Therefore in light of this I will adopt the persona and guise of what I would take to be the exemplar of such a position, Spitio the spiteful philosopher.

Spitio [text by Spitio indicated by italics]: No thanks, to my alter ego as he has left me with all the work of writing this piece.

We should start by asking “What is it to be dysfunctional?” and in particular “What would be most dysfunctional?” I’m not qualified to begin such an analysis, but who’s going to stop me! I say that being overcome by emotion is the most apt psychological dysfunction. Losing oneself, one’s identity, all care for future outcomes, all care for past obligations to the flux of strong emotion. Now what emotion is the most irrational, the most dysfunctional. I, of course, say it is spite:, hatred, the desire for retribution against those who you perceive as wronging or offending you.

So to develop a Dysfunctional Decision Theory we must cultivate this emotion to its highest disagree and also its disregulation of rational and constructive behaviour. it is a sentiment well expressed in Captain Ahab’s famous statement in Herman Mellville’s Moby Dick “to the last I grapple with thee; from hell’s heart I stab at thee; for hate’s sake I spit my last breath at thee”. Still this expresses a mere attitude or stance and is not even a philosophical view much less a developed decision theory.

Decision theory is the formal study of decisions both descriptive and normative (prescriptive). In its classic form it derives a formalism for describing how decisions are made, what options are being deliberated between and how preference between them are compared, the way options are weighted by estimated probability of outcomes and so on. In its prescriptive form it identifies some ways of making decisions (making decisions in conformity with some set of axioms or principles) as rational or conversely some ways as being irrational.

DDT is clearly a normative theory, although given the state of the world many decisions are made out of spite, yet many are not. DDTers do not attempt to describe those who lower themselves to suffer the slings and arrows of outrageous fortune with good humour. patience and general ataraxia. Instead DDTers counsel all to embrace spite and malice and as far as possible get your own back.

Normally one might try to codify ones decision theory with a set of symbols, a formalism for representing dilemmas, positing axioms and proving theorems about how one ought to decide questions. I have neither the patience, facility nor good will to undertake such a task, so I will just give some of the axioms I take the scheme to entail:

1. Maxim of Maximum Malice: Always extend the circle of hatred as far as possible hate not only your neighbour, not only humanity, not only all sensate animal life, but all life and every particle of matter as well as the universe as a whole. Not a homicidal malice but a general antipathy, a willingness to ask What have you done for me lately? And be quick to answer nothing. It is not enough to mime the same actions to hate a puppy and to hate a rock require very different treatment, one must consider the individual’s needs and wants that you seek to frustrate. If criminals seek to martyrdom via execution for their crimes by no means should you give it to them and so forth.

2. Principle of uncharity or the Contrarian Criterion or the Perversity Principle: It is not enough to strive for the emotional stress, frustration and discomfort of others, one must also unsettle and frustrate them intellectually. Never miss an opportunity to misunderstand others, bring up pedantic exceptions or problems for their proposals and seek everywhere confusion and contradiction. For example if someone said to me “I’m hungry.” I would respond “Hello hungry, I’m Spitio.” If you can through your actions bring about a paradox or contradiction do so. If someone asks you if you are lying when hooked up to a polygraph say “yes!”. Always be ready and willing to defy expectations, always ask yourself how dare anyone try and confine your field of action with their limited vision.

3. Principle of paranoia: never attribute to incompetence or neglect what can be attributed to malice against you. Just because people don’t realize their actions stem from ill-will against you means nothing. As Daniel Dennett pointed out it is possible for people to be unaware of their own intentions. Don’t let their ignorance prevent you from attributing their actions to an attack against you. Remember just because you’re paranoid doesn’t mean they aren’t out to get you.

4. Maximize capriciousness: We should as far as possible make all decisions to take action at the last possible moment unconstrained by past judgements or decisions and future expectations. If our spite moves us we move, regardless of whether we made opposite choices in the past based on the same information and motives. Live in the moment. If you have the slightest desire for that cake eat it now, no matter how much you are going to wish later you saved some.

5. Maximize expected disutility: This is much like the standard maximizing expected utility principle in other decision theories (and game theory etc.). The utility of a potential outcome is weighted by its probability given a choice, the choice with the largest utility weighted by its probability is preferred. In this principle though it is the disutility inflicted on people which is weighted and maximized. There are some complications, the circle of hatred should always include oneself, never hesitate to cut off your nose to spite your face. If that stupid face thinks it’s better than you action must be taken. This raises a paradox given self-hatred if you thwart yourself, you actually succeed, this makes self-hatred mostly a wash. Even if you fail to hate yourself and indulge yourself instead this is hypocrisy and so also spiteful.

   There is also need to pursue a golden mean in your hatred of others. Provide only token resistance and scorn and they won’t suffer at all. However, rain down too much malefaction on them and they will die or become so wretched that there suffering will lessen. So in the mean between these two extremes will one find maximum expected disutility for all.

6. Principle of Dominance: Again much like dominance in decision and game theories, but flipped since we are pursuing disutility, an option that has no more benefits to those you spite and brings all the same misery and then some more should be preferred. In general always dominate in any discussion or situation. Never submit always confront. Some will say that these senses of dominance are completely different and all I can say is you would say that wouldn’t you.

Having established our principles let’s work through some famous dilemmas.

A) Newcomb’s Problem:

A predictor presents you with two boxes, one is transparent, in the transparent box is $1000, the contents of the other box are unknown. You may either take both boxes or only the opaque box. It is the case (and you have good reason to believe etc.) that the predictor has put $ 1 million in the opaque box if he predicts you will only take that box. The box is empty if he predicts you will take both boxes or consult some random process such as flip a coin to choose between the options. It is the case (and you have good reason to believe etc.) that his predictions on these matter are significantly better than chance.

Given the stakes even relatively small accuracy better than chance makes the expected disutility of two boxing greater than 1 boxing (the expected utility of 1 boxing is some substantial portion of $1 million which will be larger than $1000 plus some smaller fraction of $1 million the expected utility of two boxing). Thus if you individuate the outcomes as independent of the choice made, the dominant choice will be one boxing for the DDTer (the good or bad of the opaque box is the same for either choice assuming the independence of choice and box, and giving up on the second box increases disutility).

This is the coming apart of the principles of dominance and expected utility that bedevilled early formulations of Decision Theory when Nozick presented this problem. For the DDTer we have further complications the Principle of Paranoia (3) one should suspect the fix is in, could there really be enough evidence that the predictor has not wittingly or unwittingly contrived the outcome in a way that makes the outcome dependent the choice (thus changing the partition of outcomes for the dominance consideration)? Leaving this aside we must consider who we can thwart or frustrate.

It would be well if we could frustrate the predictor and make his predictions wrong (see principle 2 the perversity principle). This is especially so on the common versions of how this dilemma is posed where the predictor is imagined to be inordinately accurate to sharpen the force of the dilemma. The more unerring the predictors prediction the more the dedicated DDTer desires to break these predictions and rub it in the predictor’s smug face. Also the dilemma the predictor gives us seems to tempt us to give up the rationality of taking all there is for the sake of the million or give up the million for the sake of consistency taking it all, and indeed by the paranoia principle 3 we should assume the predictor is trying to force both outcomes and we should resist. Therefore one might want to pay attention to whether the predictor is notably worse at predicting one action or the other and pick the one he is worst at to maximize the chance of a screw-up. Unless one became convinced the predictor was only doing badly on that prediction to entice credulous fools to pick that option, in which case don’t play into his hands.

Usually presentations understand the rate of false positives and negatives for the predictor to be the same for either choice. However there have been some notable discussions which considered that accuracy might be achieved by a predictor who is actually very inaccurate on one side. See for example Levi’s 1978 paper a model of pedantic needling of a problem. Still this seems an unprofitable avenue.

(Bourget & Chalmers 2020 PhilPapers survey)

It seems as though given the predictor’s assumed accuracy and the predictee’s inability to thwart them on this point we must defer or rather refute the common herd. Opinions on what to do are split between one boxing, two boxing and picking a third option (such as rejecting the entire dilemma) without a clear majority opinion. However in fact two boxing holds a slight plurality. The margin for two boxing increase if one considers philosophers who specialize in decision theory. Therefore it seems possibly the best argument given the current state of play which will piss off the most people is to one box. You causal decision theorists with your min-max tables are not the boss of me!

