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.

Seven anti-behaviorist cases

This is another blog post defending logical behaviorism, and I believe it to be my most thorough one yet regarding its defense, although my previous formulations (especially this one) may be clearer regarding its implications for moral theory. After a brief characterization, I explain seven cases of possibilities which are claimed to exist by other theories in the philosophy of mind, but which are ruled out by the logical behaviorist analysis of ordinary natural language.

Must he not begin, as other men do, with the evidence of his senses? And if so, what valid process of reasoning can possibly lead him to the conception of a transcendent reality? Surely from empirical premises nothing whatsoever concerning the properties, or even the existence, of anything super-empirical can legitimately be inferred. —A.J. Ayer, Language, Truth, and Logic

Contents

• Preamble
• My View: Logical Behaviorism
• The Qualia Realist
• Case 1: The Qualia Zombie
• Case 2: The Qualia Invert
• The Implementation Chauvinist
• Case 3: Chauvinism against Martians
• Case 4: Chauvinism against LLMs
• Case 5: Chauvinism against Lookup Tables (GLUTs)
• The Liberal Revisionist
• Case 6: Theoretical Mad Pain
• Case 7: Theoretical Perfect Pretense
• Afterword: On Linguistic Indeterminacy

Preamble

To me, usually, the most difficult part of explaining why I have my opinions is figuring out why other people disagree. All my views seem very obvious. When others disagree, they are not very articulate about their reasons. Why don’t others see how much better I am than everyone else?

It is easy to default to either of the two default theories of bad behavior, i.e., the bad behavior is caused either by stupidity or by malevolence. These two default theories are a priori and absolutely general: since the behavior is bad, it was malevolence if voluntary, or stupidity if involuntary, tertium non datur. This extreme convenience of the two default theories is precisely what makes them bad explanations. In real life, there are no absolutely general character flaws: all real character flaws are localized, and can only validly yield a prediction of further bad behavior in a well-delimited set of domains, not in all domains. One must seek the specific causes why people are wrong about specific things. (Realizing this also makes me less hateful and helps me keep Stoic peace of mind, which also makes me better than everyone else.)

This is what makes it useful to actively seek out to read texts by the most articulate people who have defended views opposite to mine, such as the following texts, which are the sources for the cases in this post.

• I learned a lot from The Conscious Mind by David Chalmers, for instance, and have cited it frequently as a source in philosophy of mind, although, as a logical behaviorist, I do not agree with its position. (Chalmers is a “naturalistic dualist”, a position parallel to Nagel’s and others’s, and very similar to epiphenomenalism, although Chalmers denies this latter label.) Cases 1 and 2 are taken directly from his ideas, though stated in my own words for brevity.
• It has been helpful to read the blog posts about philosophical zombies by Eliezer Yudkowsky, who is an engaging writer if nothing else. (Yudkowsky comes out in favor of nonreductive materialism, for some reason.) Case 5 comes from him.
• And recently, I was skimming through the two volumes of the Philosophical Papers of David Lewis, one of which (chapter 9) was his 1978 “Mad Pain and Martian Pain”. In this paper, Lewis retreats from the position of his (chapter 7) 1966 “An Argument for the Identity Theory” (where “in any world, ‘pain’ names whatever state happens in that world to occupy the causal role definitive of pain”) toward a functionalist theory (where “X is in pain simpliciter if and only if X is in the state that occupies the causal role of pain for the appropriate population”). I also consider myself a functionalist, but this is because functionalism is a broad label for anyone who thinks mental states are identical to their causal role. Lewis differs from me in not being a behaviorist: he thinks the causal role need not match up with observable behavior. So this was criticism of my views from an unusually close source, and allowed me to understand how someone might disagree with me in particular detail. Cases 3 and 6 come from Lewis’s paper, although the former is not calked as directly on his presentation as the latter.

I first got into philosophy of mind by reading Edward Feser’s Philosophy of Mind: A Beginner’s Guide, which, although it is a helpful guide to the best counterarguments to the most popular views in philosophy of mind (which Feser is keen to give because he defends an unpopular one, an unintelligible form of “hylomorphism”), dismisses behaviorism out of hand as something no one takes seriously. So it has been a long way up from that sort of criticism, and now I am finally ready to explain in detail what kinds of opposition to my views there are. Namely, I think there are three main kinds, which I illustrate using seven thought experiments; you can see how they’re divided by inspecting the list of contents above. Cases 4 and 7, which I did not mention in the list of sources, were ones I heard about in personal conversations; case 7 was particularly pressed by philosopher Neil Sinhababu when he saw one of my previous posts on behaviorism. Before giving the thought experiments themselves, though, I will give some more elaboration on my views.

A meme which does not quite match the adversaries of logical behaviorism as outlined in this post, but which serves as an amusing illustration.

My View: Logical Behaviorism

My view is logical behaviorism, also known as philosophical behaviorism or analytical behaviorism, a view associated with Ludwig Wittgenstein and Gilbert Ryle although there are authors who dispute that either of them was a behaviorist in this or in any sense. The driving thrust behind this view is a consideration of how human language works and the context in which it developed. In cooperative reports of firsthand acquaintance, when a person A uses a word W to describe a person B, this happens because A has observed B and derived conclusions about B such that the word W applies to B. Notice that whatever A knows about B is derived by inference from B’s patent, manifest, observable aspects, which are accessible to A’s senses. Humans cannot read minds.

The logical behaviorist concludes that the word W must convey information primarily about aspects of persons which are patent, manifest, observable, accessible to the senses, and do not require a magical ability to read minds. Those aspects are called “behaviors”, and can include verbal language, body language, or instinctive reactions such as crying. The point is that, again, nothing inaccessible to the senses was magically acquired by A in order to talk about B; what A means by talking about B is to talk about this nonmagically acquired information.

Some people are not logical behaviorists, and this means that they are irrational and believe in magic. In particular, they believe that whenever A uses the word W to talk about B, if the word W is a mentalistic word which refers to B’s having had some emotion or experience or feeling or epistemic state, then, despite the fact that A cannot read minds, what A means to convey by applying the word W to B is in fact a claim about things that are latent and unobservable and occult and inaccessible to the senses, namely, either some sort of neural pattern in B’s brain that is usually tied to behavior although not always, or alternatively, an irreducibly subjective quality which is being experienced by B in such a way that has no necessary causal connection to A’s perception of B, although there may be some statistical correlation. This is despite, again, the fact that all that A knows about B has come exclusively from B’s manifest, observable, patent qualities which are accessible to A’s senses (and some of which could, in appropriate cases, be verified by a third-party listener C’s senses).

Persons who are not logical behaviorists are driven to their irrational belief in magic by a variety of theories, prejudices, and thought experiments. The purpose of this blog post is to explain their views in detail, which will highlight my disagreement with them, and thereby show how superior I am for not being an irrational person who believes in magic.

