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Fads and Fallacies in the Social Sciences by Steven Goldberg: Part IV

This article summarizes the main statistical arguments and the one logical argument used for and against Goldberg’s ideas. To be clear: I am convinced by his arguments in the main and differ from him only at the edges, and trivially. If you have not read him, I urge you too. He writes beautifully and clearly and has given much thought to answering his critics, and has more room in his three books than we have here.

  1. Group A members are more variable than group B members : The usual implication of this is that, even if there are just as many group A and B members near the mean, more of group A members than group B members will be found at the extremes of behavior. This is only “usual” because it is possible for group A members to be more variable but for group B members to have a higher or lower average and so be found more often in the upper or lower extremes. Each trait has to be judged on its own empirical findings.
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  3. Correlation is not causation: This is true. But it is also true that when there is causation, there is correlation. When causation is absent, correlation can be present spuriously or it may be absent. Too often, Goldberg’s critics acknowledge a correlation but then drag out the “correlation isn’t causation” card, as if by displaying it they have proved that causation is absent. The proof of causation is extra-statistical in the following sense: we have to look beyond the data presented and the model used and ask whether or not the causation is plausible, highly probable, and consonant with other information we possess. What makes a statistical argument worthy is if it can be used to make reliable predictions and not just that is explains previously observed data well.
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  5. The SAT/IQ test isn’t correlated with success: This is false in general but potentially true when conditioning on a subgroup. Suppose you follow graduates of University A, the best in the country (in a particular subject) that accepts only the best according to the SAT/IQ test. All graduates will have an SAT/IQ test and all will go on to success and failure. In this group, any measure of success will not be correlated between the SAT/IQ score because all of these scores are high. Across the population in general, however, SAT/IQ tests are highly predictive of success (and should only be used in their predictive sense).
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  7. Between-group differences are larger than within-group differences: So what? As Goldberg points out, the within-group difference of height in men or women is much larger than the between-men-women difference, but nobody is foolish enough to think this means that men and women are equally tall, or that the small between-group difference doesn’t lead to large differences both on average and at the extremes. Several very good statisticians have been caught making this error.
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  9. The difference in number of genes is small: And so it is. But again, so what? The number of different genes between humans and higher primates is small but the phenotypical differences are enormous. It’s not the number of different genes that count but what those different genes do.
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  11. After controlling for income, group A is the same as group B: This is true, but in using this argument, Goldberg’s opponent has agreed with him. We return to our initial question: if Sally is over six feet and so is Bill, are both Sally and Bill over six feet? And if people are paid by height—the taller receiving more—Sally will be paid as much as Bill, but on average women will receive less than men because, on average, women are shorter than men. Therefore, if you took a group of men and women (all remunerated by height) and statistically controlled for height you would find that tall women received as much as tall men. You will not have proven that men and women are equally tall. It is the tallness —the difference—that has caused the economic success.
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  13. You cannot derive an ought from an is: David Hume first taught us this and it is true. It does not follow, and nobody believes it is true, that therefore there can be no oughts. It is only true that whatever oughts exist are believed without reference to external evidence or empirical findings. Thus, the oughts we believe are based on a priori evidence; that is, our intuitions. This type of evidence should not be castigated: all of mathematics, for example, is founded on the very same kind of beliefs (the axioms). Further, we might not be able to prove an ought is true but we might be able to infer it is with high probability. It is also true that all cultures hold many of the same oughts.

A corollary to the last, and what comprises Goldberg’s main uphill battle, is to convince detractors (usually on the Left) that their criticisms are founded on unspoken and unacknowledged oughts.

Please use the letter of the item in question when replying to make it easy on the rest of us.

32 thoughts on “Fads and Fallacies in the Social Sciences by Steven Goldberg: Part IV Leave a comment

  1. I haven’t read Goldberg, but an concept expressed earlier in the discussion, but seems should be in the synopsis. What is true for the group is not necessarily true for the individual.

  2. Bernie,

    I’d like to see that letter.

    For those who don’t know what Bernie is talking about: see this link then this one. (Hat tip, as ever, to A&LD).

    Doug M,

    Amen.

    DAV,

    I’m with you. Well—I hope to God—discuss causality sometime soon. We don’t need to know too much about it here to understand Goldberg.

