Review of Toby Handfield’s “A Philosophical Guide to Chance”

This blog post will review “A Philosophical Guide to Chance” by Toby Handfield. Throughout, I talk about its implications for the relevance of probability theory in its usual applications to the broad category of chance, risk, uncertainty, etc. (which is, ultimately, what all “interpretations of probability” attempt to capture), without of course intending to convey that this has any spillover effects on the application of the abstract mathematical theory to nonstandard entities such as tables, chairs, and mugs of beer (and therefore intending to convey no implications either for the unapplied, “pure” mathematical probability theory in itself), but nevertheless referring to it simply as “probability theory” (or “probability”) rather than “applied probability theory” or some other such bracketing locution.

Allegorical representation, drawn by Nano Banana, of Toby Handfield’s “A Philosophical Guide to Chance” destroying probability theory, with various themes from the book seen surrounding it. I had it drawn like this because my main takeaway from the book, as you will see, is that there is no good semantics for probability theory, meaning that, in an important sense, probability theory does not contribute anything to anyone’s understanding of anything.

Contents

• Why I am reviewing this here even though, from some points of view, this is a bad idea
• Summary of Toby Handfield, “A Philosophical Guide to Chance”
• Remarks on the book

Why I am reviewing this here even though, from some points of view, this is a bad idea

There are two good reasons for me not to review this book here.

1. It goes against my usual policy: I don’t usually review books on my blog, since I don’t usually have much to say about them besides giving a summary and saying “I recommend this” or “I don’t recommend this”. I have usually relegated such brief comments, sans summary, to my X/Twitter. Summarizing is dull, usually rather uncreative work, which I would only undertake for books that I am especially interested in disseminating, such as when I summarized Agnes Callard’s Aspiration and, back in the day, various books that I tried to summarize for Wikipedia (most interestingly The Open Society and Its Enemies and A Preface to Paradise Lost). Although my verdict on Handfield’s book is that it is good, I am not especially interested in disseminating it, especially since I believe much of its value is in its survey of other works, so that much of a summary of the book would consist in a second-hand summary of those other works, which feels like overdiluting things. There will be a summary of Handfield’s book here, but only a rather perfunctory one, to give a feel for what I’m talking about, not a detailed one like my summary of Aspiration, which was intended to help the reader follow Agnes’s argument. (I had found Agnes’s argument hard to follow because I thought she wrote paragraphs that were too long, which is ironic, given the length of the paragraph I’m writing now.)
2. I haven’t read this book with as much attention as I’d like. There was some skimming. When I talk about this book, I don’t fully know what I’m talking about. However, given how little detail this review will have, I will certainly not say anything confidently about any part of the book that I did not pay attention to, so this is not a big problem. The fact that I don’t have detailed comments on each microsection of the book is part of why I have kept the book summary separate from my broad, sweeping, ‘reviewing’ remarks.

The reason I’m reviewing the book here, which overrides the two reasons above, is that the book is very relevant to some of my past projects and will be relevant to some of my future projects. Probability theory is important in science and philosophy; it is a going concern. Handfield’s book establishes an important thesis about probability theory, and it has implications for all of my past and future work involving probability theory. So I need to at least have some sort of note, uploaded somewhere, signposting that this book exists and roughly more-or-less what its implications are. This post is that note. Also, reviewing the book on X/Twitter would not allow me to hyperlink other things from the review very nicely, which I want to do. So much, then, for the justification of the review.

Summary of Toby Handfield, “A Philosophical Guide to Chance”

Toby Handfield’s A Philosophical Guide to Chance is a guided tour of a single, stubborn problem: we treat “chance” as both (i) something objective in the world and (ii) something that tells us what it’s rational to believe and how to act—yet chance-guided belief can still “fail” in a particular case, and it’s surprisingly hard to say what makes a chance fact true.

The book begins by fixing the target. “Chance” isn’t (just) ignorance or a personal hunch; it plays a distinctive role in thought and science: it’s supposed to be a physical probability that normatively constrains credence (your confidence should match the chance you take there to be), without guaranteeing success in any one trial. That normative role is sharpened via Lewis’s Principal Principle (credence should track known chance, absent inadmissible information), but the early chapters also foreshadow the central sticking point: what counts as admissible, and—more deeply—what could ground chance so that it earns this authority over rational belief.

