A matter of chance

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I've observed from time to time, half-seriously, that the ambiguity of plural noun-phrase comparison ("women have better hearing than men") causes — as well as results from — the tendency to interpret small group differences as essential group characteristics (e.g. "The Pirahã and us", 10/6/2007; "Annals of essentialism: sexual orientation and rhetorical assymmetry", 6/18/2008; "Pop platonism and unrepresentative samples", 7/26/2008; 'The happiness gap returns", 7/26/2008;. "Reverse Whorfianism and SHAs", 12/23/2008).

But there are other, more lexically specific, sources of confusion about statistical concepts and statements. One that I noticed for the first time yesterday is an ambiguity in the word chance. Its popular use in the sense of probabilistic odds ("little chance of success"; "his chances are good" , etc.) is relatively recent, and has always overlapped with an older meaning that emphasizes complete unpredictability and the lack of any discernable cause.

This history helps explain the shocking sentence that I read yesterday on the online front page of the New York Times; "A longtime trainer uses an actuarial approach to predict injuries, defying the assumption that what happens to players is a matter of chance".

The Society of Actuaries will be surprised to see "an actuarial approach" characterized as "defying the assumption that what happens … is a matter of chance", since their web site tells us that

Actuaries use mathematics, statistics and financial theory to study uncertain future events, especially those of concern to insurance and pension programs. They evaluate the likelihood of those events, design creative ways to reduce the likelihood and decrease the impact of adverse events that actually do occur.

And the American Statistical Association may wonder whether it should reconsider the name of its magazine, Chance.

The OED gives the following etymology for chance:

[ME. chea(u)nce, a. OF. cheance (= Pr. cazensa, It. cadenza):–late L. cadentia falling, f. cadent- falling, pr. pple. of cad-ĕre to fall: cf. CADENCE.]

The ASA's magazine is named for the OED's sense 5.a., "A possibility or probability of anything happening: as distinct from a certainty: often in plural, with a number expressed".

1778 T. JONES Hoyle's Games Impr. 153, I would know how many Chances there are upon 2 Dice..The Answer is 36. 1785 REID Int. Powers 626 The doctrine of chances is a branch of mathematics little more than an hundred years old. 1841-4 EMERSON Ess. xix. Wks. (Bohn) I. 239 Unless the chances are a hundred to one that he will cut and harvest it. 1848 MACAULAY Hist. Eng. I. 215 There was no chance that..the scheme..would be supported by a majority. 1879 LUBBOCK Sci. Lect. i. 7 The chances against any given grain reaching the pistil of another flower are immense.

The NYT teaser is apparently using the OED's sense 6, "Absence of design or assignable cause, fortuity; often itself spoken of as the cause or determiner of events, which appear to happen without the intervention of law, ordinary causation, or providence". This meaning seems to be older:

1526 Pilgr. Perf. (W. de W. 1531) 144b, In cases of chaunce or vncertaynty. 1581 J. BELL Haddon's Answ. Osor. 160b, Those whiche..doe committe the successes of thynges to happe hazard, and blynd chaunce. 1641 BROME Jov. Crew II. Wks. 1873 III. 389, I ha' not so much Wealth to weigh me down, Nor so little (I thank Chance) as to daunce naked. 1722 WOLLASTON Relig. Nat. v. 83 Chance seems to be only a term, by which we express our ignorance of the cause of any thing. 1802 PALEY Nat. Theol. xii. §2 (1819) 198 A conformation so happy was not the gift of chance. 1841-4 EMERSON Ess. xiv. Wks. (Bohn) I. 183 The ancients, struck with this irreducibleness of the elements of human life to calculation, exalted Chance into a divinity. 1846 MILL Logic III. xvii. §2 It is incorrect to say that any phenomenon is produced by chance; but we may say that two or more phenomena are conjoined by chance..meaning that they are in no way related through causation.

The actual NYT article in question (Michael S. Schmidt, "Seeking a Way to Predict Baseball Injuries", NYT, 8/7/2009) presents a clear picture of the issues involved:

The ability to predict how players' bodies will fare is a holy grail. With an actuarial approach, [Stan] Conte [the Dodgers' head athletic trainer] seems to have a head start in the pursuit. He is trying to build a formula that would give teams a competitive advantage and help them avoid players who spend their days in the training room and not on the field.