  3. Matt:
    Again I have to confess that the Goldberg books have not arrived. One thing struck me from reading the academic reviews of the Inevitability of Patriarchy is the levelling of the charge of biological reductionism. In truth, I have never given much thought to the pluses and minuses of this type of criticism. What struck me in reading Goldberg’s essays and responses to the reviews was that he appeals to parsimony as the basis for his theory. The light bulb went on: Parsimonious theories tend to be reductionist! Well for others this may be obvious – but for me it was a genuinely new thought. It also means that the reductionist criticism has to be assessed in a different light. In particular, if one levels the criticism, one must surely provide evidence to support the inclusion of other factors that add significantly to the theoretical explanation of the issue under discussion. I suspect that Goldberg uses this requirement to counter the biological reductionism criticsms

    Depending on whether you agree or not that parsimony is a hallmark of Goldberg’s theorizing, perhaps there is a letter “H”?

    P.S. I also found a letter by Goldberg in the American Philosophical Association where he, among others, gave a spirited defense of Christina Hoff Sommers. Philosophers can get pretty mean spirited as well as illogical and imprecise. (http://www.jstor.org.ezproxy.bpl.org/stable/pdfplus/3130578.pdf or Letters in Proceedings and Addresses of the American Philosophical Association Vol. 66, No. 7, Jun., 1993)

  4. “Correlation is not causation”

    I think this is only true for only two variable observations. With more than two it’s possible in some (but not all cases) to deduce causality through graphical+statistical means, albeit not purely statistical (see Judea Pearl and Peter Sprites). I submit that ALL empirically determined causality is achieved through statistical means — implicitly if not explicitly.

  5. O/T

    Something not correct with the sequence? Matt is answering 3 replies of which 2 are posted afterwards.

  6. Jan:
    Very perceptive. I asked Matt to delete an earlier copy of essentially the same comment because of a typo and an omission.

  7. Matt:
    I just read via the link you provided the discussion between Lemon and Sommers plus the comments. If that is the level of debate one is likely to encounter on campus, it is sad. If that is level of logic, objectivity, precision and accuracy one can expect from a law lecturer, i.e., Dr. Lemon, it is very sad.

  8. A, D, E. Some groupings, such as genders, are fairly easy to discern and distinguish between. Other groupings, such as race, are not. If the groups are not readily differentiated — that is, if the binning procedure is arbitrary and capricious — then analyses that depend on fuzzy, inaccurate, and imprecise groupings are pretty much bogus.

    For an amusing example of race stretching, see Andrew Bolt’s essay: ‘Aboriginal’ man helped

    http://blogs.news.com.au/heraldsun/andrewbolt/index.php/heraldsun/comments/aboriginal_man_helped/

  9. He promised to do it
    – an is

    Therefore he ought to do it
    – an ought

    Is this deriving an ought from an is?

  10. Michel:
    I do not think so. Your pair of statements amounts to a single statement, namely, “all who promise something should (ought to) deliver on their promise.” It amounts to an ethical statement.

  11. The notion that one cannot derive an “ought” from an “is” — the notion that no “oughts” can be derived from empirical evidence — is simply not true.

    The notion of an “ought” presupposes the possiblity of choice in the face of alternatives — amd there is only one type of entity that faces alternatives and choices: a living being. The concept of an “ought” of “good” and “bad”, “right” and “wrong” — all have meaning only to a living being. It would be nonsense to ponder the question, “What “ought” a rock to do?”

    Further, is objectively provable that the nature of each living being dictates what it “ought” to do to remain alive.

    I will give you a few simple examples pertaining to man:

    – If you wish to remain alive, the “is” of your human biochemistry dictates that you “ought” to eat nutritous food, and not eat poison.

    – If you wish to remain alive, the “is” of the fact that you are a being that uses reason to apprehend and deal with reality dictates that you “ought” to look at reality and think, not evade reality and be blindly guided by your emotions or whims.

    – If you wish to remain alive, the “is” of the fact that man (generally) must produce the material values he needs to survive — his food, clothing, shelter, etc. — dictates that he “ought” to engage in productive work, and “ought not” sit back and idly wait on these things to fall from the sky.

    – If you wish to remain alive, the “is” of the fact that you must work to sustain your own existence means that you “ought” to have the freedom to engage in such productive work.

    In short, if you wish to remain alive, you must carefully consider many “ises” to determine what you “ought” to do. Ignoring what “is” — behaving with no regard to the facts of reality — normally produces disastrous consequences.