From there Handfield builds the most tempting “scientific” staging ground: the classical picture of a deterministic world of particles, positions, and velocities evolving under time-reversal-invariant laws. To talk sensibly about uncertainty in such a world, we represent “ways the world might be” as points and trajectories in phase space, and we represent ordinary propositions (like “there’s an elephant in the room”) as sets of microstates—regions in that space. This apparatus works beautifully for physics’ own categories, especially macrostates (temperature/pressure/etc.) as large phase-space “blobs,” and it sets up statistical mechanics’ key move: explain thermodynamic regularities by saying anti-thermodynamic behavior is not impossible but overwhelmingly improbable relative to a natural measure (“volume”) on phase space.

That statistical-mechanical picture is the launching pad for the first major metaphysical proposal: possibilist theories, which try to ground chance in “how the actual world sits among possibilities,” typically via relative modal volume. Handfield treats this as initially attractive—almost the default temptation once you’ve absorbed phase space and measures—but then systematically presses why it doesn’t deliver what chance is supposed to be. Volume-based chances struggle with conditioning on measure-zero events, with the vagueness and open-texture of ordinary propositions, and—most importantly—with the justificatory demand: why should that measure have any normative authority over rational credence? Attempts to vindicate the privileged measure by appeal to learning, frequencies, or “how well peers do” run into circularity: you end up using the very notion of “most” or “typical” that the measure was meant to explain. Even more sophisticated “washout” ideas (microconstancy/typicality) capture real robustness in practice, but still appear to smuggle in an ungrounded measure over possibilities.

The next major strategy is actualism: keep chance objective and real, but reduce it to purely actual, this-worldly facts—paradigmatically, frequencies or (more subtly) the Lewisian “Best System” account where probabilistic laws and chances are whatever best balance simplicity, strength, and fit to the actual history. Handfield grants the sophistication and influence of this approach, but argues it distorts how chance is meant to work. Crude frequentism fails because chance and finite frequency can come apart (and single-case chances collapse to 0/1), while Best-System actualism threatens counterfactual weirdness (chances depend too heavily on what actually happens), reverses the explanatory direction we ordinarily use (outcomes/frequencies explained by chances, not vice versa), and risks making chance’s normative force depend on an anthropocentric modeling compromise (tailored to limited creatures like us).

At that point the book opens the anti-realist landscape. If the realist reduction programs don’t ground chance, perhaps chance talk is (in one way or another) not tracking mind-independent chance properties. Handfield distinguishes: error theory (chance discourse aims at objective facts but none exist), subjectivism (chance claims depend on agents’ credences), and non-cognitivism (chance talk functions more like a guiding or expressive tool than a straightforward description). Subjectivism, he argues, collapses genuine disagreement and wrecks chance’s explanatory role in science; error theory and non-cognitivism remain live but owe us a story about why chance-talk is so successful and entrenched if it doesn’t describe objective chance facts.

Quantum mechanics then becomes the stress test: if anything forces objective chance on us, surely it’s QM. But Handfield’s survey of the main interpretive families—collapse, Bohm, Everett—aims to show that QM doesn’t straightforwardly rescue chance realism. Collapse interpretations can take chance as primitive (which doesn’t illuminate chance), Bohmian mechanics is deterministic and pushes probabilities toward typicality/ignorance-style stories, and Everett replaces “one outcome happens with probability p” with “all outcomes happen,” creating a new problem: reconstruct genuine uncertainty and justify the Born rule as uniquely rational. The many-worlds chapters push hard on the idea that self-locating uncertainty and decision-theoretic derivations can simulate the role of probability, but struggle to secure the robust, explanatory, uniquely action-guiding “objective chance” we started with—especially around death and selection/weighting worries.