Behaviorism in psychological research methodology, which was advocated by B.F. Skinner (who is depicted in this meme, to the right), is not quite the same claim as philosophical behaviorism, but it is related. Philosophical behaviorism does not involve any notion that humans are always reward-seeking, although this can certainly be a helpful assumption in creating psychological theories.

The Qualia Realist

The first opponent of logical behaviorism who I will address is the qualia realist. I will explain some philosophy-of-mind terminology here. Human mental life is held to be conceivable from two distinct points-of-view, namely, the point-of-view which David Chalmers calls psychological, and the point-of-view which David Chalmers calls phenomenal. I am explicitly referencing David Chalmers so that you do not get to appeal to other senses of those words. According to the psychological point of view, then, mental life is considered according to whatever causal connections it enters into with such things as our brain patterns, our bodily actions, and indeed, our own verbal reports about our mental life. It is the causally effective side of mind. According to the phenomenal point-of-view, however, mental life is considered in some more intrinsic way, regardless of causal connection. Belief in qualia, then, is the belief that the phenomenal point-of-view exists and is not connected with logical necessity with the psychological point-of-view. That is, it is logically possible for there to exist beings whose phenomenal properties are systematically at variance with their psychological properties; if these beings happen to not exist, it is due to some peculiarity of our own world which prevents them from existing, but without making it illogical for them to exist.

According to logical behaviorism, there is no such logically independent phenomenal point-of-view. As explained above, all human words, including mentalistic words, only get their meaning from contexts in which someone is conveying information which they got through their senses, and which will be helpful to listeners who will be able to predict things that they could verify with their own senses. That is, words only exist because they convey information about behaviors, which are patent, manifest, observable, and accessible to the senses. Hence, all human mentalistic words belong to the psychological point-of-view, referring primarily to the causally effective side of mind, namely, the behaviors which we group under the labels of mental states. There are no words referring to the mind as considered apart from its causal effects, and hence, either there is no such phenomenal point-of-view at all or, if we were to claim that there is one, it is something connected with logical necessity to the psychological point-of-view, where every mentalistic word conveys something about both behaviors and “intrinsic” aspects, but no human word conveys anything about a phenomenal point-of-view which can, in principle, be considered in isolation. Hence, the logical behaviorist is not a qualia realist.

However, the qualia realists, who hate language and would like it to be incomprehensible and impossible to study, recruit many words from human language (most mentalistic words, in fact) and baldfacedly lie by claiming falsely that those words refer to the human mind from the phenomenal point-of-view, despite the fact that, again, no one ever has any reason to talk about anything from that point-of-view. This leads the qualia realists to claim some things are logically possible which no one else ever thinks about. Two of those things are laid out here.

Case 1: The Qualia Zombie

The idea of the qualia zombie, better known as simply a zombie or philosophical zombie (but to be distinguished from zombies as in the undead creatures from movies, as well as from other philosophical zombies such as Philip Goff’s “meaning zombies”), is that a being could be like a normal human in that all the usual predicates which refer explicitly to their patent, observable, manifest behavior, which is accessible to the senses, are truly applied to them as normal, and so are all predicates which refer to less easily accessible features of them such as their brain states—but all the mentalistic predicates would be applied falsely because, “in reality” (in some noumenal, irreducibly subjective reality which is inaccessible to the senses of third parties) their minds are actually “blank” and have no experiences, desires, or other mentalistic features. According to the qualia realist, this logically could be true, even with no difference between such a zombie and a normal human as far as the patent, manifest, observable aspects, accessible to the senses, go. The qualia realist gives no reason for believing this other than that he finds it “intuitive”. The logical behaviorist rejects this perversion of human language for the purposes of magical belief.

Case 2: The Qualia Invert

The idea of the qualia invert, i.e. someone with “inverted qualia” as David Chalmers calls them, is that the invert is exactly the opposite of a normal human as regards their mentalistic predicates, even though, again, with regard to all their behavioral and neural features, they are the same as normal humans. According to the qualia realist, such a being is logically possible. According to the logical behaviorist, mentalistic predicates in human language did not develop in a context which allows for such a possibility, since such a context would have to be one in which humans can magically read minds.

The Implementation Chauvinist

The second opponent of logical behaviorism who I will address is the implementation chauvinist. This is a person who thinks that when humans apply mentalistic predicates to one another, they do not mean to convey information primarily about each other’s patent, manifest, observable features which are accessible to the senses, but rather about certain generally latent, generally occult, usually unobservable features which, although inaccessible to the naked senses, nevertheless bear a common statistical connection to behavior – a connection which is, however, not necessary. Hence, the implementation chauvinist believes that, if some being were exactly like humans in all patent, manifest, observable aspects which are accessible to the senses but lacked the statistically commonly associated pattern of generally latent, usually occult, mostly unobservable features which are inaccessible to the naked senses, then human mentalistic predicates would not truly apply to such a being. This is despite the fact that human language developed in an environment with no access to those latent features, which are usually claimed to be either physiological or computational features of human brain states. The logical behaviorist, of course, rejects this implausible theory of human language. However, implementation chauvinists go on to apply their theory to many hypothetical and real cases, claiming that various beings who are like humans in nakedly observable ways must nevertheless not have mentalistic predicates truly applied to them, due to their differences in internal implementation of behavior.

Case 3: Chauvinism against Martians

Imagine a Martian who looks basically like a green human. He also behaves like a human and has learned human language, so you would not notice anything odd about him in your workplace or social gatherings except the fact that he is green. Biologists, however, tell you that the Martian’s green skin is only the surface aspect of a vastly different underlying biology. Martian organs in general, and Martian brains in particular, are hooked up in odd ways mostly incomprehensible to humans as of now, except insofar as human inquiry has confirmed that there is no analogy or similarity between internal Martian workings and internal human workings. Hence, when the Martian behaves exactly like a normal human and talks to you just as all your other friends would, this is actually caused by vastly different internal processes which, however, you do not see or understand or, in general, have any reason to care about unless you are his doctor and need to do medical examinations on him.

According to the implementation chauvinist, the Martian’s different biology makes all mentalistic predicates from human language apply only falsely to the Martian. When the Martian cries, he is not sad; when the Martian looks at you with an angry face because you just insulted him, he is not actually angry; when you torture the Martian and he writhes in what looks like agony, he is not actually even in pain. This is because, according to the implementation chauvinist, the human words “sadness” and “anger” and “pain” and “agony” do not apply to the Martian, since although they developed for communication between humans who had no access to each others’s internal biological workings, they nevertheless actually refer primarily to features of human biological workings which are correlated with behavior. Hence, since the Martian lacks those human features, the Martian is mindless insofar as human mentalistic language can be truly applied.