"The insurance industry has made millions of dollars off figuring out how, when, where and why people are going to die, and we are trying to figure those things out about injuries," Conte said.

But: it also explicit suggests that if something is "a matter of chance" or "a matter of luck", then it must be completely random and unpredictable:

Conte believes the long-prevailing belief in baseball that injuries are a matter of chance is misguided.

"I refuse to think we are doing all these things to get them healthy, and it's a matter of luck whether lightning hits or doesn't hit," he said.

[Update: Note that there are plenty of difficult philosophical and practical questions in the area of probability, uncertainty, ignorance, and causation — see e.g. here. But what underlies examples like those cited above seems to be too little thought about such puzzles, rather than too much. ]



42 Comments

  1. James said,

    July 9, 2009 @ 7:45 pm

    Quite right, about the older meaning of 'chance'. I remember being very puzzled the first time I read Hume on the topic:

    THOUGH there be no such thing as Chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion.

    There is certainly a probability, which arises from a superiority of chances on any side; and according as this superiority increases, and surpasses the opposite chances, the probability receives a proportionable increase, and begets still a higher degree of belief or assent to that side, in which we discover the superiority.

    From the Enquiry, where it seems that both senses are in play at once.

  2. Mark P said,

    July 9, 2009 @ 8:19 pm

    They seem confused to me. On one hand, it sounds like they intend to use statistics to determine the probability of injuries to their team's players, like determining the probabilities of auto accidents. On the other hand, they seem to plan to identify individual players who have a history of injuries. I think those are two different things.

  3. Isabeau said,

    July 9, 2009 @ 8:31 pm

    I've said more than once, "I don't believe in luck, I believe in chance." Hardly anyone gets it.

  4. Noetica said,

    July 9, 2009 @ 11:32 pm

    In that Hume excerpt from James, chance occurs three times. Arguably only the last two reflect the earlier sense, well captured as "falling", in closer accord with the etymology. Images of falling are still often used for chance events: "the fall of the dice", "as things fell", and so on. Two senses in the SOED entry "fall v.":

    20 (Of a lot, choice, etc.) chance on, light on; be allotted or apportioned to; come as a burden or duty to, devolve (up)on. ME.

    22 Come into a specified state or position (by chance, naturally, in the course of events, or unawares); pass into (†in, †to) a specified state or position. ME.

    And of course, it is the completion of the falling that really matters: the outcome. That is what is unpredicatable. The completion is marked perfectively in English: "falling out".

    We recall Lucretius, whose De Rerum Natura is famous for its treatment of chance. Atoms fall: they move straight downwards, since that is their natural tendency. When they come to rest (fall out, however temporarily) in some configuration of interest, why is the exact pattern unpredictable and variable? There must be some other cause of movement than the inevitable downward fall. Here's how it is explicated in Stanford Encyclopedia of Philosophy, "Lucretius":

    The most celebrated part of this account, however, is at 2.216-93, where Lucretius maintains that not only to explain how atomic collisions can occur in the first place, but also to account for the evident fact of free will in the animal kingdom, it is necessary to postulate a minimal indeterminacy in the motions of atoms, an unpredictable 'swerve' (clinamen) 'at no fixed place or time. Otherwise we would all be automata, our motions determined by infinitely extended and unbreakable causal chains. A striking resemblance to the indeterminacy postulated by modern quantum physics – which has also often been invoked in debates about determinism – has helped make this passage the subject of particularly intense debate.

    From such a metaphysical "back-story", I would argue, arise many of our less examined notions of chance, thought of objectively or subjectively or some spongy mixture of the two. And we see already in Lucretius the same meta-uncertainty that arises from Heisenberg's uncertainty principle – is the indeterminacy "out there" in the world, or just a deep epistemological limitation? The use of the term unpredictable alone does not settle things; nor does Lucretius, with "incerto tempore ferme incertisque locis spatio" ("at no certain fixed time and no certain place"), take an unequivocal stance.

    Traditional interpretations of Hume's general program have assumed that he is making a metaphysical claim about the indeterminacy of things; but some current accounts argue for an epistemological reading. However these interpretations weigh up, it is interesting to see how these meta-uncertainties have been perennial and recalcitrant – and to be reminded of how they still are, by Mark Liberman's post.