Late in the book, Handfield turns to time. We experience chance as future-directed, yet many fundamental laws are time-symmetric. His proposed reconciliation is evidence-first: chance is tied to what credence is recommended by available evidence, and evidence is radically time-asymmetric because the past leaves records while the future does not. Statistical mechanics plus the Past Hypothesis (a low-entropy boundary condition) is brought in as the deeper physical explanation of why records and traces overwhelmingly point one way in time—why we get “footprints from the past” but not “portents from the future.” This supports an overall picture where “chance” varies with evidential situation and context, rather than being a fixed world-feature readable off the total microstate.

The final chapter makes the book’s argumentative posture explicit by analogy to moral debunking: chance concepts carry norms (coordinate credence with chance; use likelihood-style updating), and we can give a compelling “natural history” of why creatures like us adopt and rely on chance-thinking—because it’s practically indispensable for decision and for restraining our pattern-hungry tendency to invent causal stories. But that practical vindication doesn’t automatically yield existential vindication of irreducible, objective, physical chance properties. Handfield’s overall drift is therefore deflationary: keep the tool (probabilistic reasoning, Bayesian modeling, statistical mechanics, quantum predictions), but be suspicious of the heavyweight metaphysics—especially the idea that there must be mind-independent “chance facts” that both ground probabilities and uniquely dictate rational credence in the strong way many philosophers hoped.

In short: the book starts from chance’s everyday-and-scientific authority over rational belief, tries the two dominant realist grounding strategies (possibility-structure and actual-history reduction), finds both wanting (especially on normativity and explanation), tests the hope that quantum theory might force realism, and ends by recommending a broadly anti-realist / debunking-friendly stance: chance-talk is an extraordinarily useful practice for limited agents embedded in an entropic, record-filled world, but its success may not require—and may not support—robust metaphysical “chance-makers.”

Remarks on the book

Handfield is an invaluable guide to all previous philosophical proposals in probability semantics. To make a pun with his name, he really puts the whole field in your hands; he possesses a rare talent for pedagogical clarity, managing to render even the most formidable proposals accessible. A prime example is his treatment of John Bigelow’s proposal that “probabilities are ratios of volumes of possibilities.” If one attempts to read the original papers where Bigelow advances this view, one is immediately thrown into the deep end of a difficult formalism that can obscure the philosophical intuition. Handfield, by contrast, reconstructs the argument with the ease of an introductory textbook, without sacrificing the necessary rigor. I am grateful for this; it is representative of the service Handfield performs in making all philosophical proposals in the semantics of chance legible.

However, Handfield’s bright clarity in exposition is equally applied to illuminating the flaws in each of the proposals, and the book leads the reader to the conclusion that there is, in fact, no good probability semantics. I find myself in full agreement with his verdict on the existing literature: every major attempt to ground probability—whether in modal volumes, frequencies, or best-system analyses—is fatally flawed. Interestingly, Handfield identifies deep problems even within anti-realist theories, despite ultimately siding with an anti-realist stance himself. The result is that the book offers no semantic theory at all on which to rest, realist or not. You put it down feeling logically thoroughly briefed, but metaphysically homeless.

When I reflect on the dim prospects for probability semantics, I feel some relief that at least I’m not a LessWrong user. LessWrong is a website where the foundation of its philosophy is, among other things, overusing probability theory, applying it to all of life and reasoning. (Mostly they are “objective Bayesians” in epistemology, although of course, the broader attitude of probability overuse is not at all part of objective Bayesianism.) As Handfield’s book demonstrates by systematically dismantling the semantic grounds of chance, this is a precarious position. If probability lacks a coherent semantic footing, then building an entire identity or epistemic system upon it is the height of irrationality. To overuse a tool that we cannot fundamentally define is to actively work toward making language meaningless, communication impossible, and inquiry fruitless. LessWrong users are happy with this, of course, since without exception they hate all knowledge and always seek to destroy any possibility of anyone understanding any truth. (Since they are often autistic, I should note that this paragraph is largely hyperbole.)