    And no, there is no “is”, no fact of reality, that dictates that you “ought” to wish to remain alive. It is your basic choice. If you do not wish to remain alive, you have no need for any “oughts” at all. You may proceed to behave at random, since you don’t care about the consequences.

    Now what IS true is that you cannot derive any of the conventional notions of morality from the facts of reality. For instance, the morality of altruism, which holds that man does not have the right to exist for his own sake, but instead must sacrifice for the sake of “others” — that notion of morality is wholly arbitrary and unsupported by any facts of reality. Likewise, the notion that morality consists of rules handed down by supernatural beings in another dimension is equally arbitrary and divorced from reality. Both are advanced as mere assertions with no supporting evidence whatsoever — and both are thus false.

    But as Ayn Rand has shown, a morality of reason — a morality that derives the appropriate “oughts” from the facts of what man “is” — is both possible and eminently desirable. See Ayn Rand’s article, “The Objectivist Ethics” in her book, “The Virtue of Selfishness”.

  12. Michael:
    I am not sure I follow the first few points you made. Your examples all appear to be of the form “if…then” where there is a biological need. There is no “ought” in the normative sense. I think the issue Goldberg raises is simpler. My assumption is that in the area of politics, sociology or social commentary there is a tendency to confuse the statements “men and women are equal” and “men and women ought to be equal”. The former is an empirically testable statement while the latter is an assertion of what should be. When the former statement is made without acknowledging obvious non-equal facts then it is an “ought” statement masquerading as an “is” statement.

  13. Michael, Wade,

    I understand, and even in part share, the reasoning behind your arguments. But you must understand we are talking about the logical status of the statement that you cannot derive and ought from an is. In no way does the logic of that statement depend on any human desire, economic need, or empirical fact.

    There is nothing in the structure of logical arguments to guarantee the existence of humans, and a fortiori, nor is there any logical, necessary truth, that shows human needs much be provided for.

    Take your example of “wishing to remain alive.” That is a contingent statement. There is no necessary truth, or set of them, that leads deductively to the truth of it. Therefore, anything following from it is also contingent and not logically necessary. And so on for the remainder of examples.

    Now, it is an empirically observed fact that most (but only most, not all) humans agree that “wishing to remain alive” is a right, or is something to assumed as desirable in themselves and in the next guy. It is true that given this desire and given certain biologically observations, some conditional oughts follow. For example: food is necessary. But those biological facts are just as contingent as the desire.

    Finally, we both will agree on some, probably even most, of our desires; further, most people agree on the same set. And lots of things, of course, follow from these. But again, these do not affect the logical status of the original statement, which is all that is being claimed here.

    Sorry for the terse reply. Running behind today and in a rush.

  14. You cannot derive an ought from an is.

    I take it to mean, for example, that killing people IS wrong, but it does not follow so clearly that death penalty is immoral and should be abolished. Am I correct? No?

  15. B: “The proof of causation is extra-statistical in the following sense: we have to look beyond the data presented..”. If you’re lucky, the correlation generates a hypothesis which you can then test in a controlled experiment.

    DAV: ‘“Correlation is not causation”

    I think this is only true for only two variable observations.’
    I don’t.

  16. Mr. Briggs wrote:

    Take your example of “wishing to remain alive.” That is a contingent statement. There is no necessary truth, or set of them, that leads deductively to the truth of it. Therefore, anything following from it is also contingent and not logically necessary. And so on for the remainder of examples.

    You have fallen prey to a variation of the “Analytic-Synthetic Dichotomy” fallacy, specifically, the “necessary versus contingent” fallacy.

    This fallacy asserts a dichotomy — that there are two kinds of “facts”: those that must exist, that are inherent in the nature of reality, i.e. that are “necessary” — VERSUS — “facts” that just “happen” to exist in the world we observe, but they do not “have” to exist, things could be otherwise, i.e. they are “contingent”. According to this dichotomy, since the “contingent” facts are not “logically necessary”, they are of inferior epistemological status — that is, they are “optional” and not “absolute”.

    But nothing justifies this attempt to separate facts into two such groups. It is true that some facts are metaphysical in nature while others are man-made and thus could be different. For example, the existence of the solar system is a metaphysical fact quite beyond man’s ability to influence: the solar system exists and was formed — however it was formed — according to the laws of physics. By contrast, the fact that the U.S. consists of 50 states is purely a “man-made” fact which could have been 49 or 51 or almost any other number.

