Bell (1981, C2-57):

“… it may be that it is not permissible to regard the experimental settings a and b in the analyzers as independent variables, as we did. We supposed them in particular to be independent of the supplementary [a.k.a. hidden] variables λ, in that a and b could be changed without changing the probability distribution ρ(λ). Now even if we have arranged that a and b are generated by apparently random radioactive devices, housed in separate boxes and thickly shielded, or by Swiss national lottery machines, or by elaborate computer programmes, or by apparently free willed experimental physicists, or by some combination of all of these, we cannot be sure that a and b are not significantly influenced by the same factors λ that influence A and B [measurement outcomes]. But this way of arranging quantum mechanical correlations would be even more mind boggling that one in which causal chains go faster than light. Apparently separate parts of the world would be deeply and conspiratorially entangled, and our apparent free will would be entangled with them.”

Hance and Hossenfelder (2022, p. 1382) on the assumption of statistical independence of supplementary/hidden variables and experimental settings:

“Types of hidden variables theories which violate statistical independence include those which are superdeterministic, retrocausal, and supermeasured. Some have dismissed them on metaphysical grounds, by associating a violation of statistical independence with the existence of ‘free will’ or ‘free choice’ and then arguing that these are not assumptions we should give up.

“It is, in hindsight, difficult to understand how this association came about. We believe it originated in the idea that a correlation between the hidden variables and the measurement setting would somehow prevent the experimentalist from choosing the setting to their liking. However, this is mistaking a correlation with a causation. And any serious philosophical discussion of free will acknowledges that human agency is of course constrained by the laws of nature anyway.”


Bell, J. S. (1981). Bertlmann’s socks and the nature of realityLe Journal de Physique Colloques42(C2), C2-41-C2-62. Reprinted in Bell (2004).

Bell, J. S. (2004). Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy (2nd ed.). Cambridge University Press.

Hance, J. R., & Hossenfelder, S. (2022). Bell’s theorem allows local theories of quantum mechanics. Nature Physics, 18(12), 1382.  [Preprint]


A cynical view of SEMs

It is all too common for a box and arrow diagram to be cobbled together in an afternoon and christened a “theory of change”. One formalised version of such a diagram is a structural equation model (SEM), the arrows of which are annotated with coefficients estimated using data. Here is John Fox (2002) on SEM and informal boxology:

“A cynical view of SEMs is that their popularity in the social sciences reflects the legitimacy that the models appear to lend to causal interpretation of observational data, when in fact such interpretation is no less problematic than for other kinds of regression models applied to observational data. A more charitable interpretation is that SEMs are close to the kind of informal thinking about causal relationships that is common in social-science theorizing, and that, therefore, these models facilitate translating such theories into data analysis.”


Fox, J. (2002). Structural Equation Models: Appendix to An R and S-PLUS Companion to Applied Regression. Last corrected 2006.

Appeal to consequences fallacy in understanding Bell’s theorem

Joan Vaccaro (2018, p. 11) on arguments against superdeterminism:

“An argument that has been advocated by leading physicists is that humans are necessarily independent of the universe that surrounds them because the practice of science requires the independence of the experimenter from the subject of study. For example, Bell et al. state that unless the experimenter and subject are independent, we would need to abandon ‘…the whole enterprise of discovering the laws of nature by experimentation’, and Zeilinger claims that if the experimenter and subject were not independent ‘…such a position would completely pull the rug out from underneath science.’ However, this argument contains a logical fallacy called an appeal to consequences. Specifically, arguing for experimenter–subject independence on the basis that the alternative has undesirable consequences does not prove that experimenters are independent of their subjects. Rather, the alternative may well be true, in which case we would need to deal with the consequences.”


Vaccaro, J. A. (2018). The quantum theory of time, the block universe, and human experience. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 376(2123).

Beautiful friendships have been jeopardised

This is an amusing opening to a paper on face validity, by Mosier (1947):

“Face validity is a term that is bandied about in the field of test construction until it seems about to become a part of accepted terminology. The frequency of its use and the emotional reaction which it arouses-ranging almost from contempt to highest approbation-make it desirable to examine its meaning more closely. When a single term variously conveys high praise or strong condemnation, one suspects either ambiguity of meaning or contradictory postulates among those using the term. The tendency has been, I believe, to assume unaccepted premises rather than ambiguity, and beautiful friendships have been jeopardized when a chance remark about face validity has classed the speaker among the infidels.”

I think dozens of beautiful friendships have been jeopardized by loose talk about randomised controlled trials, theory-based evaluation, realism, and positivism, among many others. I’ve just seen yet another piece arguing that you wouldn’t evaluate a parachute with an RCT and I can’t even.


Mosier, C. I. (1947). A Critical Examination of the Concepts of Face Validity. Educational and Psychological Measurement, 7(2), 191–205.