Yet, even for those of us who have not staked our identity on Bayesianism, the drift toward anti-realism is uncomfortable. I do not particularly enjoy being forced into a position of philosophical scepticism regarding such a widely accepted field of research. Probability theory is everywhere: it appears in scientific explanation, in everyday deliberation, in statistics, and in decision theory. And it even appears in many proposals in philosophical semantics, such as the following three:

1. Adams’s Thesis, which analyzes natural-language conditional statements (“If A, then B”) by equating their assertability with the conditional probability P(B|A). This is extremely famous and you can read about it at the SEP, for instance, so there is really no reason for me to say more about it, even though it is more important than the other two.
2. Hannes Leitgeb’s rehabilitation of verificationism, which proposes that a sentence A is meaningful if, and only if, there exists some evidence B such that P(B|A)≠P(B). (I am very sympathetic to verificationism, but I have mostly been following a form of Gordian Haas’s version. Haas’s Minimal Verificationism is a great book. Notice how I don’t have much to say about most books, beyond recommending them. Besides its original proposal, which fully rehabilitates the verificationist criterion of meaning with only some small holes to patch regarding counterfactuals, Haas’s book serves as a great survey of historical verificationism, and I have used its information to make some improvements on the Wikipedia article about verificationism.)
3. My own previous work on concessive statements. In a post that I decided was not good enough for this blog, so that I instead posted it to my X/Twitter, I have previously modeled concessives like “even if p, [still] q” using a probabilistic threshold. If we let τ be a robustness threshold (e.g., 90%) and δ be a measure of how much p is implied to hinder q, the concessive assertion can be formalized as: P(q|¬p) −δ ≥ P(q|p) ≥ τ. (In plain English: q remains likely above threshold τ even given p, and p does not lower the probability of q by more than the “hinderance factor” δ compared to when p is false.) This work was inspired by Crupi and Iacona’s earlier, much better work which modeled concessives using a conditional logic, as well as the axiomatic (“Hilbert-style”) proof system that they built for this logic together with Raidl. Still, it further shows that, if probability theory could be understood, it would help understand some parts of language.

It is disappointing that these proposals, which had felt like they were clarifying vague linguistic phenomena, might simply be translating one thing we don’t understand (conditionals, meaning, concessives) into another thing we don’t understand (probability).

Granted, perhaps this translation is not entirely in vain. Even if probability lacks a fundamental “truth-maker” in the physical world, treating these problems probabilistically is helpful because it imposes structural coherence; we may not know what a “chance fact” is, but we know exactly how probabilities must relate to one another mathematically to avoid Dutch books or incoherence. By translating a linguistic problem into probability calculus, we trade vague, shifting linguistic intuitions for a rigid, checkable structure, albeit one which “hadeth no semantics”. We may not have found the ground, but we have at least found a rigorous syntax for our uncertainty. Handfield leaves us with the tool, but takes away the comforting illusion that the tool describes the furniture of the universe.

Against the Academics

This blog post tells the story of my intellectual development from an indeterminate point shortly before my memory cutoff around 2018 until today.

Saint Augustine wrote a dialogue whose title can be literally rendered “Against the Academics” (Contra academicos), but since this can be misleading, it is also often rendered into English as “Against the Academicians”. Augustine’s title was targeting the philosophers of the late Academy, which had begun as a Platonist school of philosophy founded by Plato himself, but had by Cicero’s time become a haven for philosophical sceptics, which is to say, people who denied the possibility of certain knowledge. With his work, Augustine intends to target the “Academic scepticism”, as it was called, and criticize it so as to refute it.

In editions of Augustine’s work in Brazil, the title in Portuguese is only ever translated “Contra os acadêmicos”, i.e., the exact same as “against the academics”. The equivalent of “Academicians” might have been “Academicianos” but this sounds odd and stilted, and I have never seen it. No matter. My intellectual development began with a Facebook page named after this work, “Contra os Acadêmicos” (CoA), at some unclear point in time shortly before 2018. The page often clarified that they had nothing against academics, but they were also against the sceptical philosophy of the late Academy, and similarly against whatever philosophies they saw as its modern descendants, such as relativism and postmodernism, etc. This is the common conservative narrative bemoaning contemporary relativism and postmodernism as the root of social ills.