    But the logical status of those two facts is the same. Quoting now from Objectivist philosopher Leonard Peikoff:

    “The (fact that some facts are man-made versus some being metaphysical) cannot be used to justify the theory that there is a dichotomy of propositions or of truths. Propositions about metaphysical facts and propositions about man-made facts do not have different characteristics qua propositions. They differ merely in their subject matter, but then so do the propositions of astronomy and of immunology. Truths about metaphysical and about manmade facts are learned and validated by the same process: by observation; and, qua truths, both are equally necessary. Some facts are not necessary, but all truths are.”

    “Truth is the identification of a fact of reality. Whether the fact in question is metaphysical or man-made, the fact determines the truth: if the fact exists, there is no alternative in regard to what is true. For instance, the fact that the U.S. has 50 states was not metaphysically necessary—but as long as this is men’s choice, the proposition that “The U.S. has 50 states” is necessarily true. A true proposition must describe the facts as they are. In this sense, a “necessary truth” is a redundancy, and a “contingent truth” a self-contradiction.”

    From “The Analytic-Synthetic Dichotomy” by Leonard Peikoff, reprinted in Ayn Rand’s book, “Introduction to Objectivist Epistemology”.

    Peikoff gives an excellent expose and refutation of this logical fallacy in all of its forms. I urge you to read that book, in particular, Peikoff’s essay, if you wish to avoid being victimized by this fallacy.

    The facts determine the truth. The logical status of a proposition is determined by whether or not it is consistent with the facts of reality. The proposition: “The ‘is’ of man’s biochemistry dictates that to stay alive, he ‘ought’ to eat nutritious food and not poison” — is both logically and necessarily true because it is based on the facts that nutritious food supports life while poison tends to end it. The proposition is not somehow made “less true” or “illogical” by the fact that some people choose to commit suicide rather than remain alive.

  17. MichaelI am not sufficiently familiar with your vocabulary to use it, though I do not at the moment see the vocabulary and the distinctions as particularly helpful. It seems to me that if the solar system is a metaphysical fact then so is the fact that 50 States make up the United States. The latter is clearly a man-made fact, and I would allow that the former is not. But why would either be metaphysical? Equating metaphysical to mean “beyond the control of man,” i.e., not man made, seems to be counter to common usage. The nomenclature is very confusing and counter-intuitive. Both statements are very different from the statement “God exists” which I would argue is a metaphysical statement as metaphysical is commonly understood.

    It seems to me to be self-evident that your nutritious food example remains an “is” statement not an “ought” statement. For example, the statement “Individuals ought not to commit suicide” is an ought statement. This is different from a statement that x% of people over 80 decide not to eat and thereby commit suicide. This is a fact statement and if X% is an accurate measure, then it is an “is” statement. If I assert that “90% of those over 80 who want to commit suicide but cannot obtain access to euthanasia, stop eating” where in fact the number is 10%, then my statement is a disguised “ought” statement, namely, those over 80 ought to have access to Euthanasia.

    I am not sure where this discussion can usefully go at this point.

    Goldberg’s point to me seems abundantly clear: People make assertions about reality that while is keeping with the way they think the world ought to be (or not be) are not accurate. The dispute between Lemon and Sommers is a case in point. Lemon asserts that Domestic Violence is a huge problem and that 20 to 30% of emergency room visits by women in the US are due to domestic violence. This is an assertion of fact conditioned by the way Lemon wants us to see the world. Sommers points out that CDC data suggests a dramatically lower number – closer to 1% of emergency room visits. Lemon’s “fact” is a Goldberg fallacy. I am sure Sommers, like Lemon and me, believes that Domestic Violence ought not to exist. The implications for public policies, government action and resource allocations are likely to be dramatically different under the two assertions of facts.

  18. D. “Between-group differences are larger than within-group differences: … Several very good statisticians have been caught making this error.“

    How do you quantify within-group and between-group differences?

    F. “After controlling for income, group A is the same as group B: … Therefore, if you took a group of men and women and statistically controlled for height you would find that tall women received as much as tall men. … It is the tallness —the difference—that has caused the economic success.”

    Controlling for income, group A is the same as group in WHAT?! Height?