Nietzsche on causa sui

‘The causa sui is the best self-contradiction that has yet been conceived, it is a sort of logical violation and unnaturalness; but the extravagant pride of man has managed to entangle itself profoundly and frightfully with this very folly. The desire for “freedom of will” in the superlative, metaphysical sense, such as still holds sway, unfortunately, in the minds of the half-educated, the desire to bear the entire and ultimate responsibility for one’s actions oneself, and to absolve God, the world, ancestors, chance, and society therefrom, involves nothing less than to be precisely this causa sui, and, with more than Munchausen daring, to pull oneself up into existence by the hair, out of the slough of nothingness.’
– Friedrich Nietzsche (written 1886), Beyond Good and Evil, translated from German by Helen Zimmern, upper case lowered again and italicised

Doings and deliberations can change things

“Naive fatalism holds that there is no point in doing anything because everything is predetermined (or is the will of God, for example), hence nothing you can do can change how things will be. It is false, because one’s doings and deliberations can change things, being themselves real parts of the (possibly deterministic) causal process.”
– Strawson (2010, p. 247, footnote 22) [Freedom and Belief, Revised Edition.]

Freedom under determinism

“Behind the whole compatibilist enterprise lies the valid and important insight that, from one centrally important point of view, freedom is nothing more than a matter of being able to do what one wants or chooses or decides or thinks right or best to do, given one’s character, desires, values, beliefs (moral or otherwise), circumstances, and so on. Generally speaking, we have this freedom. Determinism does not affect it at all, and it has nothing whatever to do with any supposed sort of ultimate self-determination, or any particular power to determine what one’s character, desires, and so on will be.”
– Strawson (2010, p. 94) [Freedom and Belief, Revised Edition.]

Variance estimation when matching with replacement

“Matching with replacement induces two types of correlations that must be accounted for when estimating the variance of estimated treatment effects. The first is a within-matched set correlation in outcomes. Matched subjects within the same matched set have similar values of the propensity score. Subjects who have the same value of the propensity score have measured baseline covariates that come from the same multivariate distribution. In the presence of confounding, baseline covariates are related to the outcome. Thus, matched subjects are more likely to have similar outcomes compared to two randomly selected subjects. The second source of correlation is induced by repeated use of control subjects. Failure to account for this correlation and acting as though the matched control subjects were independent observations will likely result in estimated standard errors that are artificially small and estimated confidence intervals that are artificially narrow. Added complexity is introduced by having subjects cross-classified with matched sets such that the same control subject can belong to more than one matched set.”

Austin, P. C., & Cafri, G. (2020, p. 1625). [Variance estimation when using propensity‐score matching with replacement with survival or time‐to‐event outcomes. Statistics in Medicine, 39(11), 1623–1640.]

A Word on Critical Realism, by Kieran Healy (2013)

I’ve just remembered this:

“[Critical realism] presents itself in a way that some social scientists—with next to no real background in philosophy—feel gives them just what they need to shore up their empirical research and metaphysical intuitions. You want to be realist in your philosophy of social science? Sure! You want your preferred level of analysis to also be an ontologically emergent level of reality? No problem! You want to talk about social structures as irreducible in some serious-but-not-really-analyzed fashion? You got it. You want your theory to be critical? I mean, who doesn’t, right? Just call yourself a Critical Realist and cite some Bhaskar. After all, he has repeatedly asserted that his work is a “Copernican Revolution” in the philosophy of science […]”


“The diffusion of CR was slightly hampered by the transformation of Bhaskar from fringe philosopher of science to full-blown guru. Having recruited followers in sociology on the basis of his realism, he began to pull the rug out from under them in the late 1990s, first with the merely absurd Plato, Etc and then with the frankly embarrassing From East to West: Odyssey of a Soul (which closed with a final chapter titled “The Dance of Shiva in the Age of Aquarius”). This work, in retrospect, seems like the culmination of the unpleasant cult of personality that grew up around Bhaskar in CR circles in the 1980s and which he seems to have done little to discourage.”

One section is constructive, providing alternatives to critical realism:

“Sociologists interested in emergence or macro-level explanations have no need to run together that interest with the specific CR position or view. (This was the point of my old article on Archer, Mouzelis, and CR.) There are large and immediately accessible literatures on all of these topics in philosophy, leading naturally to more technical or specialist work. Consider the SEP article on Emergent Properties, for instance, and the one on Supervenience, or the one on Scientific Explanation, or Scientific Realism. Go from there to, say, Jonathan Schaffer’s Is there a Fundamental Level? (for the metaphysics) or Michael Strevens’ Depth for one take on the philosophy of science, or—for something in parts similar to Bhaskar but far more creative and central—read Nancy Cartwright on laws of nature. I feel confident in asserting that different sociologists could ally themselves with quite incompatible positions in these debates and much of our work would go on as before.”