The group running CoA was vaguely conservative-leaning, but they saw themselves as “anti-ideological” and were huge fans of Eric Voegelin; they often criticized right-wing “ideologues” as well as left-wing. The page mostly posted quotes by philosophers and sometimes shared relevant videos by Olavo de Carvalho or Clóvis de Barros Filho or whoever. (The most famous video by the latter, of course, is the video about “brio”, which is very applicable to CoA’s mission. Just today, the day when this post was written, Clóvis posted a reaction video to his own years-old video. More on the former in the next paragraph.) Their most popular posts were memes that they sometimes made to make fun of some philosophical opinions that they disliked. These were infrequent enough; they didn’t want to be a meme page, but they appreciated the increased reach that they got from the memes.

CoA was obviously downstream of Olavo de Carvalho, who, as I have mentioned before, single-handedly began the entire Brazilian right wing. They had clearly been students of Olavo to an unclear extent and appreciated the old man’s teachings and advice, but they weren’t dogmatic “olavistas” in any way and did not emphasize him much. They respected him and shared relevant clips from his lectures (e.g. clips of him giving study tips or summarizing some body of literature) at some points, moreso in the group that was associated with the page than in the page itself. The group was for discussion, I don’t recall many details of it.

CoA also posted reading lists. The biggest fan favorite was their general reading list about philosophy, which was roughly “in order of difficulty”, beginning with easier texts and moving on to more difficult ones. This list was first published as an image, then as an expanded image, and eventually, when they had a website, the very long latest revised version was published on their website. The website also hosted blog posts and various other reading lists on various subjects, as well as “ordered reading lists” about particular authors they recommended, because they often got the question “which book by this author should I read first?”, so they decided to set up a path through each author. Often they simply recommended reading everything by the author in chronological order, but there were exceptions.

Obviously I loved all these resources, and was earnestly edified by the philosopher quotes and study tips and videos that they shared. But the picture of what they provided to me is incomplete without the general vibe, or climate, of talking to them, which was the motivation that they implicitly gave for an intellectual life. It was the idea of getting serious about culture war. You may have heard the conservative concern about how left-wingers control academia, and which is sometimes used to defend “DEI for conservatives”. Well, not for them. They wanted to inspire the conservative movement to study harder than the left-wingers, to become more knowledgeable than their opponents, to expose their charlatanry, and take academia back by the force of their merits. That was the vibe that I got from them, anyway. And in some way I wanted to be part of that, too, although I never became an academic.

In this sense, they really were “Against the Academics”, although they didn’t say it in so many words. They were defined by their desire to be better than the academics who opposed their views, although of course, they had nothing against academics as such, and many were studying to become academics themselves. They wanted their constellation of online study groups to be an academia unto itself, and take back academia from the academics. This was certainly a cause that Olavo de Carvalho supported, indeed it was plausibly the main goal of his entire teaching career, and he praised CoA at some points (although I don’t care to find the Facebook posts where he did this).

I began to read serious books with much help from CoA’s lists, but also from my own curiosity, attempting also to follow some “Great Books” lists I found (see Greater Books). Eventually, what I followed in my readings was roughly an historical order (first the ancient philosophers, then the medievals, then the early moderns, etc.), but the introductory books that they recommended got me to wet my feet. During this time, in which I was still first learning about intellectual topics, I never got much into Olavo de Carvalho beyond what is called The Minimum, which is a collection of newspaper columns written by Olavo. My curiosity about Olavo intensified only years later, leading to the page on my blog about him.

Eventually CoA became much less active for whatever reason, although thankfully, their website is still up. I began to follow various English-speaking philosophy meme pages on Facebook, and became friends with some meme page admins. During this time, which was still 2018–2019, I had just converted to Catholicism due to some of my readings and some encouragement that I had found in religion discussion Discord servers, and some of my Facebook philosophy meme page friends were Catholic philosophy nerds who also encouraged me. I was still relatively early into getting into intellectual topics, and I did much of my discussion in a now-defunct Facebook group that was run by two of these meme page admins, who have since fallen out, hence I am not giving names and details about them so as to avoid stoking the drama again. But discussions among these people who I found through Facebook were also very formative to my intellectual development.