    G. “You cannot derive an ought from an is:… It does not follow, and nobody believes it is true, that therefore there can be no oughts.”

    Examples please.

  19. Bernie:

    In Rand’s philosophy of Objectivism, “metaphysical” is used in the sense used by Aristotle: as pertaining to the most fundamental branch of philosophy, the branch that deals with the nature of existence as such, or, in Aristotle’s words, with “being qua being”.

    Regarding “metaphysical facts”, a more precise formulation would be to call them “metaphysically given facts”. Here is a quote from Rand clarifying this point:

    “Any natural phenomenon, i.e., any event which occurs without human participation, is the metaphysically given, and could not have occurred differently or failed to occur; any phenomenon involving human action is the man-made, and could have been different. For example, a flood occurring in an uninhabited land, is the metaphysically given; a dam built to contain the flood water, is the man-made; if the builders miscalculate and the dam breaks, the disaster is metaphysical in its origin, but intensified by man in its consequences. To correct the situation, men must obey nature by studying the causes and potentialities of the flood, then command nature by building better flood controls.”

    (From the article, “The Metaphysical versus the Man-Made” in Rand’s book, “Philosophy: Who Needs It?”)

    I have not read Goldberg, but if he is pointing out that it is a fallacy to let one’s preconceived “oughts” distort what one reports as the “is”, I certainly agree with him! There is a great deal of that going on in the debate over global warming — and in just about every other significant debate going on at the moment. So I applaud Goldberg’s effort to expose this.

    I’m simply contesting the broader, more fundamental claim that “you cannot derive an ‘is’ from an ‘ought’ — whatever oughts exist are believed without reference to external evidence or empirical findings” — to quote Mr. Briggs.

    I offered, as an example, an “ought” that exists in my mind — “I ought to eat nutritious food, not poison” — and pointed out that this “ought” is most definitely based on “external evidence and empirical findings”. It’s based on the evidence that nutritious food keeps me alive while poison tends to kill me. Those are hard, “logically necessary” facts dictated by my metaphysically-given biology.

    It is certainly true that the decision to remain alive is optional. But it is a non sequitur to say that since this goal is optional, all alleged “oughts” are arbitrary and divorced from any external evidence or empirical findings.

  20. dearieme, What is an experiment but yet another way to generate statistics? It would be nice if manipulation were always available.

    One place to start: link
    Or here: book link
    Or read some of the papers at Pearl’s home site (use Google)

    Suppose there are three variables (A,B,C) all mutually corellated but further suppose A is independent of B given C. One definition of ’cause’ yields C causes A and B. An example: the price of rum, New England preacher salaries and inflation.

  21. Michael,

    I do not accept Rand’s bifurcation of “metaphysical”, nor am I convinced by Peikoff’s arguments. I do, however, find Aristotle’s definition of “contingent” convincing. A tree falling in a forest, or a distant star going supernova are contingent events, in Aristotle’s sense. They are not logically necessary events, by which I mean, there are no necessary true premises that allow those events to be deductively proved. Rand’s version suffers from being unable to adequately and unambiguously define “human participation.” I haven’t come across any definition that isn’t circular, or worse.

    This being said, we are not far apart. Given we accept certain facts (empirically or not), then certain other things follow. For example, I am with you on your example: given that humans must not eat poison and that I want to live, then if I want to live I ought not to eat poison. Empirically, we know the first premise is true and I accept wholeheartedly the second (based on my intuition, but only on that; nothing logically guarantees I should feel that way; as you know, some people do not feel that way; suicides, for example).

  22. Candy,

    D. Within-group differences are just differences concerning only those members inside a group. For example, men. The within-group differences of the heights of men are large (in subgroups: from jockeys to superior statisticians). Between-group differences are usually expresses as differences between averages. The difference between the averages heights of men and women, for example, is only a couple of inches. Yet everybody knows that men are taller than women, and that most of the very tall are men. This is true even though some women are taller than some men, and some of the tallest women are taller than tall men.

    F. Yes, after controlling for income, we find that the two groups are the same in height. Does that prove that men and women are equally tall? Obviously not. The typical misuse of this kind of argument comes from people not understanding what is causing what, or getting it exactly backwards. In our example, height is causing high income; high income is not causing tallness.

    G. Every human desire is an example. Not one follows from any necessarily true statement.

  23. Briggs, I didn’t make an argument, I asked a question if Normative and Positive analysis were another way of saying “ought” and “is”.

