the jist across.

  9. 9
    crandaddy says:

    Hi Geoff,

    Theists like you and me believe that all of nature is designed by a supernatural Creator, but such a belief cannot be subjected to scientific observation. What design theorists try to do is look for patterns in nature which stand apart from the background noise of understood physical processes and determine whether or not these patterns are best explained as being the result of intelligence. Understand that a design inference cannot prove absolutely that a pattern is intelligently designed or tell who or what the designer is. Are you familiar with Dr. Dembski’s “Explanatory Filter”?

  10. 10

    I’ve heard of it but I need to read more.

  11. 11
    RyanLarsen says:

    Adding to what Dave said. The “random” shuffling of a deck of cards is often cited as an example of improbable things happening all the time. eg~ “What are the odds that they would be in precisely that order? And yet they are!” Of course, there was a 100% likelihood of them being in that order because the person who shuffled the cards PUT THEM IN THAT ORDER! They moved in deference to the forces acting on them. A more extreme example is a glass of water from a tap. When the glass is full you could say,”What are the odds that the molecules of water would end up in their exact places? (at that given moment)” This could be used as an example of a highly improbable thing happening. But the molecules of water were merely moving in deference to the forces acting on them. It was not truly improbable at all. What would be improbable is if the tap is turned on and out comes freshly squeezed lemon juice. We would not expect that to be the result of the forces acting on the water. And yet no one would say, “that’s no big deal, it’s just lemon juice. Improbable things happen all the time.” No, someone would suspect that someone was playing a joke on them or, perhaps, human error.

    By the way, for anyone interested, I dug up a real gem of a quote from Carl Sagan in his influential paper *The Quest for Extraterrestrial Intelligence*:

    “It is easy to create an interstellar radio message which can be recognized as emanating unambiguously from intelligent beings. A modulated signal (“beep,” “beep-beep,” ) comprising the numbers 1, 2, 3, 5, 7, 11, 13, 1 7, 19, 23, 29, 31, for example, consists exclusively of the first 12 prime numbers-that is, numbers that can be divided only by 1, or by themselves. A signal of this kind, based on a simple mathematical concept, could only have a biological origin. No prior agreement between the transmitting and receiving civilizations, and no precautions against Earth chauvinism, are required to make this clear.
    Such a message would be an announcement or beacon signal, indicating the presence of an advanced civilization but communicating very little about its nature…”

    Again, that’s Carl Sagan, in his paper The Quest for Extraterrestrial Intelligence.

  12. 12
    bradcliffe1 says:


    The prime number sequence you cited from Sagan’s paper is exactly the way that Ellie Arroway, the heroine of Sagan’s novel Contact, discovers the existence of an advanced extraterrestrial civilization.

    It’s a good book. You might want to read it (or see the movie adaptation starring Jodie Foster).

  13. 13
    RyanLarsen says:

    Thanks, Brad,

    I thought that the way Sagan phrases some of his claims regarding the sequence could be particularly strong ammunition against anti-IDer’s. For example:

    “It is easy to create an interstellar radio message which can be recognized as emanating unambiguously from intelligent beings”

    “A signal of this kind…could only have a biological origin”

    “No prior agreement between the transmitting and receiving civilizations, and no precautions against Earth chauvinism, are required to make this clear.”

    The argument is often raised that intelligent design can not be inferred when there is no direct knowledge of a potential designer. But, as Sagan points out, we don’t need to know anything about the designer in order to infer design. Opponents of design would have to explain why they disagree with Sagan, and they would have a hard time arguing that Sagan was wrong on this one.

  14. 14
    DaveScot says:


    Nice work with the Sagan quotes. I’m beginning to think you might escape banning. 😉

    I’ve read hundreds upon hundreds sci-fi novels beginning in the 1960’s with Heinlen, Asimov, and Clarke. That was in the 7th grade when I got to the high school library. Right about that time I finished memorizing the World Book Encyclopedia and annual science supplements so needed some new material to explore. It was a love affair that’s gone on for almost 40 years now. This certainly colors my world and keeps me open minded to the possibility of advanced civilizations not supernatural but, as Arthur C. Clarke famously put it “Any sufficiently advanced technology will appear as magic.” So maybe the apparent works of God in the machinery of life on earth are merely the works of a sufficiently advanced technology. Certainly the universe is old enough and big enough to keep alive the possibility that we aren’t the first intelligence to emerge in it. I will, however, concede that SETI has been a huge disappointment so far and while negative evidence is never a proof the accumulation of mountains of negative evidence (can a negative pile up?) at some point becomes persuasive.

  15. 15
    RyanLarsen says:


    Good to hear that you like me…

    I wish I had the patience to read. I like stories but reading has always been a chore for me. Oh, I have no problem writing, but opening something up and turning pages is difficult for me. I’m glad you enjoyed the Sagan quotes and I hope they come in handy. I figured something specific like that would be more powerful than a general description of SETI.

  16. 16
    Red Reader says:

    To es
    [I’m afraid you would fail an introductory probability course. At any rate, you’ve failed the requirements to continue with this blog. You’re out of here. –WmAD]
    Dr. Dembski has written the formal requirements for this blog:

    But my observation of what is appreciated is:
    – honesty
    – openmindedness
    – willingness

    It’s not that hard.

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