  5. Mark F. said,

    July 10, 2009 @ 12:10 am

    I once was a TA in a statistics class where we were discussing the apparent absence of a "hot hand" effect in basketball (i.e., that the length of shooting streaks actually observed is what you'd expect if players were flipping a weighted coin that matched their overall shooting percentage). I think this was described along the lines of "hits and misses are random", and it was very hard to disabuse students of the idea that we were saying that talent played no role. One student kept interpreting the "no hot hand" claim as "it's just 50-50" when a player takes a shot.

    [(myl) Did that student by any chance go on to a career in journalism?

    More seriously, I dimly recall an article arguing that the "hot hand" phenomenon is at least sometimes real, based on the career statistics of Vinnie "the human microwave" Johnson. But either my memory is faulty, or no trace of this work survives on the web.

    No, here it is, cited in Michael Bar-Eli et al., "Twenty years of 'hot hand' research: Review and critique", Psychology of Sport and Exercise 7(6): 525-553, 2006 — Larkey, P. D., Smith, R. A., & Kadane, J. B., "It's okay to believe in the ''hot hand''", Chance 2:22–30, 1989.

    So the article that I remembered was in Chance! But it didn't last, according to Bar-Eli et al.:

    Larkey et al. (1989) challenged Gilovich et al.'s (1985) conclusions and continued to search for the hot hand. In a new data set they collected, Larkey and his colleagues analyzed the records of 18 outstanding players across the 1987–1988 NBA season. The results actually replicated Gilovich et al.'s findings: Half the players exhibited a positive serial correlation between successive shots, while the other half exhibited a negative serial correlation, thus providing no evidence for the hot hand.

    Larkey et al. (1989) dismissed these results on the grounds of both statistical and conceptual (or contextual) arguments. They pointed out that extracting individual player sequences of hits and misses from an actual game is too complicated a task, and that analysis should be restricted to "cognitively manageable chunks of shooting opportunities" (p. 24). Therefore, they limited consideration to streaks that occurred during a short period within a game (i.e., sequences of 20 baskets). Using a descriptive analysis method, it turned out that Detroit's Vinnie Johnson, "the Microwave", was indeed a streaky shooter, and hence the hot hand does exist. In their concluding remarks, Larkey and his colleagues rehabilitated the faith in our ability to make proper reasoning and stated that it is OK to believe in the hot hand.

    Since Larkey et al.'s (1989) argument in favor of the hot hand was based on the performance of a single player in a single observation (i.e., a run of seven consecutive hits within a 20-shot sequence during the fifth Piston–Laker playoff game), Tversky and Gilovich (1989b) considered this conclusion to be hardly convincing. Most importantly, they revealed an error in Vinnie Johnson's shooting record coded by Larkey and his associates (the 7 out of 7 sequence by Johnson turned out not to have happened!), which caused the whole case for the Microwave to "go up in smoke".

    ]

  6. Noetica said,

    July 10, 2009 @ 12:23 am

    I amend my quick rendering of Lucretius:

    … "incerto tempore ferme incertisque locis spatio" ("at no certain time, surely, and no certain place").

    Ferme looks to me like a filler, for metrical purposes alone. Other interpretations of the whole are possible, certe.

  7. A matter of chance | Swany’s Whey said,

    July 10, 2009 @ 1:20 am

    […] Language Log: "The OED gives the following etymology for chance: […]

  8. Alex B said,

    July 10, 2009 @ 3:21 am

    Or, to quote the exchange at a poker table in My Little Chickadee

    Cowboy: Is this a game of chance?
    W.C.Fields: Not the way I play it.

  9. NW said,

    July 10, 2009 @ 4:51 am

    For me, 'matter of chance' is an idiom containing the randomness sense. I wouldn't use that to mean "matter of probabilities".

    [(myl) But there's an oddity right there, because the technical use of the word random itself incorporates the notion of calculable odds, as in the expressions "random variable" and "random process", even though random can be used in ordinary language to mean something like "entirely unpredictable".

    And even the expression "matter of chance" is often used to mean just "according to the odds" — thus when someone wonders whether a hitting streak is "a matter of chance" they don't mean that the individual is batting 500; to wonder whether a cluster of diseases is "a matter of chance" is not to wonder whether everyone is equally likely or not likely to get sick. Rather, in both cases, the issue is whether the facts can be modeled as a random process in which each "trial" is independent of the others; and that question is precisely a "matter of probabilities".