B) The Prisoner’s Dilemma:

Two criminals have been apprehended by the police. They are each interrogated in separate rooms unable to communicate and without prior agreement on what to do in this eventuality etc. The police make each an offer, if neither talk they will prosecute the pair on a lesser charge and each will serve a year in prison. If however one were to turn rat and implicate the other for the graver crime the informant might get off scot-free while his compatriot spends a dime (10 years) up river (in prison). However if both implicate the other each will be spending that dime up river.

Some problems are easily dissolved by DDT. For the normie conventions there is an observation that the stable outcome is for both suspects to rat and for both to end up spending 10 years in prison when both could have kept silent, which is troubling (seem suboptimal). For the DDTer this is the optimal outcome and the lesson is if you are dumb enough to get caught you deserve to rot in prison as long as possible.

C) MAD (Mutually Assured Destruction) Problems:

You are the president of the USA (or if you prefer the Premier of the USSR) during the cold war. You are informed that the USSR has launched a decisive first nuclear strike against the USA. The ICBMs are in flight and all human life in the USA will be wiped out. You must now decide if the USA will retaliate and wipe out human life in the USSR, this will save no lives and in fact kill tens of millions of people including children, the elderly and other non-combatants who had nothing to do with the strike and are wholly innocent of this aggression.

Again on some conventional accounts an argument is made that the only rationale for MAD (Mutually Assured Destruction), the promise that if you are struck by a nuclear firestorm you would respond in kind, is to deter a first strike. Having failed this to keep to MAD is unjustified and even deeply immoral. There is no virtue in consistency on this policy. This has no force on the DDTer.

Instead the spite in the heart of every true DDTer not only suggests but demands, swift and terrible retribution. There are no accidents (principle 3 again), no innocents all on the opposing side deserve their fate for their association with our enemy. MAD is not a mere instrument to some end for the DDTer it is an exemplification of basic principle.

A side note descriptively we can recognize indications that in real life the efficacy of MAD as deterrence seems to depend on the expectation of retaliation by the other side in nuclear war. It seems we have good reason to expect this because we recognize that most human beings are just that spiteful. They would retaliate even if it benefits themselves not a jot and condemns untold innocents. While not a full throated endorsement of DDT this popular sentiment is reason for a sense of vindication among adherents of DDT.

However let it not be said that DDT is without compassion or moral motive. It has been noted that given the effects of nuclear fallout, desperate refugees, unclear winter and other malignancies of nuclear war the living will envy the dead should it ever come to pass. By deciding on a massive retributive strike the DDTer is also doing their up most to ensure that no one survives to face the horror of a post-apocalyptic hell-scape. Instead granting the sweet relief of death. This exemplifies the golden mean in pursuing maximum malice.

D) Time Inconsistency Problems:

The Time Inconsistency problem in economics has to do with the question of the effect and desirability of consistency of government policy (policy announcements and subsequent action) in monetary policy (the money supply, central bank interest rates etc.). It has been noted that this can create scenarios analogous to the Newcomb’s problem. A less abstruse non economic version I learned goes roughly as follows:

On Monday the teacher announces to the class that on Friday there will be a quiz on this week’s material. If everyone studies everyone will pass and that will be the end of it. If however students fail they will be required to stay after class with the teacher to go over material.

If the students believe the teacher they so dread revising on Friday night that they will be motivated to apply themselves and so pass the test. On the other hand if they don’t believe the teacher they will fail (or at least some of them will). As it turns out the teacher has a hot date on Friday night, if he ends up revising the week’s material with his students he will give up his shot, a significant cost. So the temptation is for the teacher to actually give up on revising the material, but if the students detect this failure of nerve, as they unfailing will they will not study.

Another dilemma easily dissolved by DDT. The DDTer is glad to see the little brats left ignorant, one’s only regret should be that the little blighters are probably content in their lazy ignorance and you are indulging them. Further the principle 4 of Maximum Capriciousness demands that we not be consistent. Even if consistency would be in line with our general plans we should never sacrifice short term satisfaction and emotional indulgence for long term goals. So while easily disposed of this scenario nicely illustrates some features of the DDT approach of general applicability that should be kept in mind.

E) The Transparent Newcomb’s Problem

This is as the standard Newcomb problem except both boxes are transparent. Somehow the predictor is still accurate.

Whereas in the standard Newcomb problem the predictor outwits us by playing cards close to their chest, here they have revealed their hand and so invited defeat. The DDT response is clear they should react as follows. If they see the million dollars they should take both boxes, thus refuting the predictors prediction. If we do not see the million dollars eschew the $1000 one box and again refute the prediction. A clear and penetrating deployment of the Principle 2 the perversity principle. It would seem if those encountering this problem were all DDTers prediction would be impossible, making one wonder if the scenario is well posed.

The satisfaction of refuting the predictor has been noted by others thinking about the problem. An illustrative case is given by dirty old man Isaac Asimov who in response to a discussion of Newcomb’s problem in Scientific American wrote a letter expressing that the predictor has the character of God and so advocated two boxing as exemplifying the desire for free will (even though he considered it an impossibility) concluding:

Now, then, suppose you take both boxes and it turns out (as it almost certainly will) that God has foreseen this and placed nothing in the second box. You will then, at least, have expressed your willingness to gamble on his nonomniscience and’ on your own free will and will have willingly given up a million dollars for the sake of that willingness-itself a snap of the finger in the face of the Almighty and a vote, however futile, for free will. ... And, of course, if God has muffed and left a million dollars in the box, then not only will you have gained that million but far more important you will have demonstrated God’s nonomniscience. If you take only the second box, however, you get your damned million and not only are you a slave but also you have demonstrated your willingness to be a slave for that million and you are not someone I recognize as human.

Although Asimov is clearly not a DDTer he admirably expresses a core ambition of the DDTer to snap a finger in the face of all who would constrain or lord over us, even to the extent of spitting in the eye of Almighty God!

Anyway, this concludes my discussion of a proposal for Dysfunctional Decision Theory. In conclusion, if anything I have said has confused you good!

Allan: Thanks to Spitio for that intense discussion. I have been doing a series of extended blog posts on Newcomb’s problem over on LinkedIn that begin here. And find below a bibliography of some of the work mentioned above.

Bibliography

Bourget, D. & Chalmers, D. J. (2023) Philosophers on Philosophy: The PhilPapers 2020 Survey. Philosophers’ Imprint. https://journals.publishing.umich.edu/phimp/article/id/2109/

The survey of philosophical opinion quote above.

Broome, J. (1989). An Economic Newcomb Problem. Analysis, 49 (4), pp. 220-222. https://www.jstor.org/stable/3328565?seq=1

A short introduction to the idea of economic time inconsistency problem as an example of Newcomb’s problem.

Dennett, D. C. , (2006). Breaking the Spell: Religion as a natural phenomenon, Viking.

In this book Daniel Dennett gives the examples of the Druse and British intelligence officer Kim Philby (pages 234-240) for evidence that even believers may not know what they believe. Spitio has understood this as a instance of people being unable to recognize their intent, which seems fair enough.

Gabler, J. (2020) What to Make of Isaac Asimov, Sci-Fi Giant and Dirty Old Man? Despite Calling Himself a Feminist the Author of the Foundation Stories Was a Serial Harasser. The Literary Hub, May 14, 2020. https://lithub.com/what-to-make-of-isaac-asimov-sci-fi-giant-and-dirty-old-man/

A blow by blow run down of Asimov’s proclivities as a dirty old man and pincher of unsuspecting buttocks over the years.

Gardener, M. 1973 Mathematical Games: Free will revisited, with a mind-bending prediction paradox by William Newcomb. Scientific American, 229 (7), pp. 104-109. https://www.scientificamerican.com/article/mathematical-games-1973-07/

Martin Gardiner presents Newcomb’s problem to the magazine’s readers and gives his own interpretation of it. Interesting as a popular presentation and more so because of the follow up several months later.