Eventually, let’s say by late 2022 at the latest, I fell mostly out of touch with the people I met through Facebook. I also became less conservative and more libertarian. Elaborating properly on this would require elaborating, for contrast, on the people whose personal details I omitted, but let’s say the main thrust of this development is something I underwent entirely on my own, through the development of my own ideas, which I systematized by writing this very blog (hence its unusual structure, with an ordered table of contents and a glossary, although much of the content is not fully up to my current quality standards).

Much later than that, in the latter half of 2023, I started using (although my account was created much earlier) Twitter, which got renamed to X, which is where I made an entirely different set of friends, which encouraged the interest in analytic philosophy that I had already developed on my own. Hence, today I am very interested in analytic philosophy, which is what informs my newer blog posts, whereas my older blog posts about philosophy were informed only by ancient and medieval writings, or Kant at the latest. I have finally caught up to the contemporary era, so to speak. But I still have much to learn.

Due to my current libertarian political beliefs, I advocate policies that would result in the destruction of academia as we know it, since that is largely state-funded. Hence, I should also like to undermine trust in academics and their theories and publications, so that people don’t feel very many qualms about nuking all of their institutions. And my sense of pride, and of wanting to know my enemy, still leads me to want to study academic theories in detail, and be an academia unto myself, so as to oppose their theories with proper rigor, indeed more rigor than those who I oppose. In this way, today, I am “against the academics”, in much the same sense as CoA were, but much more intensely than they ever were, and not particularly for culture-war reasons (since I am culturally progressive myself). In terms of general attitude and motivation for intellectual development, I am back somewhere near where I started.

Demonstrated preference

Murray Rothbard’s theory of demonstrated preference is not explicit enough for my taste, and hence I hereby endeavor to make it more explicit. The goal of Rothbard’s theory is to develop a weak, operational notion of preference which can be used to ground utility and welfare judgments in a “value-free” way, without importing a heavy metaphysics or ethics, but still delivering important economic welfare theorems such as “voluntary trade leaves all participants better off”, etc. The theory comes from his awesome paper, “Toward a Reconstruction of Utility and Welfare Economics”.

This blog post records the main results of an enlightening conversation I had with Jade, who led me to notice that the precisification was needed and pointed out the oddity about exchange and the vagueness of “disturbance”, as well as the core idea of the HDRT.

Infographic based on this blog post (Nano Banana)

Contents:

• Rothbard’s statement
• Preliminary objections dismissed
• Precisification
• Derivation of Rothbard’s results
• Questions, oddities, and worries
• VBDP oddity: Interpersonal exchange not better than autistic exchange?
• PPDP questions and worries
• 1. Legitimately owned goods
• 2. Consent and disturbances
• 3. Harmless Death Ray Theorem
• 4. Irrelevance worries
• Conclusion

Rothbard’s statement

As stated by Rothbard, the concept is as follows (p. 2):

Human action is the use of means to arrive at preferred ends. Such action contrasts to the observed behavior of stones and planets, for it implies purpose on the part of the actor. Action implies choice among alternatives. Man has means, or resources, which he uses to arrive at various ends; these resources may be time, money, labor energy, land, capital goods, and so on. He uses these resources to attain his most preferred ends. From his action, we can deduce that he has acted so as to satisfy his most highly valued desires or preferences.

The concept of demonstrated preference is simply this: that actual choice reveals, or demonstrates, a man’s preferences; that is, that his preferences are deducible from what he has chosen in action. Thus, if a man chooses to spend an hour at a concert rather than a movie, we deduce that the former was preferred, or ranked higher on his value scale. Similarly, if a man spends five dollars on a shirt we deduce that he preferred purchasing the shirt to any other uses he could have found for the money. This concept of preference, rooted in real choices, forms the keystone of the logical structure of economic analysis, and particularly of utility and welfare analysis.

Comic based on the core argument of Rothbard’s paper (Nano Banana)

Preliminary objections dismissed

Even before making it more precise, it may seem that this concept of preference is simply wrong, and cannot serve as a foundation for determining utility or welfare.