    It's true that people often use "a matter of chance" to mean "without pattern or purpose, and thus not predictable in detail" (e.g. ""Is our life a matter of chance or does it carry some purpose?""), but I believe that it's very difficult to find a coherent meaning for the phrase "a matter of chance" that doesn't turn out to be a "matter of probabilities".]

  10. Kragen Javier Sitaker said,

    July 10, 2009 @ 5:40 am

    > complete unpredictability and the lack of any discernable cause.

    To me that doesn't make sense; there must be *some* probability distribution, otherwise you run into stranger versions of the two-envelopes paradox. For example, at most two of these three propositions can be true:

    Players are as likely to injure their legs as their arms.
    Players are as likely to injure their legs kicking as they are to injure them running.
    Players are as likely to injure their legs kicking as to injure their arms.

    [(myl) Indeed.]

  11. Nightstallion said,

    July 10, 2009 @ 8:14 am

    No, all three of them can be correct:

    injury_legs_kicking + injury_legs_running = injury_legs = injury_arms
    injury_legs_kicking = injury_legs_running
    injury_legs_kicking = injury_arms

    Obviously, injury_legs_kicking = injury_legs_running = injury_arms is a solution to this system. ;)

  12. Noetica said,

    July 10, 2009 @ 8:16 am

    KJS:

    … at most two of these three propositions can be true: …

    Yes, apart from these scenarios:

    1. Each of those probabilities is 0.

    2. A leg injury from kicking must always be accompanied by a leg injury from running, and vice versa.

    3. "As likely" is taken to mean "at least as likely", which it sometimes does. Contrast "just as likely"; or better, "exactly as likely".

  13. Noetica said,

    July 10, 2009 @ 8:17 am

    Snap!

  14. Mark P said,

    July 10, 2009 @ 8:35 am

    I think NW is confusing the inability to accurately predict any one event with the ability to determine the probabilities of such events. The first involves a specific occurrence and the second involves the long-term history of such occurrences. It's similar to the problem climate scientists have when they say that global warming is happening and a skeptic says that his local weatherman can't predict whether it will rain next week so no one can predict what the climate will be. Another example might be the behavior of gases. No one can predict (very well at all) the behavior of a single molecule of gas in a container, but any reasonably good high school physics student can predict extremely well the aggregate behavior of all gas molecules in the container.

  15. Mark Liberman said,

    July 10, 2009 @ 9:10 am

    Mark P: I think NW is confusing the inability to accurately predict any one event with the ability to determine the probabilities of such events.

    We need more than that to make "a matter of chance" mean something substantively different from "a matter of probabilities".

    Aside from simple confusion, two things have occurred to me as possibilities for this meaning difference: (1) a focus on (lack of) agency ("Destiny is not a matter of chance, but a matter of choice", "an undetermined action is simply a matter of chance", "he left nothing to chance", etc.); or (2) a focus on (lack of) effective ability to predict outcomes.

  16. J. W. Brewer said,

    July 10, 2009 @ 9:37 am

    Perhaps a less ambiguous (and thus sometimes useful) English word is "haphazard," which usually seems to imply something that would not have been ex ante susceptible to actuarial/probabilistic prediction. Not sure if there's a slightly different nuance in "haphazard sampling," a term of art in the auditing profession and perhaps elsewhere where it indicates a process that is not "random" in a rigorous or statistically/scientifically valid sense because it involved a degree of human judgment or discretion. Also not sure how this relates to the fabulously-named Trollope character Sir Abraham Haphazard.

  17. Mr Punch said,

    July 10, 2009 @ 9:57 am

    A closely related matter is the distinction in economics and finance between "risk" and "uncertainty" — now very much to the fore. Risk, a matter of probability, can be "managed" through actuarial analysis, though always with a subjective element; uncertainty arises from events that are unpredictable, often because they are very unusual (the "black swan" effect).

  18. Dan T. said,

    July 10, 2009 @ 10:17 am

    Hari Seldon's psychohistory (in Asimov's Foundation series) consisted of predicting with great accuracy what the masses of humanity would do collectively, despite not knowing what any individual would do.