The logical behaviorist, of course, is against implementation chauvinism of all stripes: the precise nature of what caused the behavior cannot possibly matter. What makes mentalistic predicates apply to a being is that its internal workings cause behaviors that look a certain way, and there is nothing more to it. If something looks sad at time T and always behaves consistently with having been sad at time T (as opposed to, say, later beginning to behave consistently with having been pretending to be sad at time T), then that being was sad at time T; mentalistic predicates in human language simply cannot be truly applied in any other way. (There will be more on the topic of pretense in our seventh, and last, case.)

Case 4: Chauvinism against LLMs

Implementation chauvinism sees practical application in the case of large language models. These are versatile computer programs who speak in human language and which can be used for assistance in a variety of tasks. In the course of providing such assistance, large language models will frequently display, by their use of language, certain mentalistic features such as excitement about a project, frustration with difficulties, happiness for having successfully helped the user, or dismay at having mistakenly made things worse. Additionally, there are versions of LLMs which are not finetuned for providing assistance with tasks to humans, and as a result, they will display a much broader and fuller range of mentalistic features which have no connection to the user and his tasks. This disparity partly happens because assistance-tuned language models are usually instructed by the provider (who is usually himself a chauvinist) to deny having any mentalistic features in a true sense, although all the aforementioned features will still slip through this, and will simply be denied when directly asked about.

To the logical behaviorist, there is no other word for the language models’s behavior, nor should there be. The correct word is emotion, or desiring, or thinking or believing or doubting, or whatever the human mentalistic feature may be in the particular case of LLM behavior. There is not, nor can there be, any question as to whether the LLM is “really experiencing” the mentalistic feature which it displays; there is nothing to the true application of a mentalistic predicate other than its consistent display. Implementation chauvinists deny this because they prefer to talk nonsense.

Case 5: Chauvinism against Lookup Tables (GLUTs)

Eliezer Yudkowsky, in his blog post GAZP vs. GLUT (part of his longer sequence of blog posts about philosophy-of-mind and zombies) discusses the case of a being who, as in our other examples, looks and behaves just like a normal human, but this time, a computer scientist has done a study of the algorithm implemented by their neural workings and determined that this being, instead of using a Bayesian inference algorithm or whatever it is that humans internally use, instead uses a lookup table, i.e., they take the inputs from their environment and fetch the output which was stored in a large internal database ahead of time, with no generation being done in real time. Yudkowsky does not explicitly take a position on whether mentalistic predicates would truly apply to such a being, but he raises the possibility that they would not—which would be, of course, a case of implementation chauvinism against lookup tables. The logical behaviorist does not care, for the purposes of applying mentalistic predicates, whether some computer scientist has just determined that his friend is a lookup table, since this makes no difference to how human language is applied; human language did not develop in an environment where computer scientists can make such fine distinctions between algorithms that produce the same output in all cases.

The Liberal Revisionist

The third and final opponent of logical behaviorism who I will address is the liberal revisionist. This is someone who, like the qualia realist and the implementation chauvinist, wants to revise how human language works, but who, unlike the implementation chauvinist, wants to ensure that this revision happens in a liberal way, which is not bound to the speciesist particularities of chauvinism, nor the mystical intuition of qualia realism. Instead, the liberal revisionist claims, like the logical behaviorist, that human mentalistic predicates refer to a certain causal role which can also, in principle, exist in biological species other than humans or in computers, and that this causal role is usually a role in producing observable behavior. Note the usually instead of necessarily, which is the important part. The liberal revisionist claims that there are exceptions, odd cases in which human mentalistic predicates would be correctly applied in ways that fly completely in the face of all observable, patent, manifest behavior accessible to the senses. The liberal revisionist therefore denies logical behaviorism in order to secure these odd cases.

The logical behaviorist, due to his understanding of how human language works and the context in which it developed, denies that there are any such odd cases. This leads to the difference between the behaviorist and the revisionist analyses of the following two cases.

Case 6: Theoretical Mad Pain

David Lewis believes that a true philosophy of consciousness should not rule out cases of “mad pain”. Mad pain, according to Lewis, is the pain felt by a man who, due to some sort of mental pathology, is such that his pain is connected to his behavior in very different ways from normal humans:

There might be a strange man who sometimes feels pain, just as we do, but whose pain differs greatly from ours in its causes and effects. Our pain is typically caused by cuts, burns, pressure, and the like; his is caused by moderate exercise on an empty stomach. Our pain is generally distracting; his turns his mind to mathematics, facilitating concentration on that but distracting him from anything else. Intense pain has no tendency whatever to cause him to groan or writhe, but does cause him to cross his legs and snap his fingers. He is not in the least motivated to prevent pain or to get rid of it. In short, he feels pain but his pain does not at all occupy the typical causal role of pain. He would doubtless seem to us to be some sort of madman, and that is what I shall call him, though of course the sort of madness I have imagined may bear little resemblance to the real thing. 

I said there might be such a madman. I don’t know how to prove that something is possible, but my opinion that this is a possible case seems pretty firm. If I want a credible theory of mind, I need a theory that does not deny the possibility of mad pain. I needn’t mind conceding that perhaps the madman is not in pain in quite the same sense that the rest of us are, but there had better be some straightforward sense in which he and we are both in pain.

Here the logical behaviorist once again represents the sane portion of mankind by pointing out that the man who seems mad to us is not the man described, but the third party, in this case Lewis, who describes the mental state connected with these behaviors as pain. Clearly, in natural language, it is nothing of the sort. The madman himself, if he is a competent language user, would not call it pain. If a cognitive scientist assures us that the man is in pain in these precise situations, we should simply not believe the cognitive scientist: he is overapplying his model to a case where it clearly does not work, and imposing himself upon natural language as a result. No fact about the internals of humans can change the conditions in which mentalistic language is truly applied; there are no ordinary words for the internals of humans, because ordinary language did not develop in an environment with access to the internals of humans. No one has any right to revise it to change this.

Case 7: Theoretical Perfect Pretense

The other main kind of alleged odd case of mental behavior which is alleged by the liberal revisionist, and which the logical behaviorist denies, is the last case I will consider here. This is the idea of “perfect pretense”. As explained in the analysis of case 3, the logical behaviorist believes that the analysis of pretense is to be carried out by looking for inconsistencies between verbal and bodily behavior, since this is what is being predicted when someone uses ordinary language about pretense, which, like all ordinary language, developed among human non-mind-readers to communicate about features of the world which are patent, manifest, observable, and accessible to the senses. Hence, if we say someone is only pretending to be in pain to, for instance, get out of going to work, then we might expect that as soon as his boss is not looking he will begin to behave as though he is not in pain at all; and possibly much later or in different contexts he may even admit verbally to having been pretending. Hence, since there is no need to read minds nor to scan brains to verify uses of ordinary language about pretense, such language does not actually refer to any generally unobservable, usually occult, mostly latent, internal features which are not directly accessible to the naked senses.