1. Regrets: People often do things that, in natural language, we would say that they did not prefer to do, in view of the fact that afterwards, they regretted doing them.
2. Addiction: Addicts are said to make choices “compulsively”, which means they don’t really want to do them in some sort of true way which is more important than whatever sort of ‘wanting’ governs their actual action.
3. Ignorance: Even if people are always doing the best action they can think of, sometimes there are actions that they simply don’t know are possible, and which they would choose to do if they knew about them, and it seems that those better possible actions are the actions that they really prefer to do, rather than the ones that they actually do.
4. Weakness: Sometimes people already know of better actions that they would do if they could do them, but they don’t do those actions because they lack the resources, or the physical strength, or some other prerequisite for the action, and hence it seems that those actions-lacking-means are the actions that are truly preferred, rather than the actions-actually-done.
5. Equal outcomes: It seems that the way that we speak of actions in natural language allows for situations where the same world-state W can be caused either by an action A being done, by an action B being left undone, or by an action C being done in violation of someone’s preference. If the outcome is the same, the action-preference structure can seem irrelevant to whether anyone prefers the outcome, and it can seem that action-preferences cannot be really as important as outcome-preferences.

These five objections are dismissed rather than answered because the demonstrated-preference economist will only answer them with a confession of poverty. The demonstrated-preference economist admits that such phenomena do exist in the world as described by natural language, and that they are not accounted for by his demonstrated-preference theory. Nevertheless, it is the demonstrated-preference economist’s assessment that there is no better, richer theory that can capture all of these phenomena without importing heavy metaphysical or ethical assumptions that are not suitable for value-free economic theory. So the demonstrated-preference economist simply confesses our poverty regarding the pursuit of a richer theory that can capture all of these phenomena, and gives up on such a pursuit. Nevertheless, the demonstrated-preference economist finds that his theory can derive many true and interesting theorems about the satisfaction of preference so-understood, which motivates his continued enterprise. However, in order to continue the demonstrated-preference enterprise in such a way as to be explicit enough for Thiago’s taste, a precisification of the theory is in order.

Precisification

Before stating the concept, Rothbard repeats his usual action axiom, that “human action is the use of means to arrive at preferred ends”. In doing this, I take him to be, among other things, taking the distinction between voluntary and involuntary behavior as a primitive, where only voluntary behaviors can be actions. Then we might think that demonstrated preference is exhausted by the following condition:

VBDP: If, at time T, an agent S exhibits a behavior B voluntarily, then S demonstrates a preference for engaging in B at T.

Rothbard clearly accepts VBDP, but as stated, VBDP does not suffice to get the conclusions Rothbard wants. For Rothbard certainly wants it to follow from the definition of demonstrated preference that aggression leaves the victim worse off, and there is nothing in VBDP that allows deriving this. So I think Rothbard needs to supplement VBDP with an additional condition:

PPDP: At every time T, every agent S demonstrates a preference for continuing to possess, without any unconsented disturbance from any other agent, all goods that S currently legitimately owns and is not currently in the process of giving away, trading away, or throwing away.

And I think that that’s enough to get Rothbard’s intended results, as I will show next, but it also raises some questions, as I will show after that.

Derivation of Rothbard’s results

I contend that together, PPDP and VBDP exhaust Rothbard’s concept of demonstrated preference, and they get the results Rothbard wants:

• Aggression Result: All aggression leaves the victim worse off, via PPDP.
• Trade Result: Voluntary trade leaves all participants better off, via VBDP.

This suffices to get Rothbard’s laissez-faire result as soon as the Unanimity Rule is added, namely (p. 23):

Unanimity Rule: We can only say that “social welfare” (or better, “social utility”) has increased due to a change, if no individual is worse off because of the change (and at least one is better off).

The Aggression Result and the Trade Result, combined with the Unanimity Rule, yield the Laissez-Faire Result:

• Laissez-Faire Result: All-and-only actions that do not interfere upon legitimate private property can be said to increase social utility.

And this was the intent.

Questions, oddities, and worries

However, the precisification leaves us with some questions, oddities, and worries.

VBDP oddity: Interpersonal exchange not better than autistic exchange?

One oddity about the Trade Result is that while it says trade leaves everyone better off, it seems to make it illegitimate to say voluntary trade leaves you more better off than voluntarily refraining from engaging in trade. After all, either kind of choice is a voluntary behavior, and by VBDP, increases welfare; and as Rothbard emphasizes, there are no magnitudes of preference to be compared. But certainly there seem to be economic theorems to the effect that trading is a better means to people’s ends than refraining from trade; so I should like to see a reconciliation of this.