Gardner, M. 1974. Mathematical Games: Reflections on Newcomb’s problem: a prediction and free-will dilemma. Scientific American, 230 (3), pp.102-109. https://www.scientificamerican.com/article/mathematical-games-1974-03/

A discussion of the many letter responses to Gardiner’s initial column, Robert Nozick himself quotes and comments on various letters and adds interesting insight into the history of the problem and his own attitude and that of Newcomb himself. This is where the quote from Isaac Asimov is from.

Levi, I. 1978. Newcomb’s Many Problems. In Hooker, A., J. J. Leach and E. F. McClennen (ed.), Ifs: Conditionals, Belief, Decision, Chance and Time. Dordrecht: D. Reidel: 369-383. https://link.springer.com/article/10.1007/BF00169104

An earlier discussion of Newcomb’s problem that focuses on some of the assumptions about the statistical nature of accuracy (or at least that is the part that I remember).

Nozick, R. 1969. Newcomb’s problem and two principles of choice. In N. Rescher (ed.), Essays in Honor of Carl G. Hempel. Dordrecht: D. Reidel: 114–46. https://link.springer.com/chapter/10.1007/978-94-017-1466-2_7

The original presentation of Newcomb’s problem.

Yudkowsky E. and N. Soares. 2018. Functional Decision Theory: a new theory of instrumental rationality. arXiv: 1710.05060. https://arxiv.org/abs/1710.05060

Where I first encountered the transparent Newcomb’s problem.

Wardens #2

Schmata Business: Part 2

Writer/Letter: Ari Gross

Artist/Cover Art: Rob Jennex

Editor: Aubrey Lyn Jeppson

October, 2025, 44 pages.

On-line at https://www.arigross.ca/wardens/.

Rating 4/5

What’s the Schmata?

Nothing what’s the schmata with you?

When we last left Rachel Tussman hard scrabbling seamstress in 1926 Toronto, the factory she worked at had just burnt down and she had been possessed by the ghost of her sister Goldie. Rachel’s beau Bertie died in the fire and his spirit joined the mysterious Schmata a mobile suit of clothing possessed by the spirits of the dead seeking vengeance. Our story picks up with Rachel awakening no longer possessed in a secret set of tunnels overseen by Rabbi Cohen who has some knowledge and experience of matters supernatural. The Rabbi explains the situation and Rachel, the Rabbi, Goldie’s ghost, Goldie’s beau Sonny Wu and the talking frog Mordecai make plans to deal with the Schmata.

The story continues inter cutting between mysterious and suspicious developments among the jazz band at a local speakeasy, the reaction to the local Jewish community to the factory fire and the murderous shenanigans of the Schmata. We take in a little of a vaudeville show. The jazz band leader is communing with the great beyond thanks to whatever he is smoking.

Things are developing in the larger story and nothing is resolved. This issue continues the snappy dialogue and friendly engaging art style of the previous issue. The tone remains mostly upbeat and adventurous, but more complicated social issues of prejudice and poverty simmer in the story and the Schmata begins to cut a bloody swath through 1926 Toronto adding some menace and horror to the proceedings.

A recent poll tweeted over on Twitter stirred up much excitement and emulation. Apparently similar polls have been run before. A schematic dilemma is sketched as presented to “everyone” “privately”, press one of two buttons, one red which offers certain safety to the presser, the other blue saves everyone but only if a majority press it.

The vote resulted in blue won the poll. The discussion around it included some very heated rhetoric. Many on one side insisted that red was what people should vote for; that it made no sense to vote other than red; that there was no benefit to voting blue; that it was equivalent to choosing suicide to vote blue; that it was not selfish to vote red; that those voting in the poll would not vote that way if there life were actually on the line; and that those voting blue did not understand basic game theory. On the other side it was insisted that there was no reason to vote red since a majority voting blue achieved the best outcome; that it was selfish to prioritize absolute safety; that some hapless innocents such as children or the colour bind would be condemned by a majority red vote and that the victory blue showed that game theory is a falsified and idle theory.

The Specter of Game Theory

The reference to game theory requires a bit of explanation. Game theory is a way of formalizing analysis of various strategies in hypothetical scenarios that allow strict rules and for what participants (players) will do and consequences. The scenarios are games, but usually not those played at a casino or the like and certainly not actual games of skill like darts. The most famous example of a game theory scenario is the prisoner’s dilemma which tries to schematize the question of two criminals who might betray the other (defect) by giving a confession. The basic scheme is that it they will each serve a short sentence if neither defects and both will serve a much longer sentence if both defect, but if one defects and the other does not the defector will go free while the other will serve a longer sentence still. Game theory famously councils defection to one in this scenario, but only when stringent conditions are met (no communication between the prisoners before they decide, no prospect of repetition of the scenario and so on). The prisoner dilemma seems like many real life scenarios and so game theory seems to council very untrustworthy behaviour however this should be tempered by knowing that advice to defect depends on all those tricky background assumptions. Several years ago a dilemma making the rounds in Twitter led Kevin Zollman, philosopher and game theorist to quip:

One can consider the button dilemma in a game theoretic way as one does the prisoner’s dilemma. They are clearly different dilemmas in that the stipulated consequences are somewhat different and that there are more than two participants. Still a straightforward game theoretic sounding argument can be given for pressing red. First we should introduce the payoff matrix, this is a way of displaying the consequences of each player’s strategy. The matrix is a list of rows and columns, one row for each strategy one player can adopt and a column for each strategy the other player can adopt, at each cell that is an intersection of a choice To allow a simple representation of the button dilemma the rows will be the possible choices of you (1 player), which are either press the red button or the blue (it is assumed there is no third option such as do nothing), but the columns are the possible outcomes of the vote (majority press the red button, majority vote blue, its assumed ties are impossible). Let me show you want the matrix looks like, I’ve schematized the presentation even further talking about Action A and Action B. It should be understood that Action A is pushing the red button and Action B is pushing the blue button. Notice that we can replace Action A and Action B with any combination of actions that have the same schematic representation as pushing the buttons, this will be important to a point I want to make later.

So here it is:

We can now easily analyze the consequences of each action if you press the red button (take Action A), you are guaranteed the benefit of survival (or equivalently avoid the penalty of death), if you press the blue button (take Action B) then you either die or survive. In this case, if you only care about your own survival, it is easy to see that pushing the red button gets you every benefit that pushing the blue button does and none of the costs. There are some complications, what if you care about the survival of some or all blue button pushers, should you take into account the chances. Normally you would way the benefits of each outcome by their probability (yield the so-called expected utility). In this case though if you only care about your own survival that does not matter.

Note strictly game theory does not need to follow how human beings actually reason and so need not predict or determine the outcome of a poll. Although that gets into the question of what the point of formal methods of analysis like Game Theory are supposed to accomplish. Do they replace ordinary folk reasoning altogether, do the attempt to reproduce the reasoning of normal humans in a rigorous form, do the explain or examine human decision making, or are they a supplement to decision makers for planners and leaders? The field of game theory was inaugurated by John von Neumann and Oskar Morgenstern in their book Theory of Games and Economic Behavior. As this title suggests it was conceived as having relevance to actual social and economic problems. However this leaves open whether this more rigorous approach was meant to supplement or understand at some more rarified policy level of dilemmas or rather to replace less rigorous thinking in general. Still the failure of normal reasoners to follow game theoretic modelling is fatal to the endeavour seems dubious. Especially as it seems clear that an analysis of situations requires the probabilities of outcomes in these sorts of situations to be stipulated they are not predicted from the axioms of game theory. What actual human beings will do in actual situations is clearly important to game theory, but the basic model need not predict and follow everyday human reasoning.

The Importance of Framing

Anyway, much disagreement surrounds this poll and scenario. Here on Substack Tommy Blanchard commented in a short note commenting on the “debate” that “it matters how things are framed” and giving an example of a framing. Blanchard presents the scenario reminiscent of the infamous trolley problem, those who press red will stay off the tracks, those who press blue will be on the tracks and be run over by a trolley unless the majority press blue which will be enough to cause the trolley to stop. It seems clear this framing will make someone it is posed to favour the red button and so the framing matters. But can we suggest why framing matters? What principles are involved? Also can we touch on what else matters in how these dilemmas are discussed? I think we can and in this note I want to take a stab at it.