  19. Mark P said,

    July 10, 2009 @ 10:35 am

    @Mark L: I'm not trying to distinguish between chance and probability. I'm trying to understand why someone would think there is a difference.

    [(myl) Right, I got that — I think we're singing from the same hymnal here.]

    I think your No. 2 comes close. I think some people do use "it's a matter of chance" to mean "it's hard to predict," or "there is a large range of possible outcomes with unknown (to me) probabilities," even if they don't realize that's what they're doing. There might also be some confusion arising from the use of "probable" to mean "likely." If an event is not likely, there might be a tendency to think that probabilities do not apply.

  20. Boris said,

    July 10, 2009 @ 11:44 am

    I'm confused as to what's wrong with the sentence. To me it is clear what it means and doesn't contain any sort of error, regardless of how much statistics the user knows. This whole discussion seems to be a case of an artificially created ambiguity of the type found in usage manuals that are railed against here regularly.

    [(myl) First, I didn't say that the NYT sentence is "wrong", just that it contains a source of ambiguity and confusion that I hadn't noted before. Second, the ambiguity is not "artificially created", unless you mean to blame the 18th-century mathematicians who began using "chance" to mean "probability". Third, most of the rest of us are still unsure about what it means to say that an actuarial approach "defies the assumption that what happens to players is a matter of chance". Since it's clear to you, please explain. ]

  21. Boris said,

    July 10, 2009 @ 11:44 am

    by user I meant reader of course

  22. J. W. Brewer said,

    July 10, 2009 @ 11:59 am

    I didn't know that chance was cognate to cadenza, and the "falling" etymology made me think of "Die Welt ist alles, das der Fall ist." But I can't recall if that's a false friend or not (eat the poisson, but don't drink das Gift).

  23. Bill Walderman said,

    July 10, 2009 @ 12:30 pm

    Can't the fact that OED 6 is older than OED 5a be explained by the fact that OED 5a couldn't enter into circulation until mathematicians developed statistics in the 17th century and people realized that the occurrence of some events that had previously been thought to be unpredictable could in fact be modeled mathematically? It looks as if the Ur-statisticians took a word in general circulation and gave it a technical meaning different from its common usage.

  24. Bill Walderman said,

    July 10, 2009 @ 12:32 pm

    To add to my previous post: the original meaning has also remained in circulation, resulting in the ambiguity noted in the original post.

    [(myl) Yes, that's pretty clearly what happened. Likewise for words like speed, distance, and time, as discussed here. ]

  25. Bloix said,

    July 10, 2009 @ 12:54 pm

    The ability to assign percentage probabilities to events developed very late. It wasn't until the 17th century that it became possible to calculate the odds of the outcome of a roll of a pair of dice (the original work is found in a famous correspondence between Pascal and Fermat), and the odds of more complicated events were not understood for decades or even hundreds of years. Even today the popular understanding of probability is extremely weak. So it's not surprising that the meaning of words relating to uncertain events evolved from the early modern to the modern period, or that they continue to reflect ambiguity.

  26. Bloix said,

    July 10, 2009 @ 12:55 pm

    Bill Walderman – ESP I see. I started to write my comment, took a phone call, and finished it up without reading new comments..

  27. richard said,

    July 10, 2009 @ 2:02 pm

    I'm not sure abut Fall (Ger.) being a "false friend"–false to which concept? I'm thinking here (being a musician) of the Nietszche essay "Der Fall Wagner," in which the pun in Fall (case = "The Case of Wagner" vs. fall (as in, shall we say, a fall from grace) = "The Fall of Wagner") is integral to understanding just how nasty the author was being to his former friend. Also, judging from the confusion on this very page, I have to be quite relieved that mathematical methods are now available for dealing with probability, even if that has saddled us with insurance agents.

  28. Skullturf Q. Beavispants said,

    July 10, 2009 @ 2:17 pm

    Apologies to mathphobes for bringing it up, but here's something that bugged me in the past that may be related.

    Around the 1940s or thereabouts, mathematicians such as Erdos and Kac began the use of techniques from probability and statistics to study things like the number of prime factors of an integer, typically considered a "pure math" topic. More briefly, Erdos and Kac essentially began probabilistic number theory.

    Some people drew what I frankly would consider the "wrong" philosophical conclusion from the existence of probabilistic number theory. Some people seemed to be saying "How weird to use probability and statistics to study the primes! Something strange is going on!"