PPDP questions and worries

The clarification that PPDP is needed for the results also leaves us with some questions that Rothbard did not raise or address:

1. Legitimately owned goods

PPDP introduces a concept of “legitimately owned goods”. It is necessary to talk about legitimate ownership rather than mere possession, or else Rothbard’s laissez-faire result does not follow as he intended it. Is this concept legitimate in economics? Is it precise enough, and is it wertfrei?

2. Consent and disturbances

PPDP introduces a concept of “unconsented disturbance”. This requires further precisification of “disturbance” and “consent”. These concepts seem to be vague and, to a large extent, culturally relative. Can they be made precise enough for economics?

3. Harmless Death Ray Theorem

We should also like an adequately formal theory of how actions play out in time, so as to avoid what I’ll call the Harmless Death Ray Theorem (HDRT), as follows. Suppose time is discrete, i.e., for the temporal ordering relation ≺, we have forward-discreteness [∀x∀y(x ≺ y → ∃z(x ≺ z ∧ z ⪯ y ∧ ¬∃u(x ≺ u ∧ u ≺ z)))] and backward-discreteness [∀x∀y(y ≺ x → ∃z(z ≺ x ∧ y ⪯ z ∧ ¬∃u(z ≺ u ∧ u ≺ x)))]. Suppose further that over this discrete temporal order, we have “atomic actions”: at time t₁ the action has not yet begun, and at the immediately next time t₂, the action has already been completed. Then if we allow that acts of aggression can be atomic actions (for color, we can call an atomic act of aggression a “death ray”), it seems that PPDP cannot allow there to be a preference against these atomic acts of aggression, since at t₁ the destroyer has not yet done anything, and at t₂ the victimized owner cannot demonstrate a preference for owning his property, which is already gone (so paradoxically, the “death ray” is proved “harmless”, since it does not reduce welfare). Clearly we do not want the HDRT to follow. Is preference theory committed to the density of time, and the non-existence of atomic actions? Or should we instead reformulate the preference conditions to be forward-looking rather than at-an-instant? Does this not, in some way, reintroduce the constancy assumption which Rothbard dreaded?

4. Irrelevance worries

PPDP seems to raise some worries about demonstrated preference having nothing to do with preference in natural language, making any concept of welfare derived from it dubious as being truly a concept of welfare as we would think of it in natural language.

Some of these worries are mere restatements of the preliminary objections that we had dismissed earlier, which tend to resurface when PPDP is stated. For instance, suppose that relinquishing your property requires performing some action, call it an act of forfeiture, which, for whatever reason, you haven’t been able to afford to do recently, but which you will do as soon as you can afford to. Is it fair to say that you demonstrate a preference to hold onto your property at every moment until you manage to perform the act of forfeiture? Aren’t you instead glad it was taken off your hands, if it was?

But others of these worries are independent of the preliminary objections and exclusive to PPDP. For instance, owners can own property that they are far away from, and currently not consciously aware of. Can they really be demonstrating any preference regarding their property just by the fact that they own it? Aren’t you instead making a forward-looking constancy assumption that, since they own the property now, then it must be true that, later, when they find out that their property was harmed, they will feel bad about this?

Conclusion

I hope to, at some point, develop a version of demonstrated-preference theory that comes with a solution to the questions, oddities, and worries above. For now, the goal was simply to record my precisification and the fact that these worries are raised from it. Rothbard’s paper was very inspiring and interesting, and I should like to see it developed into a truly reconstructed welfare theory, vindicating the Laissez-Faire Result and its wertfrei nature, if that can be done.

Postcript: Admittedly, it would be closer to the text if we could somehow derive PPDP from VBDP. I am not sure how to do this, but assuming private property is conceived of in Rothbard’s libertarian way, I think maybe it can be done by means of an ontology of “purposes”, as sketched here. For prior work on analysis of demonstrated preference, see this paper, which was pointed out to me by Dabchick.