My analysis will begin by pointing out that the poll has a completely schematic question, no details are given on the mechanics the button lead to death etc. So an endless number of different framings (or completely different scenarios or hypotheticals as some will call it) all just fall under the same schematic scenario outlined. I take it all and none of those scenarios may have been intended. It seems plausible Tim Urban asked it to see how different people would fill out the schema in answering the question. The game theoretic pay off matrix is even more open to being filled in different ways, as I displayed it, it only requires two possible courses of action be available to be adopted and does not say which ones. However this is controversial on both sides it is complained that the various framings actually change the nature of the scenario completely, but controversial as this may be it is my assumption. Hopefully my discussion will explain why it is controversial but ultimately correct.

Let me now spin out a few framings. Imagine if pressing the red button doses the red pusher in a chemical that perfectly repels bees, pushing the blue button doses the blue pusher in a chemical that will repel bees as long as enough (50%+) of people around you are also doused in that same chemical. Now imagine there are a strain of super killer bees even one is enough to wipe out mankind. In scenario A every time the red button is pressed one such bee is released, so if everyone presses red no one dies (killer bees are repelled), if more than 50% press blue no one dies (again bees repelled), but if between 0-50% press blue every blue presser dies. Under Scenario 1 super killer bees have their cage opened if anyone presses a blue button. Again the consequences are the same (thanks to the bee repellent everyone is being drenched in). People will have different reactions to Scenario A and Scenario 1, but in terms of the posed red and blue button problem, both conform to the conditions laid out so both instances of the dilemma. If you de-idealize even a little scenarios A and 1 come apart (have very different consequences), but given how idealized the question was why must you do that?

If you idealize even more and treat it just as a game theory dilemma beholden to the payout matrix I drew above where you have two possible choices and two possible states of the world the number of scenarios vary even more. You could have scenario Alpha (or rather set of scenarios alpha) where we replace pushing the red button by doing nothing (if everyone does nothing no one dies) and replace pushing the blue button by pushing a white button, the payout matrix for the dilemma is the same as for scenarios 1 and A. Likewise you could have scenario Prime where you replace the blue button with doing nothing (if 50%+ of the population does nothing no one dies) and the red button with a black button, again the payout matrix stays the same.

In general people suggested that people would prefer the option that is framed as doing nothing (such as not releasing bees in my scenarios A and 1 or not pressing a button in Alpha and Prime). Some people even intimated that you should prefer doing nothing, that it was more rational or moral to do so. This means people see at stake in the framing the principle that acts of omission requires less justification, motivation or deserves less censure or are easier to motivate than acts of commission. So one reason framings make a difference is that it changes pressing one of the buttons from being seen as an act of commission into an act of omission. I claim that the question as asked is compatible with either button press being interpreted as an act of omission or commission. This analysis just raises the question of whether the preference for acts of omission makes sense, indeed does the distinction of acts of commission and omission make sense? Many are skeptical of such distinctions. I’d like to explore why there is at least a certain sense in the distinction.

What Even Is The Question?

First we should note that there are other issues of framing. Such as what does the poll question actually want an answer to. What you a particular human being would do is maybe the most obvious and common interpretation. Each of these is different framing of the question, and it seems clear some people take it as a question of what you judge it would be rational to do, or moral to do, or indeed selfish to do. Some would take it that it is always rational to do what is moral, others that it is always rational to do what is selfish. One might also take it as a question of what you expect others to do, guess which button more people will say they press. Certainly one reaction to blue winning and disparaging those who chose red seems to imply their failure was chiefly in not knowing what people would chose.

This question of the framing of the question in the poll also relates to another issue that comes up in this debate. Some people make the point that how you vote will all but certainly not be the deciding vote in the question (certainly not if all mankind must push one or the other button). They thus judge absolved the button pushers from any culpability or consequence in pushing red (even if the majority pushing red culpably murders blue button pushers, no one red button pusher is culpable) and judge it impossible that pushing the blue button could save anyone. This is a variation on the paradox of voting which is that its not rational to vote because the costs outweigh any benefits it could cause. Some complain about calling this a paradox, this ignores two things: one paradox often implies something counter-intuitive or surprising rather than strictly paradoxical (contradictory). Second there is a contradiction, if everyone were “rational” and so did not vote, then if one person were to decide to vote, his vote would be efficacious and so it would be rational to vote because it is irrational. One could claim the second point assumes that people are rational. However that returns us to the question of whether rigorous models of rational decision are supposed to reproduce or replace actual human reasoning. We can also ask if human reasoning is unreliable then how can we come to reliable formal reasoning methods, what was our standard to judge them. As the saying go to shape an axe handle requires an axe.

Anyway, I think we can cut that off if we think about the question of the poll as what people in general should do, rather than what an individual person should do. However I will circle back at the end and suggest an argument why thinking of the question as individual may still be much the same as thinking of it in general terms like what is rational or what people in general will do.

There is another framing issue I want to touch on. This is how the consequences of the outcome were framed. When those advocating for pushing the blue button suggested that red winning would lead to the death of innocents such as infants or the colour blind some advocating pushing red insisted that this was not implied by the question. Depending on how you frame the question or what dilemma you replace it with this contention about the consequences may seem to admit of clear resolution. So framing again changes how the question is judged for people. I will get into some of the consequences that may be frame in discussing the questions of omission and commission.

Acts of Omission and Commission

Returning to my scenarios A and scenario 1 involving bees. Here in scenario A the act of omission is that of pressing the blue button, no bees are released by pushing the blue button rather each red button pusher commissions the release of a potentially apocalyptic bee. In scenario 1 it is the blue button pushers who commission the release of bees. Why does this matter. As I said above in the ideal scenarios where everything works perfectly as stipulated (and is also perfectly expected to), it seems like it doesn’t. However in any real life scenario we expect there are things that do not go as planned especially when dealing with the entire human race.

What if one or both of the chemicals fails sometimes to protect from the bees (perhaps it fails to be sprayed onto some button pushers), how many would die? In scenario A everyone might press red, but if the chemical fails in an encounter between 8 billion humans and 8 billion bees many thousands or millions might die. If the blue button bee repellent requires more to work it seems as though there is more that could go wrong, likewise making scenario 1 risky if everyone votes blue. Here avoiding an act of commission (releasing the bees) minimizes the danger of something going wrong and so that is going to help make it preferred if those risks are high enough. Although if a single bee released is potentially deadly to a large population that favours having contingencies for if the bee is released that protect as many as possible and so on.

Note here we are assuming that doing nothing has fewer risks than doing something. However one can easily imagine scenarios where doing nothing is the riskier proposition. If there were a truck hurtling towards you staying in front of it would be riskier even if it will probably stop before it hits you. Moving out of the way is probably the safer and more certain move even if it is an act of commission. So the distinction should be treated as more of a guideline or rule of thumb at least if you are justifying the distinction on the sort of grounds I have laid out.

De-idealizing also changes the prospects for side effects. In Scenarios 1 and A what if these bees wipe out all non-human vertebrate life on the surface of the Earth say? This might cause massive losses in the agricultural sector or a world wide ecological collapse or some other calamity. This again focuses us on strategies that minimize what can go wrong (minimize the release of deadly bees). Presumably the mechanics of the scenarios should be understood to have no extra bad effects other than the ones explicitly stated, but that would depend on everything going as planned. Or does it? In real life when listing pros and cons of a decision only major effects may be made explicit small effects may be ignored and secondary knock-on effects may be left implicit. When assessing dilemma’s actual people give us rather than strange hypotheticals we will often be sensitive to the possibility they are leaving things out or taking a misleading interpretation and so that is another way framing can change one’s interpretation, making one ask what might be hidden or too confidently assumed away.

The question of implicit consequences is I think particularly important. As mentioned the Twitter discussion included disputes over whether small children were included by implication among the button pressers. Other implications seem disputed for example some insist there was no possible draw back to voting red, some of this is no doubt rhetorical excess, but I inferred a somewhat cavalier attitude to downstream effects in it. After all if 50%-1 vote blue surely that mass death would have a negative effect on the economy. Also what if the people who die, die suddenly while driving their car say. The negative effects could easily be widespread, depending again on the mechanism by which the condemned are to die. Also there is the rather direct consideration of the fact that a red button pusher may have blue button pushing loved ones.