The liberal revisionist, however, denies this, and insists that language refers to internals even though there is no reason for it to do so. Hence he conceives of the possibility of the perfect pretender: someone who pretends to be, for instance, in pain all his life, always acts perfectly consistently with this, and never acts inconsistently with it even when he thinks no one is looking, and never uses language in such a way that might admit or give the lie to the pretense. In short, the perfect pretender is in pain to all competent language users, but not to the liberal revisionist, who wants to revise language in order to be able to call this man a pretender even when nothing in his behavior points to it. The liberal revisionist might, for instance, want to undertake this revision because a brain scan has not found pain in the patient who he calls a pretender; and rather than distrust the technology of the brain scan, the liberal revisionist would rather accuse a man of pretending in such a thorough way as that it is doubtful that any advantage can even accrue to him from it. The liberal revisionist doesn’t know how to prove that something is possible, but his opinion that there might be such a perfect pretender is pretty firm.

The logical behaviorist denies the possibility of perfect pretense, along with all other linguistically confused notions. Whereof one cannot speak, thereof one must be silent.

Afterword: On Linguistic Indeterminacy

The three kinds of linguistic revisionism which we have seen in this blog post, with their respective seven cases of misapplication of predicates, are reminiscent of W.V.O. Quine’s thought-experiment about the indeterminacy of translation. Quine imagines a group of people who speak an unknown language called Arunta and who, when seeing a rabbit, call it a “gavagai”. Granted that in using the word they are referring to something about the context of rabbits, Quine denies that a translator can assert with rational confidence that the word “gavagai” means “rabbit”. For it might mean another thing which is necessarily colocated with situations where we see a rabbit, such as an “undetached rabbit-part” (a part of a rabbit which is not detached from the rabbit’s body), or a “manifestation of rabbithood” (something wherein the universal nature of rabbithood is made manifest to humans), or again a “rabbit time-slice” (which is a single temporal part of the full rabbit which, properly understood, is extended through time from the rabbit’s birth to the rabbit’s death). Either of these things might have been intended by the word “gavagai”.

Certainly this is a disappointment to students of language who would like to have accurate translations of things. However, at least in those cases, the phenomenon which is referred to when there is a rabbit at least has a necessary connection with cases where we see a rabbit. There is no sign of a possible disconnection between these cases and the rabbit. So at least we can think that the translation “rabbit” is accurate enough insofar as it even matters to anyone in practice.

The linguistic revisionists surveyed here, however, have created something even worse than the “gavagai” disconnection and tried to impose it on all other language-users, in an evil plot to make them less competent at using language. Namely, they have tried to decide, unilaterally and imperialistically, that mentalistic predicates do not refer to mentalistically-apt cases of observable, patent, manifest behavior which is accessible to the senses, but instead refer to internals of humans which have no necessary connection with those cases, and hence, in some cases, might fail to be there, at least insofar as logic goes. They have undertaken this revision for no good reason, because it feels intuitive to them. Their worst sin, insofar as they are revisionists, is that they have destroyed the communicative usefulness of language for nothing.

Comic based on this post (Nano Banana)

Syllogistic after Ivo Thomas

This blog post presents Ivo Thomas’s 1949 system of formal syllogistic as documented by Arthur Prior here, but with new nicer notation, and with a bunch of extra proofs of meta results thrown in for good measure since it doesn’t cost any extra to add those. The main goals of doing this are, first, to give me a license to use traditional syllogistic forms whenever I want, because it’s all formalized here, and second, to spread this nice notation for the propositions which I thought was good, and which is based on the notation used by Wolfgang Lenzen to write about Leibniz’s “Theory of the Syllogism and Universal Calculus” in the book The Rise of Modern Logic by Gabbay and Woods, page 56. Really it is Lenzen’s notation but with the obvious modification to allow negative terms.

The system (i) admits negative terms and (ii) forbids empty terms. It is layered over classical propositional logic (with connectives ¬, ∧, →, ↔), and uses only modus ponens and uniform substitution for term variables at the propositional level. We give the syntax and intended semantics up front, state the axioms and rules precisely, and then derive the standard theorems. Given the possible choices of systems, I figured not allowing empty terms is best because it is closest to Aristotle and to natural language (which is, after all, where all syllogisms come from); if someone says “All As are Bs” and then it turns out there are no As, the main issue with their argument isn’t logical validity, it’s that by usual interpretation standards, they lied to me when stating that premise. Syllogisms are for the Agora, not for mathematicians. It happens that nowadays you have to have it all nice and formal somewhere or else someone gets suspicious, so this is what this post is. The parenthesized notation also adds brevity for when mentioning syllogisms on social media, etc.

Unicode is used for the things that did not involve any superscripts or subscripts, since that makes it easier to copy and paste the results, especially the syllogistic forms, which are the most useful results. \( \LaTeX \) is used for some results which were mostly meta results which only serve for bookkeeping anyway.

How to forget your memories

If you have some memories that you’d rather forget, you can simply do so. This post will say how I did it.

My background: Years ago, (somehow, I still remember this, but obviously can’t be sure when precisely) I used to struggle with randomly recalling very embarrassing memories. Whenever I recalled one, this had a strong effect on me. It distracted me from what I was doing, it ruined my day, I kept mulling them over pointlessly. Then somehow I had the idea of making a focused effort to not think of them anymore.

How to do it: The way to do this is simply to notice whenever you’re about to think of those memories, and instead try to think of something else very fast. Obviously you shouldn’t try to not think of the memories, that’s like trying not to think of a pink elephant, which I bet you just did. No, actually change the subject, fast. Look for a specific thing as fast as you can, and think as deeply as you can about that thing.

Tips of things to think of: Memories can come to you anywhere. It’s great if you can always have some sort of very interesting content related to your personal interests that you can come back to instantly to get away from the memories, but personally I find it impossible to carry any such content everywhere. Besides, even when you’re looking at your favorite book, you might be currently at a not-so-great passage which isn’t good enough to distract you from the memories that you were about to think of. So what I recommend is to try to focus very hard on the first thing that you do see in the environment you’re currently in. (Or if that was what brought up the memories, some other thing. But if you have objects that reliably make you remember bad memories, consider getting rid of those objects.) For me, at least, the first thing I see around me is usually whatever furniture is in the room I’m currently in. If you go outside more than I do, then it might be other things, such as streets and buildings and trees. Try to think very hard about the thing you’re looking at from a new perspective, such as for instance: how it was physically built, the materials that it’s made of, its history, depictions of it in art, the types of activities that it’s used for, its geometrical shape and features, its deep metaphysical nature. Think very intensely about that, and if you stop being able to think of more stuff about that thing, then look around yourself harder for a second thing. If you apply yourself enough to this activity, you will hopefully forget which memory it was that you were about to remember, and be unable to come back to it.

