Red and blue pills

The top concern in the mind of a good person, at all times, is, “how much of a good person am I?” If a person has any concerns other than being a good person, which are not instrumental to their own being a good person, then that person is certainly not good, and is instead evil.

A problem is given us where each member of a population P must choose the item Blue or the item Red. In the event (call it a “Red win”) where more than 50% of the population P choose the item Red, then the ones choosing the item Blue will die; but, in the event (call it a “Blue win”) where more than 50% of the population P choose the item Blue, then no one dies. Either a Red win or a Blue win must happen; there is no third.

• Features of a Death Event
• Culpability of Blue-choosers
• Culpability of Red-choosers
• Final comparison of assumptions
• Appendix

Features of a Death Event

If there are any deaths, then, clearly those causing the deaths are culpable for this. The foremost concern of a good person is to be as little culpable as possible. An event where deaths happen is composed of two features:

• Red win (RW): The fact that a Red win occurs.
• Failure of Red Unanimity (FRU): The fact that not everyone chose Red. (If a Red win happens but everyone chooses Red, no one dies.)

In an event that does not have both of RW and FRU, no one dies, so no one is culpable for any outcomes, although they may be culpable for their own intentions. So we can leave those events aside. Who is culpable for the deaths?

Culpability of Blue-choosers

Clearly Blue-choosers are not culpable for RW, since they tried to prevent it. Red-choosers may, however, want to blame the Blue-choosers for the fact of FRU.

However, each Blue-chooser is only responsible for FRU to the extent that he added himself to the Blue-chooser pile. He did not contribute to any other additions to the Blue-chooser contingent, and he did not contribute to RW. Hence, each Blue-chooser is culpable at most for his own death, if for that. (At the time of first posting, I thought this argument was pretty unassailable, but shortly afterwards, a question was raised about it; see the appendix.) Some Blue-choosers may think that they are not culpable even for this, since they may find risking one’s own life to be a blameless act, or they may see themselves as attempting a heroic sacrifice and not intending a RW & FRU outcome. So it is possible that Blue-choosers are culpable for 0 deaths, and it is possible that they are culpable for 1 death, but no assumptions come to mind by which they could be culpable for any other number of deaths. So let us name these possible assumptions:

• Suicide Culpability (SC): In the event of RW & FRU, each Blue-chooser is culpable for 1 death, namely his own.
• Suicide Non-Culpability (SNC): In the event of RW & FRU, each Blue-chooser is culpable for 0 deaths.

Culpability of Red-choosers

Clearly Red-choosers are culpable for RW, although they are blameless for FRU. Since they are culpable for RW, and the event with RW & FRU is what caused all the deaths, it is plausible that they are each culpable for all deaths. Let us call this Damage-Proportional Culpability (DPC): if the number of Blue-choosers in a RW & FRU event is $ B $, then each Red-chooser is culpable for $ B $ deaths.

An alternative is that each Red-chooser is only partially culpable for the deaths, since all the other Red-choosers were necessary for RW. Let us call this Contribution-Proportional Culpability (CPC): if the number of Blue-choosers in a RW & FRU event is $ B $, and the number of Red-choosers is $ R $, then each Red-chooser is culpable only for $ \frac{B}{R} $ deaths. Note that, in cases of murder conspiracies, no legal system on Earth accepts CPC, but someone may possibly think that a death event in this problem is different.

A third alternative is that, since Red-choosers are blameless for FRU, and FRU is just as necessary for a death event as RW, then Red-choosers are culpable for 0 deaths. Certainly all Red-choosers prefer this assumption, although it makes no sense at all. The idea, for them, is presumably that they could only be culpable for the deaths if their action were sufficient for the deaths, rather than merely necessary. So let us call this Sufficiency-Constrained Culpability (SCC): in a RW & FRU event, each Red-chooser is culpable for 0 deaths.

Final comparison of assumptions

The possible choices of assumptions are compared in the table below. The cells are shaded for which choice of item they advantage, assuming that it’s possible that $ B > 1 $ in a death event, and that necessarily (due to the problem constraints) we have $ \frac{B}{R} < 1 $ in a death event.

Culpability Type	SC (Blues culpable for 1 death)	SNC (Blues culpable for 0 deaths)
DPC (Reds culpable for $ B $ deaths)	Blues culpable for 1 death; Reds culpable for $ B $ deaths; Blue advantage	Blues culpable for 0 deaths; Reds culpable for $ B $ deaths; Blue advantage
CPC (Reds culpable for $ \frac{B}{R} $ deaths)	Blues culpable for 1 death; Reds culpable for $ \frac{B}{R} $ deaths; Red advantage	Blues culpable for 0 deaths; Reds culpable for $ \frac{B}{R} $ deaths; Blue advantage
SCC (Reds culpable for 0 deaths)	Blues culpable for 1 death; Reds culpable for 0 deaths; Red advantage	Blues culpable for 0 deaths; Reds culpable for 0 deaths; Red advantage

I personally accept DPC, although I’m not sure about SC versus SNC; so I think all Red-choosers are evil, whatever the Blue-choosers may be.