Rejection of some of the imaginable consequences of mass death (traffic accidents for example) seems debatable but in-line with the requirement that the scenario spell out its negative consequences. However sometimes those arguing pushing red has few or no negative repercussions seem to be arguing for a reinterpretation of what death means. Death is so horrible in part because of all its attendant negatives including economic costs and the loss felt by loved ones. To view that as an extra added penalty not compassed in the original scenario, risks viewing what it means to “survive” is just that one’s name is toted in a list as survived, with no negatives for anyone. This parallels the complaint that people voting blue in the poll are not considering the gravity of death.

Intending vs. Foreseeing

Anyway, given this it is I hope straightforward how framing or spelling out the mechanics of the scenario may affect appreciation for some less obvious or certain consequences of blue button pushers dying. There remains another aspect I notice that also relates to consequences and ideas of omission and commission. This is the question of what we intend intent rather than merely foresee. Some contend one can take an action that has an obviously foreseeable consequence and not intend that consequence, this is most famously seen in the doctrine of double effect in Catholic theology (which has various other aspects). However I don’t think one has to go that deep into the weeds to see the basic principle and disagreement.

I’ve already touched on how either side tends to characterize the other as responsible for the deaths that may occur in the scenario. Those arguing for the merits of blue button pushing often characterize pushing the red button as a betrayal, an intentional defection from cooperation, those arguing for pressing red disagree. Part of this returns to the notions of omission and commission, if you see pushing the red button as doing nothing then how can doing it be an intension. As pointed out this gets tricky since standing unmoved as a truck hurtles towards you is doing nothing, but might still be seen as culpably negligent, if not strictly intentional. There are reasons to eschew any notion of intention in this after all no one chooses to be in this scenario, it is the architects of this scheme who are in control and intend things.

Certainly in the dilemma’s schematic form it seems tricky to attribute any clear intentions to button pressers. Adding more detail (framing the dilemma differently) may make it seem clearer that intent is involved, but the intent is mitigated by the necessity or coercion of the situation. In my Scenario A someone pushing the red button knows it will release a killer bee, but they probably only do it so they may be covered in life preserving bee repellent. What if we imagine a scenario 1A like scenarios 1 and A except that pressing either button releases bees, does one intend to release bees if one has no option not to?

We could imagine scenarios where one must not only press a button but due to some mechanism that achieve mind reading one must have a certain intent. So perhaps one scenario where you can only successfully push the red button if you not only foresee the death of blue button pushers but intend it. In this case it may be that those inclined to push red would lack the ability to form the requisite intent, they might even lack the ability to know what that intent would be. They do not know who will push blue after all or if anyone will. Thus if only pushing one button had an intent requirement one might have to change one’s answer to the one without it and if both required plumbing some esoteric notion of intent the question might become unanswerable. Of course even without esoteric mind control technology inability to form proper intent might prevent one pushing a button. One might judge pressing blue the moral option, but find yourself unable to do so as forebodings of your possible subsequent death invade your mind.

I think its worth fleshing out more by example what intention means, since the meaning of intent remains unclear and circular. One example that comes to my mind, is imagine a riot is forming, if you join the riot you will be safe from the rioters, if not they will fall upon you and kill you. If more than 50% become riotous the riot starts. This scenario is ludicrously farfetched, but perhaps not completely divorced from the reality of mass psychology (in reality rioters are probably neither so homicidal nor so discerning and there are practical problems such as being attacked by non-rioters fighting back). What is clear is that to actually become riotous in the relevant sense one would have to be willing to kill (beat to death with one’s bare hands). So for one who would choose that option could one really bring oneself to overcome one’s native disgust at violence, fear of reprisal, compassion and so on to join the riot so cold-bloodedly, this would probably prevent many from choosing this answer. On the external side as a society it is good that we do not have people who can turn into murderous creatures at the drop of a hat, we would be ill at ease if we thought anyone might turn homicidally violent to easily. Hence it makes sense we value the lack of intent (unwillingness) to tear each other limb from limb and have internalized that value. Given that value one could with some legitimacy claim that scenarios that make participants take active rolls in the death change the consequences implied by pushing the buttons (add costs not implied) and so are different scenarios. However it seems clear that even unbidden by such alterations people on both sides impute such active participation (claim that red button pushing is homicidal or blue button pushing suicidal).

This goes to show another reason we make somewhat scholastic distinctions between intended and unintended outcomes. As with my point earlier about acts of omission and commission, it seems as though there is a tendency to more risk in acts done with a strong intent to cause harm. Again this is more a guideline then a fast rule as we have things like self-defense that may justify violence as necessary in certain circumstances. One final example in this vein seems warranted. Imagine the dilemma was whether to inject a sort of zombie serum, unlike the zombies of popular media it would not render you a shambling rotting corpse, it would have little discernable effect. In scenario Z if the majority take the serum then the serum takers temporarily enter an automaton-like state and purge the rest of the population and then awaken to normal mentality with no memory. In scenario Omega a similar effect happens, but only if a minority of the population has taken the serum and instead of becoming murderous automatons they become suicidal. Although here no specific murderous intent is perhaps implied by taking the serum, yet it still seems like culpable negligence. I suggest scenarios Z and Omega to make clear that a framing can alter the interpretation of the scenario in favour of either horn of the dilemma.

A quick note some framings reveal the artificiality of only having two responses to the dilemma. The giant blender scenario imagines that there is a giant blender that the entire human population might be able to throw itself in. If half the population does throw themselves in their collective weight will stop the blender. This framing emphasizes the idea that blue button pressing is suicidal. However it also is telling that in real life dangerous industrial equipment (like giant blenders) is usually operated behind locked doors, in areas separated often by fences, guard rails or cordons from the general population. Likewise bridges, cliffs and ravines in urban areas will often be fenced off. This illustrates that contrary to some hyperbolic pro red button rhetoric we consider the possibility of people accidentally putting themselves in harms way and take measures to prevent it at cost to ourselves.

The Paradox of Voting Reconsidered

I want to circle back to the voting paradox. Whether what an individual should do is tempered by the fact that one vote will not change an election. I want to argue that one should just try and figure out what is rational (or moral or maybe just what people will do) and do that, rather than worrying whether you can change the outcome. For why I want to consider the implications of a common genre of debate on social media like Twitter. Debates about how to interpret arithmetic statements.

A typical example of such debates on Twitter is seen here:

One arithmetic equation is given, but two answers are presented by various people.

The problem the statement

may be interpreted as either

or as

because the division sign (÷) does not have a strong convention associated with it that indicates the numerator or the denominator. Various examples are seen not all involving division. People often become very insistent on their own interpretation and incredulous at the different takes other people have.

I want to draw an example: what if some eccentric billionaire issues the following challenge as they are wont to do in these hypothetical situations. Participants (isolated lets say in exam type conditions) are challenged to write an answer to the equation and submit it. Which ever answer gets the most submissions will be taken as right and everyone who submitted that answer will receive appropriate prize money.

If people each answered independently then the chances of anyone winning (of any number being submitted more than once) is basically zero. Of course the participants submissions will not be independent rather they will heavily cluster around the two suggested interpretations.1

It seems to me there are two strategies to follow. One is assume the interpretation of the equation that is correct, looks right, follows convention or what have you is the one more people will take and so rationally calculate the value for that. Or assume most people who will submit an answer are bad at math, but you one of the math cognoscenti, the mathia if you will, are good at math, so assume they will do it wrong and work through rationally what that will be.

Both of these reflect our sense that people have a common set of conventions from basic mathematics education. We also have experience with how good the general population is at math (how prone to deviation from convention as we understand it). As a result our reasoning through what answer to write will be highly correlated and so we can rest assured that we have a chance by voting according to that reasoning to constitute the winning convention one way or the other.

I think this contradicts the application of the variation of the paradox of voting I mentioned earlier. The argument that one should not believe that one has any culpability or power to bring about a majority blue vote. The flaw I think here is that the question is not can one change an outcome from what one’s reasoning will lead to into something else (which would indeed be all but impossible), but rather is your reasoning in question reasonable in these circumstances (where others have been trained much as you have and you’ve interacted with them).