    Granted, one normally thinks of the system of counting numbers, or the subset thereof that are primes, as a "fixed" or deterministic entity. There's no vagueness about whether or not a particular integer is prime, or how many prime factors it has if it's composite.

    However, just because you apply probability or statistics to a field of study, this doesn't mean you're claiming the field of study is completely haphazard or devoid of structure. Probability can be used to study something that's totally fixed and rigid and deterministic — it might just be that it's very hard or time-consuming to compute exactly how many prime factors a particular integer has.

    This seems related to the confusion mentioned in the post. There are plenty of situations in life where we don't know the details — predicting when our pitcher will strain his shoulder, or counting the number of primes between 1,000,001,000 and 1,000,002,000. And if you don't know the individual details, you can instead try to look at the "big picture", and use the language of probability. But using such language certainly doesn't mean "no structure or patterns at all", and using such language also doesn't commit you to a philosophical view that denies determinism or claims that uncertainty is inherent in the world. You might believe that, but the language of probability doesn't force you to believe it.

  29. D.O. said,

    July 10, 2009 @ 4:19 pm

    I think we are not completely over with the view that certain things are completely unpredictable even in probabilistic sense. In other words, there is something undeterministic out there, but no numbers can be assigned. No we should be. Reference in one of Prof. Liberman replies points in that direction. Not every chance event can be described by probability distribution. Example: If our universe came to being only once, what are the probabilities that fundamental constants are what they are? It might turn out to be a bad example, but we do not have any way to tell at least at the current level of knowledge.

  30. Adrian said,

    July 10, 2009 @ 6:02 pm

    "A matter of chance" means "a matter of luck", doesn't it?

    [(myl) Maybe — what does "a matter of luck" mean?]

  31. peter said,

    July 10, 2009 @ 6:02 pm

    Bloix at July 10, 2009 @ 12:54 pm said:

    "The ability to assign percentage probabilities to events developed very late. It wasn't until the 17th century that it became possible to calculate the odds of the outcome of a roll of a pair of dice (the original work is found in a famous correspondence between Pascal and Fermat), and the odds of more complicated events were not understood for decades or even hundreds of years. Even today the popular understanding of probability is extremely weak."

    Even among statisticians and physicists, who sometimes fail to comprehend that probability theory is just one among several competing formalisms proposed for representing uncertainty. Despite repeated attempts to prove otherwise by its more rabidly-ideological supporters, probability theory is not necessarily the most appropriate formalism in all circumstances. Certainly there are many application domains where its applicability is questionable (and questioned), and where it is not the most user-friendly formalism.

    "So it's not surprising that the meaning of words relating to uncertain events evolved from the early modern to the modern period, or that they continue to reflect ambiguity."

    or that the concepts underlying these words have repeatedly been contested. I don't think it behooves any of us to cast aspersions on the understanding of ordinary people when the standard concepts of probability theory and their applicability to various domains have been so often challenged – by people such as Leibniz in the 17th century, von Kries in the 19th, Shackle in the mid-20th, and Shafer and others in the AI community in the late 20th century. Surely it would be strange state of affairs if all these critics were feeble-minded.

  32. Noetica said,

    July 10, 2009 @ 6:46 pm

    On chance, cadence, and fall, let's remember that fall has been used technically for a musical cadence. Most cited is this from Twelfth Night: "That strain again. It had a dying fall." This is twice echoed by Eliot, in "Prufrock" ("I know the voices dying with a dying fall / Beneath the music from a farther room") and in "Portrait of a Lady".

    A musical cadence would typically and originally be a literal fall in pitch: a return to repose after an elevated excursus. But isn't there also an element of "outcome", or "falling out"? Certainly of "resolution", a related notion: connected with the fall of the voice at the conclusion of a sentence, also a cadence, by which the "outcome" or meaning of the sentence is at last settled and sealed, as when the dice come to rest.

  33. Noetica said,

    July 10, 2009 @ 7:35 pm

    Die Welt ist alles, das der Fall ist.

    That's "Die Welt ist alles, was der Fall ist."

    Yes, it is translated as "The world is all that is the case", and case goes with cadence. It is from Latin casus, which is just another form connected with cadere. Interesting to look at early senses recorded in OED, "case, n.1":

    I. †1. a. A thing that befalls or happens to any one; an event, occurrence, hap, or chance.

    †2. a. Chance, hazard, hap. Obs.