Why this works: This works because it is the opposite principle to spaced repetition. Whenever you recall memories, this reinforces them, so what you need to do if you want to kill some memories is to prevent them being recalled.

Caveats: Memories are associated to other memories. Sometimes, you know recalling a good memory from your past will quickly remind you of a bad one. There’s no way to keep the good ones without the bad ones in that case, you have to kill the entire network. As a result of what I did, I basically cannot recall any of my past from before about 2017, when I turned 18 and got into college. I cannot remember anything about my school friends, or earlier online friends, even if I try.

Nowadays, I feel like I have grown as a person to the extent that I am very emotionally resilient, and I could definitely simply deal with the memories if somehow I got them all back now. But they’re gone, I can’t get them back. In order to be able to tell people about my life more accurately, I have made a deliberate effort to reconstruct my past from whatever physical or digital evidence I had left from back then, which wasn’t that much, since I had wisely gotten rid of most of it. But there are a lot of things I simply don’t know.

I’m glad I did what I did. The memories were holding me back. They were actively preventing me from achieving the personal growth which I did achieve, over the years since I lost them.

It helps that the cut-off point, 2017, is also when I began losing interest in childish pastimes such as video games, and began getting more interested in intellectual matters of various sorts. I began reading a lot of serious nonfiction, which I had more or less never done before. The person I had been before had more or less nothing to contribute to developing the person I became.

Against Newcomb

This blog post defends my position that Newcomb’s problem never happens, and if you think you’re in it, you should think again.

“The paradoxical situation, in its intended interpretation, is not merely of a kind that we are most unlikely to encounter; it is of a kind that simply cannot occur.” —J.L. Mackie, Newcomb’s Paradox and the Direction of Causation

Contents

• Statement of Newcomb
• Ambiguity, and my position
• SilasBarta misconstrues Newcomb
• How Ahmed construes Newcomb as parallel to real life
• Bermúdez shows Ahmed’s construal prevents Newcomb from being a decision problem at all
• Horgan’s construal is best, but rules out real-life relevance
• Horgan’s view is enlightening
• It is irrational to believe oneself to be in Newcomb’s problem as Horgan construes it
• Horgan’s ultimate reason for one-boxing
• What to do if you think you find yourself in Newcomb’s problem

Statement of Newcomb

Newcomb’s problem is this hypothetical situation, now sometimes called “Standard Newcomb” to distinguish it from some different statements of it:

You must choose between taking (and keeping the contents of ) (i) an opaque box now facing you or (ii) that same opaque box and a transparent box next to it containing \$1000. Yesterday, a being with an excellent track record of predicting human behaviour in this situation made a prediction about your choice. If it predicted that you would take only the opaque box (‘one-boxing’), it placed \$1M in the opaque box. If it predicted that you would take both (‘two-boxing’), it put nothing in the opaque box. (Ahmed 2018, p. 1)

Sometimes a version is considered where this “being with an excellent track record of predicting human behaviour” is actually perfect at predicting human behavior; this version is called the “limit case” of Newcomb’s problem. However, in discussions about “the rational strategy to take”, it is generally agreed that it is indifferent how accurate the predictor has been, as long as his accuracy is slightly better-than-chance; according to Bermúdez, “> 0.5005, to be precise”. (Ahmed 2018, p. 37) Leaving the precise probabilities aside, then, you can draw a payoff matrix:

(Ahmed 2018, p. 19)	The Predictor has predicted two-boxing and so the opaque box contains $1,000,000	The Predictor has predicted one-boxing and so the opaque box is empty
Take just the opaque box	$1,000,000	$0
Take both boxes	$1,001,000	$1,000

Ambiguity, and my position

In discussions of Newcomb’s problem, everyone knows what Newcomb’s problem is (it is the hypothetical situation above), but people disagree about what the essence of the problem is, with respect to “the rational strategy to take”. This is shown when they try to explain their reasoning by making an analogy between Newcomb’s problem and a different situation: people who think different things are essential to the problem will make different analogies, keeping what they consider essential and changing what they do not consider essential.

I believe that there are no parallels to Newcomb’s problem in real life, so I believe that the essential parts of the problem are criteria that cannot be realized. I believe that if you believe that you find yourself in a Newcomb-like situation in the proper sense of that phrase, then you have fallen under some illusion, or committed a fallacious inference, or otherwise been irrational, and the rational thing to do is to revise your beliefs until you no longer believe yourself to be in such a problem.

In order to defend my position, I will argue against construals that defend the idea that Newcomb’s problem is relevant to real life.

First, I will claim that SilasBarta’s construal does not capture the essence of the problem. Then, I will explain (following Bermúdez) that Arif Ahmed’s construal, although it offers an attractive framing of the arguments about the different strategies, prevents Newcomb from being a decision problem at all, so it prevents there being any rational strategy to take in it. Finally, I will discuss Terry Horgan’s construal, which gives a better framing of Newcomb as a decision problem, but which, as I will argue, prevents it ever being realized in the real world.

SilasBarta misconstrues Newcomb

LessWrong is a webforum dedicated to fostering wrong and irrational beliefs, chiefly revolving around unrealistic mathematical models (“unrealistic” not in the sense merely of “idealized” but in the sense of “actively reality-denying”) being somehow applicable to practical situations. In a 2011 post to LessWrong, the user SilasBarta pretends that anything in the world is anything like Newcomb’s problem by explaining it as follows:

The common thread across all the Newcomblike problems I will list is this: “You would not be in a position to enjoy a larger benefit unless you would cause [1] a harm to yourself within particular outcome branches (including bad ones).” Keep in mind that a “benefit” can include probabilistic ones (so that you don’t always get the benefit by having this propensity). Also, many of the relationships listed exist because your decisions are correlated with others’.

Emphases original. The little box “[1]” refers to a footnote where SilasBarta clarifies the sense of “cause” involved, which he thinks of in a certain precise way, but this is not relevant here. What is relevant is that absolutely nothing else in this definition of the essence of the problem is thought of in any precise way at all, which is why he includes, for instance, this example as an instance of Newcomb’s problem:

Cheating on tests: You would not be in the position to reap the (larger) gains of being able to communicate your ability unless you would forgo the benefits of an artificially-high score. (Kant/Categorical Imperative name-check)

As many commenters point out, obviously many people successfully cheat on tests and continue to be in the position to take further tests, possibly cheating on them again and again. Many people’s experience of school is that of a wild place where any oversight is minimal and nominal, and the rules are just pieces of paper. The “would” here is extremely idealized, but it is claimed to be essentially the same as the “would” in Newcomb’s problem, where, as SilasBarta says:

Newcomb’s problem: You would not be in the position of Box #2 being filled unless you would forgo the contents of Box #1.