If one applied the logic suggested to the bet on arithmetic interpretation, each voter would if they considered it rationally, rationally conclude that they can’t bring about any outcome (there vote won’t make a difference as to what the convention is) and so be unable to choose and thus not be able to set the convention, by voting in a consistent way (they would revert to writing a number at random). However it seems rather that people can indeed by following their educated premises coordinate their actions and so by reasoning in the way they naturally do they constitute the convention (or by recognizing the way others reason and following it to get the “wrong” majority answer).

Note I imagined that the billionaire offers a monetary prize, but it seems as though many people would happily participate in such a competition for free. So its not the prospect of money irrationally laid out that makes people irrationally believe they can set a convention.

Conclusions

I’d say likewise in a dilemma of the kind proposed by the red and blue buttons we would expect participants reasoning to be highly correlated. Yet we would also expect their to be ambiguity’s in such a schematic question and so there to be multiple popular responses. Hence the controversy seen in social media. Different framings change again the plausibility of different interpretations of ambiguity and so change one’s tendency in how to respond (how to reason about the problem).

In some cases this might take the form of values we have so deeply ingrained that we can not without severe psychic trauma contemplate taking the action. As mentioned before such reservations and requiring their violation would change the reward and cost framework of the dilemma significantly from how it is sketched. Technically though it might not for all participants.

For example imagine the scenario as usually laid out with that in order to gain the benefit of pressing the red button one had to have the intent that by doing so one boiled a lobster alive (or perhaps we should reverse it and imagine pressing the button fills one with the intent to boil a lobster). Well in many societies (including I think the one I live in) this would be very easy and for most people it would not really change the cost benefit analysis. However there are certainly individuals and perhaps whole societies for which boiling a lobster alive is a dastardly crime and they could not easily contemplate it, so it would change the dilemma substantively.2 Note if one lived in such a society of lobster respecters and were forced into the challenge one could probably with great confidence conclude that since only a deviant few could easily contemplate such a thing that blue is sure to win and your life is in no danger by pushing the button and one may confidently avoid contemplating a lobster’s painful death.

Now I suppose that the analysts who insist on the powerlessness of individual reasoning will say is something like. Having a strong taboo playing a role just changes the cost structure and so what reasoning should arrive at. Yes, but that’s just how people’s reasoning works, if people adopt an arithmetic convention it becomes uncomfortable (probably only very mildly uncomfortable) to break that convention. So indeed following’s one own’s reasoning is not some independent act that defies the population level context of a decision, but rather a dependent act that reflects the cost implicit structure of the problem imposed by one’s background faculties of reasoning, the associations one makes, the principles one follows and so on.

So what button one decides to press will reflect how one thinks about problems in general: how one default expects things to be implemented; what you think words, phrases and arrangements and practices connote; how one expects things to go wrong; what sort of consequences and fall out from bad things you are naturally drawn to think about and so on. No wonder there is such disagreement about what the dilemma is and what different answers imply. It is unfortunate that in my estimation it tends to produce more heat (disagreement) than light (understanding).

There are other issues like what roll the threshold (50% of button pushers needing to push blue to save everyone). That also reveal something about the issues or issues assumed by people discussing the problem. I will not go into them here as I have gone on enough. I will just note that if one’s ideal response varies with threshold that suggests problems with the totalizing arguments (arguments where some one factor is ALL that matters). Another issue is how could be convinced such an outlandish dilemma confronts you (where the consequences are so certain and necessary and the options so necessarily limited), this is implicit in considering that worries about say acts of omission versus commission often relate to our sense that things will not go as expected (as stipulated in the rules of a scenario).

Anyway I hope all this goes to show why framing does matter, not just in that it changes the capricious and superficial psychology of participants, but that in it brings forward principles that are actually at work in more reliable decision making.

Some other takes on Substack:

As I was writing my take I noticed these two articles on this same issue:

This briefly considers how framing makes the scenario different by appealing to and activating different psychological situations.

This take gets heavily into the weeds of a rigorous game theoretic or decision theoretic sort of technical analysis of the problem red versus blue button question as posed. It does spend time analyzing different framings and parallel cases and arguing why they are not relevant or decisive. In some cases I might think that what is taken as a different case is allowable under the schematic original description given of the dilemma. However I have to admit that the author has a much sounder grasp of some of the formal apparatus then I do.

Before discussing relativity Einstein begins by distinguishing two types of scientific theories. Constructive theories and theories of principle:

“Most of them are constructive. These attempt to build a picture of complex phenomena out of some relatively simple proposition. The kinetic theory of gases, for instance, attempts to refer to molecular movement the mechanical thermal, and diffusional properties of gases. When we say that we understand a group of natural phenomena, we mean that we have found a constructive theory which embraces them.

But in addition to this most weighty group of theories, there is another group consisting of what I call theories of principle. These employ the analytic, not the synthetic method. Their starting-point and foundation are not hypothetical constituents, but empirically observed general properties of phenomena, principles from which mathematical formula are deduced of such a kind that they apply to every case which presents itself. Thermodynamics, for instance, starting from the fact that perpetual motion never occurs in ordinary experience, attempts to deduce from this, by analytic processes, a theory which will apply in every case. The merit of constructive theories is their comprehensiveness, adaptability, and clarity, that of the theories of principle, their logical perfection, and the security of their foundation.” (Einstein 1919)

He then explains relativity is a theory of principle and attempts a short survey of those principles and compares them to Newtonian mechanics. Einstein’s emphasis on principle makes sense given the importance just such abstract principles play in relativity. The special theory of relativity is explicable by two short postulates (and the implicit structure of physics). The emphasis on abstract logical form allows him to connect relativity to Newtonian mechanics and suggest how his own work has strong continuity with and dependency on those earlier theories.

The distinction is also pregnant with various issues in physics and science more generally. The importance of understanding or explanation as a merit of scientific theorizing. The question of the strength and enduring nature of evidential support (the security of foundation) of some theories over others. It also hints at a major scientific change and debate of the 19th and early 20th century, the development of thermodynamics and how statistical mechanics (consisting of theories such as the kinetic theory of gases) arose to elucidate mechanisms for thermodynamics that were resisted (such as the existence of atoms). Einstein was involved in these developments in his 1905 paper deriving properties of molecules such as size from features of Brownian motion.

It is probably in part because of this that Einstein’s 1919 paper has become, in my estimation, a common reading in history of science courses and collections of essays about Einstein, relativity and science. I have known several philosophers who found the distinction interesting and suggestive. The Stanford Encyclopaedia article by Don A. Howard and Marco Giovanelli on Einstein’s philosophy of science for example says “Einstein’s most original contribution to twentieth-century philosophy of science lies elsewhere, in his distinction between what he termed “principle theories” and “constructive theories.”” (Howard & Giovanelli 2025)

I and every person I ever remember talking about this distinction with took the distinction as original to Einstein (although Einstein does not himself make that claim). As I will now relate I think the distinction is much older. I don’t want to make too much of this. I don’t think the sources I’m going to now cite are particularly obscure, many others may unbeknownst to me made the same distinction. Howard and Giovanelli’s Stanford Encyclopedia article suggests some influences and precursors. However this also includes this thought that I think definitely requires some correction “What is puzzling, and even a bit sad, is that this most original methodological insight of Einstein’s had comparatively little impact on later philosophy of science or practice in physics. Only in recent decades, Einstein constructive-principle distinction has attracted interest in the philosophical literature, originating a still living philosophical debate on the foundation of spacetime theories.” (Howard & Giovanelli 2025) Let me now detail some things Howard and Giovanelli at least overlooks.