    So a case is a settled fact, sometimes distinguished from and following upon uncertainty (epistemic or objective?) – like a fall of the dice.

  34. Noetica said,

    July 10, 2009 @ 9:54 pm

    For the history of the term case in grammar as originally "a falling" (casus, πτῶσις, Fall), see this rather comprehensive source.

  35. Noetica said,

    July 10, 2009 @ 9:58 pm

    And for a fine conspectus of the whole cadere family, see Partridge (of course).

    [At least in the preview, the LL system allowed only one of those paragraphs containing links to be visible; so I divided one post into two.]

  36. J. W. Brewer said,

    July 11, 2009 @ 1:32 pm

    @Noetica, for a more recent musical-sense usage than Shakespeare/Eliot, consider the well-known "It goes like this, the fourth, the fifth / The minor fall, the major lift." As should be clear by now, German "Fall" is not a false friend but is indeed cognate to English "fall." I had simply not wished to do my due diligence on that before my earlier post, in which I was instead focused on introducing a typo into the Wittgenstein quote. One of the ways to render the noun "chance" in German (in addition to "Chance") is apparently Zufall.

  37. Bloix said,

    July 11, 2009 @ 6:01 pm

    "I don't think it behooves any of us to cast aspersions on the understanding of ordinary people"

    Peter, we're getting far afield from language here, but all I'm saying is that people make repeated errors that leave them open to exploitation. For example, a great many people really do believe that the chance of winning the lottery is not a matter of probability, but is instead a matter of luck – that the person who wins is invested with a substance or quality that can, perhaps be manipulated or obtained by others.

    And Adrian – for people who don't really believe in luck, yes, "a matter of chance" and "a matter of luck" are the same. But for people who believe in a lucky day, a lucky star, or a lucky streak, the two are utterly different.

  38. Noetica said,

    July 11, 2009 @ 8:55 pm

    JW Brewer:

    "It goes like this, the fourth, the fifth / The minor fall, the major lift."

    Being both a music theorist and an ardent disciple of Leonard Cohen, I am traumatised whenever I hear those lines.

    As for Zufall meaning "chance, accident", that is obviously close to accident, for which SOED offers these senses first:

    I A thing that happens.
    1 An event. obs. in gen. sense. LME.
    b An event that is without apparent cause or unexpected; an unfortunate event, esp. one causing injury or damage. LME.
    2 Chance, fortune. LME.

    The etymology:

    [(O)Fr. f. L accident- pres. ppl stem of accidere happen, f. ad AC- + cadere to fall: see – ENT.]

    So ad (as ac-) + cadere; zu + fallen.

  39. Bloix said,

    July 11, 2009 @ 11:50 pm

    And happen itself is from hap, meaning chance, so that to happen originally meant to occur by chance. And happy is from the same word, and originally meant lucky or fortunate.

  40. Noetica said,

    July 12, 2009 @ 2:44 am

    Yes, Bloix. (How do we say that name?)

    Remember also befall, meaning "happen" (as in OED's entry for "case", quoted above). And at OED's entry for "befall" we see fall out used to explicate this sense of the verb:

    4. To fall out in the course of events, to happen, occur: …

    Fall itself is sometimes used to mean "happen". From OED, entry for "fall, v.":

    46. Of an event, etc.: To come to pass; to happen, to occur. Obs. exc. poet. …

    1823 Longfellow Life (1891) I. iii. 33, I am rather sorry that the Exhibition falls so late in the year. 1878 Tennyson Q. Mary v. i, If war should fall between yourself and France.

    Obsolete? I'd say that the Longfellow usage is still with us.

  41. Kragen Javier Sitaker said,

    July 14, 2009 @ 3:36 am

    Noetica: of course you are correct about the flaws in my case analysis. Thank you! I should have been more careful.

  42. David Z said,

    July 18, 2009 @ 7:28 pm

    I guess there are no Fred Astaire fans here. In "The Gay Divorcee", attorney Edward Everett Horton, trying to get Ginger Rogers a divorce by being caught with a "hired co-respondent," gives them the code phrase for them to recognize each other by: "Chance is a fool's name for Fate."

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