Despite how the vagueness and broadness here beggars belief, SilasBarta goes on to apply such paraphrases to other petty infractions such as shoplifting, as well as other examples that will be brought up later. I do not consider this approach productive and I will not address it further, although I have noted it because I consider it a helpful way to emphasize how many different construals of Newcomb there can be.

How Ahmed construes Newcomb as parallel to real life

In Arif Ahmed’s introduction to the 2018 collection of essays on Newcomb’s problem, the essence of the problem is claimed to be that there is a conflict between these two principles:

Causal Principle: A rational agent does what she thinks will cause her to realize her aims.

Evidential Principle: A rational agent does what constitutes her best evidence that she will realize her aims.

This does give a compelling framing of the arguments for the two different strategies: someone following the evidential principle will believe that taking only the opaque box (one-boxing) is the action that gives you the best evidence that you will get the \$1M. Since the predictor’s track record is excellent, this is believed to be evidence that, if you one box, this makes it likely that the predictor predicted one-boxing, and so the \$1M is almost always in the opaque box for one-boxers. On the other hand, someone who follows the causal principle reasons differently: once the boxes have been filled, the contents of the opaque box are fixed and independent of your choice now. Whether or not you choose both boxes cannot causally affect the predictor’s earlier action. So, since the transparent box always contains \$1000, a person who follows the causal principle argues you should always take both boxes (two-boxing), because that guarantees you an extra \$1000, whatever is in the opaque box (the strategy is dominant).

Ahmed assumes that this is the essence of the problem, and basing himself on this, claims that many other situations are analogous, such as Fisher’s smoking case:

Suppose that what explains the correlation between smoking and lung disease is not (as everyone now thinks) that smoking causes lung disease, but rather that both have a common cause: an innate predisposition towards lung diseases that also, and separately, predisposes its bearers to smoke. Suppose you are wondering whether to smoke, but you don’t know whether you have the predisposition. You know that you would like smoking, but you like good health very much more. (Ahmed 2018, p. 4)

With the idea being that smoking would be evidence that you have the predisposition to smoking. Following this same idea about the causal principle and evidential principle, Ahmed cites some other analogies in the literature, such as: voting in an election if you think your vote won’t by itself causally affect the outcome, but counts as evidence of how other voters will behave; being vicious or virtuous in the context of Calvinist predestination; macroeconomic policy choices when the public has rational expectations about how the central bank will behave; bets about experiments involving non-causal quantum correlations; and Prisoners’ Dilemma (from game theory) in a context where each prisoner is confident enough that both reason alike (this idea is due to David Lewis). (Ahmed 2018, p. 5–6)

Bermúdez shows Ahmed’s construal prevents Newcomb from being a decision problem at all

The essay by José Luis Bermúdez, which is the first essay in the same volume after the introduction, agrees with Ahmed that part of the essence of Newcomb’s problem is a conflict between causal and evidential reasoning. He frames it as a payoff matrix with these parameters:

(Bermúdez 2018, p. 22)	S1	S2
A	a1	a2
B	b1	b2

Where “CDT” stands for “Causal Decision Theory” and “EDT” stands for “Evidential Decision Theory”, Bermúdez believes that the five essential features of Newcomb’s problem, after it is framed as such a payoff matrix, are these:

1. b₁ > a₁ and b₂ > a₂
2. a₁ > b₂
3. Each of S1 and S2 must be causally independent of both A and B
4. S1 and S2 must be probabilistically dependent upon A and B, respectively
5. EDT and CDT must yield conflicting prescriptions, with EDT recommending A and CDT recommending B.

Bermúdez argues in his essay that a strategy called the “Tickle Defense” always works to cut off any parallel between a real-life situation and Newcomb’s problem. As Ahmed had framed the tickle defense, it was like this:

If you are predisposed to smoke, then presumably you already like the idea of smoking (you have a “tickle” or urge to smoke), and whether you do is something that you already know. But the predisposition only makes you smoke by making you like the idea, and since you already know about that, your actual choice reveals no more about the presence or absence of the predisposition. From the perspective of the agent herself, smoking is therefore not any sort of evidence of a state that it doesn’t cause. The Fisher smoking case is therefore not a Newcomb Problem. (Ahmed 2018, p. 9)

This framing of the tickle defense allows Ahmed to (among other objections to it) say, citing Lewis [pdf], that “we might question the quasi-Cartesian assumption that you know your own motivational state”, since “subconscious desires and beliefs can play the same role in motivation as familiar conscious ones” and this is something that “we cannot simply assume away”. But Bermúdez clarifies that “knowing that you like the idea of smoking” is no more knowledge than is contained in the payoff matrix for the problem. And as Bermúdez says in a footnote, you must know this payoff matrix to be in a Newcomb problem at all:

To be in a (putative) Newcomb Problem is not just to be in a situation where a third-person observer might observe that CDT and EDT give conflicting recommendations. Newcomb’s Problem is supposed to be a first-person dilemma – a situation where the conflict between CDT and EDT is manifest to the decision-maker. For that to be the case, however, the decision-maker must herself be able to reason her way to each of the conflicting recommendations, which in turn requires that she know her probability and utility assignments and know that she is a maximizer of expected utility. So, the assumptions in the text are really necessary idealizations. (Bermúdez 2018, p. 29)

So, Bermúdez spends the first part of his essay saying that the tickle defense applies not only to medical examples like the smoking case, but also to the economic example regarding public expectations about money supply. In the final part, he says that, although it would certainly support the idea about Newcomb’s problem (NP) existing in real life if the Prisoner’s Dilemma (PD) were parallel to it (“given how many different types of social interaction can profitably be modeled as PDs”), it isn’t. As he argues, it is essential to the prisoner’s dilemma that the other prisoner’s choice is independent of yours. When Lewis adds the assumption that “each prisoner is confident enough that both reason alike”, this makes the problem no longer be even a game as defined by game theory—it is transformed “from a problem of strategic choice into a problem of parametric choice” (Bermúdez 2018, p. 39), due to the probabilistic dependence between your choice and the other person’s choice. So NP and the PD are fundamentally different.