Back in May of 2020, I was for some reason skimming bits of a 1934 book on logic and scientific method co-authored by Ernest Nagel (who is my favourite 20th century philosophical Nagel) and Morris Cohen (I’ve never heard of Cohen so I put Nagel 1st but Cohen has top billing on the title page). I can not remember why exactly. Perhaps I was looking for responses to John Stuart Mill’s Logic or perhaps I just wanted to see what Nagel had to say about philosophy of science in 1934. It was the height of the pandemic, and I was reading a little more then, but I spend a lot of time reading odd things here and there. Whatever the reason I was struck by this passage:

“There is however, another interesting distinction between theories. Some theories appeal to an easily imagined hidden mechanism which will explain the observable phenomena; other theories eschew all reference to such hidden mechanisms, and make use of relations abstracted from the phenomena actually observable. The former are called physical theories; the latter are called mathematical or abstractive theories.” (An Introduction to Logic and Scientific Method, 1934, M. R. Cohen and Ernest Nagel, p. 397)

Here was Einstein’s distinction between constructive and principled theories with the slight change of labels. A constructive theory became a physical theory, a theory of principle becomes a mathematical or abstractive theory. They rehearse some examples and the classification matches Einstein, the kinetic theory of gases is a physical theory, the theory of relativity an abstractive theory. Although the basic distinction is the same Cohen and Nagel do not give it the same significance or implications that Einstein does. They see the two types of theories as indicative of the idiosyncrasies of scientists and the trends of the time.

“As we suggested, it is useless to quarrel as to which type of theory is the more fundamental and which type should be universally adopted. Both kinds of theories have been successful in coordinating vast domains of phenomena, and fertile in making discoveries of the most important kind. At some periods in the history of a science, there is a tendency to mechanical models and atomicity; at others, to general principles connecting characteristics abstracted from directly observable phenomena; at still others, to a fusion or synthesis of these two points of view. Some scientists, like Kelvin, Faraday, Lodge, Maxwell, show an exclusive preference for “model” theories; other scientists, like Rankine, Ostwald, Duhem, can work best with the abstractive theories; and still others, like Einstein, have the unusual gift of being equally at home with both kinds.” (Cohen and Nagel, p. 399)

So unlike Einstein they see no special virtues (such as clarity or logical rigour) in the two types of theories. Also although they reference Einstein as a scientist here they make no reference to his use of the same distinction (and may well have been unaware of it). They do however reference an 1855 paper by Scottish physicist William John Macquorn Rankine and give a long quote of his distinction between the two types of theories. Rankine’s 1855 Outlines of the Science of Energetics is the earliest source I have found making the distinction. I have not really looked for any earlier instances. Still it is worthwhile to see how and what Rankine makes of the distinction.

The paper is mostly an attempt to outline what will become standard thermodynamic concepts and link them to existing ideas in physics. Such as defining kinetic and potential energy in Newtonian mechanics. However the paper begins by outlining how theories are derived form observation. He then continues:

“Two methods of framing a physical theory may be distinguished, characterized chiefly by the manner in which classes of phenomena are defined. They may be termed respectively the ABSTRACTIVE and the HYPOTHETICAL methods.

According to the ABSTRACTIVE method, a class of objects or phenomena is defined by describing, or otherwise making to be understood, and assigning a name or symbol to, that assemblage of properties which is common to all the objects or phenomena composing the class, as perceived by the senses, without introducing anything hypothetical.

According to the HYPOTHETICAL method, a class of objects or phenomena is defined according to a conjectural conception of their nature, as being constituted in a manner not apparent to the senses, by a modification of some other class of objects or phenomena whose laws are already known. Should the consequences of such a hypothetical definition be found to be in accordance with the results of observation and experiment, it serves as the means of deducing the laws of one class of objects or phenomena from those of another.

The conjectural conceptions involved in the hypothetical method may be distinguished into two classes, according as they are adopted as a probable representation of a state of things which may really exist, though imperceptible to the senses, or merely as a convenient means of expressing the laws of phenomena; two kinds of hypotheses, of which the former may be called objective, and the latter subjective. As examples of objective hypotheses may be taken, that of vibrations or oscillations in the theory of light, and that of atoms in chemistry; as an example of a subjective hypothesis, that of magnetic fluids.” (Rankine 1855)

So we see that Rankine’s terminology differs slightly again from Cohen and Morris. Instead of physical theories Rankine talks of hypothetical theories. Also he distinguishes between objective and subjective hypothetical theories. Rankine differs also in that he takes it that there is a significant difference in the implications of being one or the other. He defines mechanics (Newtonian mechanics) as the exemplar of the abstractive method and the only complete physical theory.

He discusses the efficacy of hypothetical theories in allowing diverse phenomena to be explained by a few simple rules, but cautions:

“Such are the results to be expected from well-framed hypotheses in every branch of physics, when used with judgment, and especially with that caution which arises from the consideration, that even those hypotheses whose consequences are most fully confirmed by experiment, never can by any amount of evidence attain that degree of certainty which belongs to observed facts.”

[...]

“The neglect of the caution already referred to, however, has caused some hypotheses to assume, in the minds of the public generally, as well as in those of many scientific men, that authority which belongs to facts alone, and a tendency has consequently often evinced itself to explain away, or set aside, facts inconsistent with these hypotheses, which facts, rightly appreciated, would have formed the basis of true theories; thus the fact of the production of heat by friction, the basis of the true theory of heat, was long neglected, because inconsistent with the hypothesis of caloric;” (Rankine 1855)

Like Einstein Rankine thinks that abstractive (principled) theories have a more secure evidential base than hypothetical (constructive) theories. However Rankine takes it further and emphasizes an absolute distinction in the evidential basis for the matter. As mentioned Cohen and Nagel deny any substantive distinction between the value and reliability of the theory.

Rankine discusses how extension of mechanics to science (such as kinetic molecular theories of heat) has been successful) and may come to encompass all of science, which is a kind of combined method of occult molecular or atomic hypothesis combined with observed abstractive laws of motion. What we might now thing of as a single unified theory of physics. He offers an alternative path in extending abstractive method as follows:

“Instead of supposing the various classes of physical phenomena to be constituted in an occult way of modifications of motion and force, let us distinguish the properties which those classes possess in common with each other, and so define more extensive classes denoted by suitable terms. For axioms, to express the laws of those more extensive classes of phenomena, let us frame propositions comprehending as particular cases, the laws of the particular classes of phenomena comprehended under the more extensive classes. So shall we arrive at a body of principles, applicable to physical phenomena in general, and which being framed by induction from facts alone, will be free from the uncertainty which must always attach even to those mechanical hypotheses whose consequences are most fully confirmed by experiment. This extension of the abstractive process is not proposed in order to supersede the hypothetical method of theorizing; for in almost every branch of molecular physics it may be held, that a hypothetical theory is necessary as a preliminary step to reduce the expression of the phenomena to simplicity and order, before it is possible to make any progress in framing an abstractive theory.” (Rankine 1855)

This sort of thinking illustrates how differently Rankine understood the distinction than Cohen and Nagel or Einstein. Abstractive methods for Rankine are more evidentially secure and there is no sense hypotheses are needed for understanding as Einstein seems to suggest. For Rankine hypothesis is necessary at the beginning of investigation to identify what properties and relations to abstract.

I feel as though it is clear that Einstein’s basic distinction between constructive and principled theories must be the same distinction as Rankine’s (Cohen and Nagel cite Rankine so the pedigree of their distinction is clear). This is not certain since two people considering the same physics might arrive at a similar taxonomy due to similarity of subject matter, but I this seems unlikely to me. If I am right how then did Einstein learn of the distinction. One possibility is that Einstein read Rankine’s 1855 paper. Einstein did work on thermodynamic and energetic subjects. Again, the possibility can not be ruled out, but it struck me that Einstein was known to have read Duhem and Duhem wrote histories of physics and so might well have come across Rankine.