    As far as the “ought from an is” argument, it reminds me of Tweedle-Dee logic. “If it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic”.

  24. Michael, Matt:
    Is there a difference between “ought” and “need to”? As my earlier comment should make clear (but perhaps it doesn’t), I see “ought” as an individual preference (Goldberg’s “wish”) among alternative states, as in “people should have ready access to the means to commit a painless suicide.” This is different from what I take to be an “is” statement that “x% of people commit suicide by resorting to very painful methods” where x% is an accurate number based upon standard and replicable measurement methods.

    P.S. Goldberg’s first book arrived this morning. It is dense, but not silly dense as is the case, IMO, with many theoretical sociologists.

  25. What do mean by “controlling a variable”? How do you decide which variable to control? Height? Income?

    Are you saying that we can move from is/ought to is/want ?

    Women OUGHT to have babies because it is in their nature.
    Women WANT to have babies because it IS in their nature.

    By the way, you promised that you would post a picture of yourself in your newly purchased linen suit, so you ought to keep your promise. It’s also desired that you keep the promise.

  26. It is only true that whatever oughts exist are believed without reference to external evidence or empirical findings. Thus, the oughts we believe are based on a priori evidence; that is, our intuitions.

    Larry Laudan (and, I would guess, others) treat normative statements (i.e., “oughts”) as elliptical (as in linguistic ellipsis, not geometric ellipses) statements of the form “X should do Y (…, because doing Y will lead to Z, which is desirable for reason W)”. Laudan does this in the context of scientific methodology, but I don’t see why it doesn’t extend to other contexts. The point being that, if “oughts” do have this implicit structure, then external evidence and empirical findings can, in principle, come to bear on their evaluation. For (non-concrete) example, if you can show that doing Y doesn’t lead to Z, or that Z is not desirable or justifiable by reason W, then X should not, in fact, do Y.

  27. Mr. Briggs, thank you for your responses. I appreciate you taking the time to discuss your views. You are one of the few logic-respecting voices on the web.

    I find it puzzling that you think Rand is advocating a “bifurcation of the metaphysical”. To the contrary, she is objecting to the bifurcation being pushed by the advocates of the “necessary versus contingent” dichotomy. The whole point of the Peikoff quote I provided is that such a bifurcation is unjustified. So I am at a loss to understand how you can read it and conclude the opposite. But I don’t know how to explain it any more clearly than I already have, so I won’t waste any more of your blog space on additional explanation.

    I am also at a loss to understand why you find it “convincing” that a tree falling in a forest and a star going supernova are “not logically necessary”. Surely both events are governed and dictated by the laws of physics. What can be more “logically necessary” than entities obeying the laws of physics? I suppose that is one point where I’d disagree with Aristotle.

    At any rate, I’m happy to hear that we are not far apart on the “is versus ought” issue. Yes, I agree, the decision to remain alive is optional — but, to offer another example, so is the decision to remain healthy. Yet no one (that I’ve ever heard) would claim that since there is no fact of reality that “proves” you must remain healthy, the science of medicine cannot use the “is” of man’s bilogical make-up to derive any “oughts” that teach us how to cure or avoid disease, disinfect a wound, surgically remove a tumor, etc.

  28. Michael,

    I apologize for taking so long to answer: one aspect was work, the other that the number of comments have been piling up and earlier ones are hidden. That later is purely laziness on my part.

    Let’s talk about the “laws” of physics since we really agree with most everything else, at least practically. So, re: the laws. There are none. There are theories and plenty of them, and there might be, and almost certainly are, rules (for lack of a better word) that run the universe, but we don’t yet know these rules completely. Further, all theories (that I know of; maybe Tom can help us here) make use of arbitrary “constants”, which are experimentally determined numbers necessary for the theories to work. The “constants”, I emphasize, have not been deduced, but induced. And since induction is fallible, so are the theories which use these constants.

    Practically speaking, “laws” are theories that have been found to predict remarkably well. That is, they are all probabilistic: even though, in some “laws”, the predictions are almost certainly true, they are not certainly, i.e. deducibly, true. In other words, their predictions are true with probability 1 – epsilon, where epsilon is as small as you like but epsilon > 0.

    So, strictly speaking—and we are speaking very strictly—no physical thing that we know is logically necessary. But of course, this means little in day-to-day life.

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