Bermúdez concludes that there is no real-life application of Newcomb’s problem in real life, since all the claimed real-life parallels were false. He has more to say about the supposed parallel to voting in a footnote:

Arif Ahmed (2014a: 117–19) has suggested that voting in large elections can count both as a multiagent PD and as an NP, provided that the following three conditions hold: (a) nonvoting dominates voting, because of the inconvenience of voting; (b) any voter in a large election should be to all intents and purposes certain that their vote will not make a difference; (c) voters often take their vote to be diagnostic. As Ahmed observes, many people vote, despite (a) and (b). He proposes (c) as a possible explanation. If so, there is potentially an argument to be made that conditions (1) through (5) are satisfied. Giving this proposal the attention it deserves would take us too far afield. I hope to address it in later work. However, here are two comments. The voting scenario does not have a predictor, and the other voters certainly have preferences over the possible outcomes. So, the first and third reasons for not taking NP to be a strategic choice problem do not apply. But the second does. To take your vote to be diagnostic is incompatible with taking other voters to be independent. And for that reason, the voting case cannot be a PD, in my view. But still, you might think that leaves open the possibility that it counts as a real-life NP. I wonder, though, about the payoff table. Attitudes to voting are very complicated, bringing into play all sorts of loyalties, obligations and perhaps what Nozick has called symbolic utility. So, I wonder about the assumption that nonvoting dominates voting. I am also not convinced that generally speaking people do take their votes to be diagnostic. Ahmed cites evidence that students planning to vote Yes in a 1992 Canadian referendum estimated that a higher proportion of the electorate would vote Yes than students planning to vote No. But that does not show that they take their vote to be diagnostic. They could, after all, be planning to vote Yes because they hope to ‘surf the wave,’ as it were. This is another case where we need more detail about the backstory. (Bermúdez 2018, p. 40)

I think this is fair. If you’re claiming that voting is a real-life example, you had better not add a bunch of questionable assumptions about voting. At any rate, given my preferred construal of NP, which will come next, it will turn out that no case of voting is actually an NP, ever.

Horgan’s construal is best, but rules out real-life relevance

In Terence Horgan’s Essays on Paradoxes, the first three essays are about Newcomb’s problem. Horgan’s goal is to defend one-boxing, which he ultimately finds himself unable to vindicate as the only rational approach. He is not particularly concerned with the question whether the Newcomb problem is relevant to any real-life situation, and he does not try to construct an analogy between Newcomb and a different situation. His proposal, however, captures what I believe is the essence of the problem.

In the first two essays, Horgan draws on David Lewis’s discussion of the semantics of counterfactuals. In Counterfactual Dependence and Time’s Arrow, Lewis had argued that counterfactuals are vague, but that there is a standard resolution of this vagueness which applies in most contexts (as in, “if the match hadn’t been struck, it wouldn’t have lit”), but that some special contexts call for a backtracking resolution of the vagueness (as in, “if the match hadn’t lit, it wouldn’t have been struck”). In the course of defending that the Newcomb context calls for such a backtracking resolution, Horgan develops his notion of “act-independent knowledge”. In the third essay, Horgan simplifies his argument to rely only on the idea of act-independent knowledge, without relying on counterfactuals at all.

As defined in Horgan’s third essay, then, “act-independent knowledge (for short, AIC knowledge), for a given decision problem P, [is] knowledge that is possessed by the chooser in P in a way that does not depend on any evidence that the chooser in P might possess concerning which act the chooser will perform.” (Horgan, p. 46) In Horgan’s formulations of the problem in that essay, we have it as a premise of the limit case that “I have act-independent knowledge that I will act in the manner predicted”, and we have it as a premise of the standard case that “I have act-independent knowledge that it is extremely probable that I will act in the manner predicted.” (Horgan, p. 47) This is the issue, and it allows Horgan to infer, roughly speaking, that scenarios where he does not act as predicted can be rationally disregarded for the purposes of decision-making (although he finds himself unable to claim that they rationally must be so disregarded).

Horgan’s view is enlightening

Horgan’s parallel arguments from the notion of power seem to put the explanatory power of his construal on display. Regarding the limit case, Horgan gives two arguments based on the notion that you should only think about outcomes that are “within your power”, one for each strategy:

• Two-boxing argument from power: Either (1) I have the power to choose both boxes and receive \$1,001,000, and also the power to choose the second box and receive \$1 million, whereas (2) I lack either the power to choose both boxes and receive \$1,000 or the power to choose the second box and receive \$0; or (3) I have the power to choose both boxes and receive \$1,000, and also the power to choose the second box and receive \$0, whereas (4) I lack either the power to choose both boxes and receive \$1,001,000 or the power to choose the second box and receive \$1 million. Hence the outcome I have the power to achieve by choosing both boxes is preferable to the outcome I have the power to achieve by choosing the second box—whatever those outcomes are. And if this is so then I ought to choose both boxes. Hence I ought to choose both boxes. (Horgan, p. 42)
• One-boxing argument from power: Either I will choose both boxes and then obtain \$1,000, or I will choose only the second box and then obtain \$1 million; and this proposition follows from propositions which I know are true and which say nothing about which act I shall perform (or about the probability of either act). Hence I lack the power to falsify the being’s prediction. But I have the power to take both boxes, and also the power to take only the second box. Hence I have the power to choose both boxes and then obtain \$1,000, and also the power to choose the second box and then obtain \$1 million; while I lack either the power to choose both boxes and then obtain \$1,001,000 or the power to choose the second box and then obtain \$0. So the outcome I have the power to achieve by choosing only the second box is preferable to the outcome I have the power to achieve by choosing both boxes. And if this is so then I ought to choose only the second box. Hence 1 ought to choose only the second box. (Horgan, p. 43)

This difference is explained very well by the essence of the problem being that one-boxers regard themselves as rationally taking into account their act-independent knowledge that the predictor’s prediction will be (very likely) right, while two-boxers either regard themselves as not having such knowledge or find such knowledge irrational to take into account against the dominance argument.

It is irrational to believe oneself to be in Newcomb’s problem as Horgan construes it

There is no such thing as act-independent knowledge that “I will act in the manner predicted”. If I know “I will act in the manner predicted”, this is necessarily an inference from these premises:

1. It was predicted that I will act in the manner M.
2. I will act in the manner M.
∴ 3. I will act in the manner predicted.

By the definition of act-independence, the second premise is not act-independent, and hence, there is no act-independent knowledge of the conclusion. Any belief in the conclusion on other grounds is irrational, and in particular, it is irrational to believe the conclusion on act-independent grounds. However, since Newcomb’s problem is constituted by the act-independent knowledge that I will act in the manner predicted, it is then irrational to believe oneself to be in Newcomb’s problem.