Sure enough in Chapter 3 of 1906 La théorie physique, son objet, sa structure (The Aim and Structure of Physical Theory), Duhem extensively quotes Rankine, introducing him with this paragraph:

“The first contributions of Macquorn Rankine to the progress of the mechanical theory of heat had been attempts at explanation; but his ideas soon evolved and, in a short paper of his, too little known, he traced very clearly the characteristics which distinguish a representative theory — called by him “abstractive theory” — from an explanatory theory — designated by the name “hypothetical theory.” (p, 52 English translation by Philip P. Wiener)1

Again we find different labels representative theory (théorie représentative) for the abstractive (principled) theory and explanatory theory (théorie explicative) for the hypothetical (constructive) theory. Also the implications that are drawn are different again. For Duhem explanatory theories and explanation are always of quite limited power, more explanations or hypotheses can be put forward by the physicist and never penetrate to the ultimate nature (the metaphysical nature) of the underlying reality. Thus for Duhem science is always ends in a representative theory, a simplified and orderly representation of phenomena. Chapter 3 where Rankine is quoted is “Representative Theories and the History of Physics”2. This is not necessarily that at odds with Einstein’s understanding since a metaphysical understanding may be a more rarified thing than Einstein was thinking of when he considered constructive theories to allow understanding. Indeed skimming Howard and Giovanelli I see that Einstein rejected talk of the hypotheses of physics being real. I have not actually read Duhem thoroughly. Again skimming the Stanford Encyclopedia article on Einstein I see that Duhem’s holistic concept of science probably militates against his view that hypothesis and explanation are easy. Under Duhem’s holism individual elements can not be evaluated and so treating individual hypotheses as loose or interchangeable is militated against. Still I feel as though Einstein is giving more credit to the value of explanation that Duhem does in the passages I’ve read.

As Howard and Giovanelli chronicles it seems likely Einstein read Duhem in 1909 when he was neighbours with the German translator of La théorie physique (1908). This would suggest a vector by which Einstein could have learned the distinction between types of theories.

Not only the labels but also the implications change greatly between the different people who make the distinction. For Cohen and Nagel (whose book continued to be reissued into the 1960s) the distinction was more a mark of the style of certain physicists and times. In defense of this one can point out that it is not merely hypothetical entities but indeed the posited relations between observables that are different in different theories. As relativity shows, the relationships of space, time and motion are subject to revision and phenomena like time dilation can be received with the same incomprehension or incredulity as notions like unseen atoms. However this might not be enough to refute Rankine’s sense that abstractions from phenomena are more reliably known than hypothesized elements or Einstein’s sense that the foundations of principled theories were more secure. Duhem’s skepticism of explanation in science and so of hypothetical methods seems stronger than any reservations Einstein or Rankine had.

Another aspect interesting to me is the way this distinction seems emblematic of thermodynamics and statistical physics. The examples in that field seem most suggestive. There are also aspects of the famous doctrine of Newton not to propose a hypothesis about the mechanism of gravity that is often taken as a general maxim for science. The depreciation by Rankine and Duhem especially of hypothetical methods suggests it. There is clearly much more to be uncovered here, but I have been sitting on this for 6 years and thought it worth getting out.

Bibliography

Cohen, Morris R. and Ernest Nagel, An Introduction to Logic and Scientific Method, Routledge and Kegan Paul Ltd., 1934.

Duhem, Pierre, La théorie physique, son objet, sa structure, Chevalier & Riviére, 1906.

Duhem, Pierre, The Aim and Structure of Physical Theory, trans. Philip P. Wiener, Princeton University Press, 1954.

Einstein, Albert, “Time, Space, and Gravitation”, in Science, 51 (No. 1305); January 2, 1920; pp. 8-10, originally published: London Times; November 28, 1919.

Howard, Don A. and Marco Giovanelli “Einstein’s Philosophy of Science” in The Stanford Encyclopedia of Philosophy, 2025.

Rankine, William John Macquorn, “Outlines of the Science of Energetics” in Proceedings of the Royal Philosophical Society of Glasgow, Volume 3, by Royal Philosophical Society of Glasgow, 1855. pp.381-399.

Here are my findings (I may have made a mistake in my arithmetic at various points).

Rank by number of works cited in top 253 most cited

9 works cited: David Lewis

7 works cited: Bertrand Russel* (one co-citation)

5 works cited: WVO Quine; J Fodor

4 works cited: John Rawls; Rudolf Carnap; Donald Davidson; David M. Armstrong

3 works cited: Williamson, Timothy; Dretske, Fred; Hare, R.M.; Grice HP; Searle, JR; Dworkin R; Blackburn, Simon; Stalnaker, Robert; Chisholm, RM

Two works cited: Kripke, Saul; Parfit, Derek; Nozick, Robert; Wittgenstein, Ludwig; Chalmers, David * (1 co-citation); Moore, GE; Putnam, Hilary; Jackson, Frank; Ross, W.D.; van Fraassen, Bas; Dummett, M.; Goodman, Nelson; Popper, Karl; Raz, J.; Nagel, Thomas; Williams, Bernard; Gibbard, Allan; Strawson, PF; Longino, Helen; Anscombe, GEM; Plantinga, Alvin; van Inwagen, Peter; Butler, Judith; Dennett, DC; Frankfurt, Harry; Nussbaum, MC; Craver, Carl F. * (1 co-citation); Fine, Kit; Cartwright, Nancy; Zalta EN; Field, Hartry; Tye, Micheal; Godel, Kurt; Wright, Crispin; Tarski, A.

Everyone else on the list is cited at most once. There are about 14 works with multiple authors or what I call a co-citation (the thing cited is not the sole work of the author listed etc.).

Ranked by number of all citations in every publication (with co-citation)

1. Lewis, David K.; 275

2. Rawls, John ; 237

3. Russell, Bertrand; 214*(177)

4. Quine, WVO; 186

5. Fodor, J. 120

6. Kripke, Saul; 118

7. Parfit, Derek; 111

8. Nozick, Robert; 106

9. Wittgenstein, Ludwig; 106

10. Carnap, R.; 105

11. Williamson, Timothy; 92

12. Davidson, Donald; 90

13. Amrstrong, DM; 86

14. Jackson, Frank; 71

15. Chalmers, David; 70* (54)

16. Putnam, Hilary; 68

17. *Scanlon, TM; 67

18. Hare, R.M.; 67

19. Searle, JR; 67

20. Dretske, Fred; 66

21. Dworkin R; 66

22. Moore, GE; 65

23. Stalnaker, Robert; 64

24. Blackburn, Simon; 62

25. Grice HP; 62

26. van Fraassen; 61

27. Nagel, Thomas; 60

28. *Kuhn, Thomas; 58

29. Chisholm, RM; 57

30. Ross, W.D.; 56

31. Goodman, Nelson; 54

32. Dummett, M.; 53

33. Strawson, PF; 52

34. Popper, Karl; 51

35. Longino, Helen; 50

36. Raz, J.; 50

37. Gibbard, Allan; 49

38. *Sidgwick, Henry; 48

39. Williams, Bernard; 48

40. *Kaplan, David; 47

41. Dennett, DC; 47

42. Nussbaum, MC; 47

43. Anscombe, GEM; 45

44. Plantinga, Alvin; 45

45. van Inwagen, Peter; 45

46. Cartwright, Nancy; 44

47. Butler, Judith; 43

48. Frankfurt, Harry; 42

49. Zalta EN; 42

50. Ayer, AJ; 41

51. Craver, Carl F.; 41* (22)

52. Fine, Kit; 40

53. *Ryle, Gilbert; 39

54. Wright, Crispin; 38

55. Field, Hartry; 38

56. *Evans, Gareth; 37

57. *Mackie, J.L.; 37

58. *Whitehead, Alfred North; 37

59. Tye, Micheal; 37

60. Gödel, Kurt; 36

61. Tarski, A.; 36

62. *Korsgaard, Christine M.; 34

From 62 on my list the rest are as in the order in the original list less the repeated names (there are about 69 repeated names in the original list).

A “*” at the start of the name indicates that this is someone who had only one citation on the list.

The number at the end is the number of citations on the list (summing across all works) a “*” after indicates that one of the works is a co-citation the number in parenthesis indicates the number of citations not including the citations for the co-authored work. Note if someone has only one publication and it is a multi author work I have not indicated this.

Anyway, it is interesting to see these numbers. Notice that David Lewis manages the most citations by having so many works among the most cited, likewise Bertrand Russell. Most of the people with more than 3 citations are near the top, but Armstrong and Davidson break that trend. Possibly this list included citations of works that are only cited once or twice it would change the rankings substantially but I suspect not. Note these numbers are for publications after 1900 in order to try and get standardized works cited.

A couple of mathematicians made the list. Kurt Gödel is the only one who I recognize as a mathematician who had multiple entries. Hilbert, Turing and von Neumann are other mathematicians who only appear once.