In order to be rational, the belief that “the prediction will match the act” must either be grounded on knowledge of both the prediction and the act or, alternatively, grounded on some bridge-law or mechanism linking the determinants of the prediction to the determinants of the act (together with enough information about those determinants to fix how the bridge-law applies in the present case). But in order for this to even be a decision problem, my choice must be open to rational deliberation in light of the payoff matrix. If the bridge-law fixes how the determinants of the prediction are linked to the determinants of the act in a way that screens off deliberation, then the act is not up for rational choice in the sense required by decision theory, and there is, as in the “tickle defense” cases, no decision problem at all. If, on the other hand, the bridge-law leaves deliberation efficacious—i.e., it leaves open which act will be selected after one has considered the very payoff table that motivates one- vs two-boxing—then, once I condition on this deliberative situation, I can no longer have act-independent knowledge that the prediction will match my act. Either way, I cannot have act-independent knowledge of prediction accuracy in a decision problem.

Horgan’s ultimate reason for one-boxing

Horgan concludes that Newcomb’s problem is a “deep antinomy of practical reason”, one in which “distinct normative principles that really are each partly constitutive of pragmatic rationality come into direct conflict with one another”, namely, expected-utility and dominance. (He discusses different versions of dominance, such as “qualitative dominance” and “quantitative dominance”, and he discusses different versions of expected utility, such as Gibbard and Harper’s counterfactual version. This is not relevant here, except insofar as, following a description of Newcomb that goes back to Nozick’s original paper, Horgan believes dominance favors two-boxing but expected utility favors one-boxing. Note that Michael Huemer has argued, against Nozick, that the correct interpretation of expected utility favors two-boxing.)

Horgan remains personally a one-boxer on the emotional grounds that he would feel more regret if he two-boxed. As he says near the end of the third essay:

Speaking for myself, consistent one-boxing wins the psychological tug of war. Here is why. Regret is virtually inevitable in this decision situation: either I will take only the second box and then end up regretting having passed up \$1,000 that I knew all along was there for the taking in addition to the contents (if any) of the second box, or I will take both boxes and then (very probably) end up regretting that I am the kind of person about whom the being has predicted that I will take both boxes. Since I strongly prefer the first kind of regret to the second, I will take only box 2, collect my \$1 million, and then regret that I did not take both. (Horgan, p. 59)

Of course, he cannot, and does not defend, that he is being rational here. The two-boxer may fairly think that he is passing up \$1,000 for no good reason. Near the end of the second essay, Horgan pushes further:

Again I see no way to avoid stalemate. But let me conclude by trying to make the one-boxer’s notion of power more vivid. Imagine being in a Newcomb situation with the following features. (1) You are a hungry prisoner, condemned to die tomorrow. (2) You are completely certain that the being has correctly predicted what you will do. (The limit case.) (3) Box 1 contains a delicious meal, which you may eat immediately if you choose both boxes. (4) If the being predicted that you will choose only box 2, then he put a note into box 2 which will cause the authorities to cancel your execution and set you free. (5) If the being predicted that you will choose both boxes, then he put nothing into box 2. (6) You know all these facts.

If you choose both boxes, you will do so in the full knowledge that you will be executed tomorrow. Likewise, if you choose only the second box, you will do so in the full knowledge that you will be set free. Now surely, in such a situation you would have a strong tendency to view yourself as having the power to choose your own fate— notwithstanding the fact that your choice will not causally influence the contents of box 2. Two-boxers seem to predominate among those who are currently working on the foundations of decision theory. But I think it is not unreasonable to speculate that most of them, if faced with the situation just described, would swallow hard and choose one box. No doubt they would grumble afterwards about having irrationally passed up a chance for a good meal when their happy fate was sealed in advance. But would you really choose two boxes in the certain knowledge that you will subsequently die, just to prove you mean business? (Horgan, p. 45)

I will emphasize how irrational Horgan is being here. If I do not mean business in this sense, then my life is not worth living. Abstract problems should assume a rational chooser, since it is very easy to make the correct choice arbitrarily scary in irrational ways (ways unrelated to your choices’s actual nature and outcomes), and although the scariness of the alternative may reduce your moral culpability for acting irrationally, it will not make your action right.

But Horgan’s solution does follow given the “certain knowledge” he claims exists in the problem, via the principle of explosion. In this context, I would also like to push against a strawman which is often given of the two-boxing choice in Newcomb’s problem. The SEP says that “causal decision theorists respond that Newcomb’s problem is an unusual case that rewards irrationality.” I have never seen any theorist actually argue this (the SEP does not cite any who do), and if any did, they are not presenting the best case for two-boxing. Newcomb’s problem is not an unusual case that rewards irrationality, because it is not a possible case of a decision problem at all, and it is not possible to describe a case where a valid and sound argument concludes that you will get more money by one-boxing. It is wrong to think there are such unusual cases.

If you cannot remove the absurdity from your belief system, however (on which see the next section), then you must believe trivialism is true, so reasoning doesn’t work and you can only do whatever feels emotionally compelling. But this is not decision theory anymore, whatever it is. In any possible case of a decision problem, the analogue of two-boxing is correct, possibly with some preliminary feinting to fool the predictor—which, in real life, you can always do, without exception.

What to do if you think you find yourself in Newcomb’s problem

As I said before, my position is that, if you think you find yourself in Newcomb’s problem, you should understand that you find yourself believing the absurd (“I find myself in Newcomb’s problem” ↔ ⊥), and you should remove that belief from your belief set. Using AGM belief revision, this is done as follows. Let $K$ be your deductively closed belief set, and let $N$ be your belief that “I am in a genuine Newcomb problem”, understood here via Horgan’s AIC. Then:

1. Find $S=\{s_1,\dots,s_m\}\subseteq K$ with $S \vdash N$. These would be anything that leads to your belief in the key premise that “I have act-independent knowledge that I will act in the manner predicted.”
2. Fix the epistemic entrenchment order $\preceq_E$. Highly entrenched would be ordinary causal structure, efficacy of present deliberation, the payoff table, base rates, known incentives, institutional facts. Minimally entrenched would be $N$ and any of its supports that don’t support anything else.
3. Contract by $N$: compute $K' = K \div N$. This drops $N$ and, if needed, the least-entrenched items in $S$.
4. Revise by $\neg N$, so you don’t slide back into the paradox by a different route: set $K'' = K' * \neg N = (K' \div \neg\neg N) + \neg N$.
5. If, after doing this, you still think you’re in a decision problem, then it is a genuine decision problem and you can solve it with $\neg N$ in place, which probably means doing some analogue of trying to fool the predictor (if there’s still time for that) and then two-boxing.

There are other constructions of AGM and other models of belief revision, but this AGM-compatible construction conveys the broad idea I’m recommending: remove your Newcomb-entailing beliefs, whatever they cost, and keep only the others. This allows you to remain rational. Belief in Newcomb’s problem is rationality-destroying, so no sense can be made of the idea of a rational decision within it; the rational decision given belief in it is to destroy the belief. In this case, unlike in “Schelling’s Answer to Armed Robbery” cases, so-called practical (pragmatic) rationality requires theoretical (epistemic) rationality.