Appendix

Ming (@diamondminercat) pointed out a third possible assumption to me regarding Blue culpability, besides SC and SNC. This assumption, which I called Culpability for Others’ Altruism (COA), is that, in the event of RW & FRU, Blues are culpable for $ B $ deaths, since all other Blues would have been at least partly motivated by their estimation of a high probability of FRU, a feature which is only possible due to the existence of Blues.

I do not accept COA because I believe Blues would have been motivated by the fact that they are good persons, and want to minimize their own culpability, regardless of the probability of a death event. But supposing someone accepts COA, it would be strange for that person to think that the Reds are not similarly culpable for the deaths that happen in a death event. So as far as I know, someone who accepts COA would think everyone in the population P is culpable for $ B $ deaths, if any occur. This is still a Red advantage in the sense that Blues would have been risking their lives for no decrease in their own culpability. Due to my coherence concerns about interactions of COA with CPC or SCC, I have not added it to the table, although I thought it was worth considering here.

Culpability distribution

Suppose a symmetrical conspiracy in which, doing equal amounts of work with equal amounts of intent-to-kill, a group of $ M $ murderers conspires to murder $ V $ victims. Suppose someone claims that, since each of the murderers contributed only partially to the outcome (but each one contributed an equal share), then each murderer is guilty, not of $ V $ counts of murder, but of $ \frac{V}{M} $ murders. Let’s call this assumption Contribution-Proportional Culpability (CPC).¹

No legal system on Earth accepts Contribution-Proportional Culpability. (To see this, consider that if $ M = V > 1 $, no legal system would charge each murderer with only 1 count of murder.) Instead, all legal systems accept Damage-Proportional Culpability (DPC): each of the $ M $ murderers is culpable for $ V $ counts of murder. We generally accept this “intuitively”—I certainly would blame each murderer for $ V $ murders, without thinking about it. But it’s not obvious why we should accept DPC, rationally speaking—and in face of the argument that “each of the murderers contributed only partially to the outcome”, we may be led to doubt. So what’s the reasoning for DPC?

My current conjecture is that we reason like this: We may grant that each murderer is culpable for $ \frac{V}{M} $ deaths, but the relevant unit of culpability is not “deaths”, but “murders”, or what one may call “culpabilities-for-deaths”. Since each member is necessary to the conspiracy, each murderer is causing all the other murderers to become murderers, and therefore, each murderer is culpable for the crime of all the other murderers as well as for his own. Hence, each murderer is culpable for $ \frac{V}{M} \times M = V $ murders, as required by DPC.

This reasoning, however, may allow for CPC to be followed in a case where $ M > 1 $ murderers are all necessary for a murder to occur, and each one contributes to the murder with intent to kill, but none of them are aware that there are any other contributors. Whether it can do so in practice, is left as an exercise to the reader.

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1. In a post to X, I referred to CPC as “Blame-Sharing”. I avoided this name in this post because the only name for the alternative would be “non-Blame-Sharing”, which isn’t very descriptive since there could be other possible assumptions about blame distribution than the two considered here.↩

How to undermine scientific authority

Benjamin Wiker is a conservative with many very particular gripes about how the Enlightenment ruined everything for civilization; in his book on the Reformation, he tells this story of how Benedict Spinoza, the famous rationalist philosopher who was also one of the pioneers of biblical philology, wanted to undermine religion:

To make sure that Scripture cannot be revived and used with the irrational, impassioned Christian multitude, Catholic or Protestant, Spinoza set forth as one of the additional tasks of the new scientific exegete, the maximizing of confusion about the real meaning of the text, by ferreting out all the possible ambiguities inherent in the original languages, and by displaying prominently all the variations that occur in the multiple manuscripts discovered since the Renaissance—and, of course, publishing the results. It’s hard for the Bible to have authority if we can’t figure out what it actually said originally. Better just to mind your own business, and embrace tolerance.

The very scholarly apparatus that both Catholics and Protestants believed would take them closer to the revealed truth, and bring about ever more accurate translations of God’s Holy Word, thereby became the vehicle Spinoza and his followers used to sow confusion and doubt, leading to the secularization of the West.

Wiker doesn’t give references to support the idea that Spinoza had this goal, but it’s an interesting thought that I have remembered even though I basically forgot the rest of the book. Undermining biblical authority by the proliferation of textual variants is something that doesn’t do any harm to the Catholic Church, which has the Pope who can simply decide for everyone else what “the Bible says” on an issue, but it does do damage to Protestantism, which has always relied on (the ridiculous idea of) there being some objective science that can determine “what the Bible says” in such a way that experts can reach consensus.

It also does work against anything else that is taken as authoritative, and for which there is no Pope. If you don’t want natural science, say, to be an authority in society, you don’t have to directly make people lose respect for its process, you just have to multiply and amplify the minority viewpoints within it, especially the ones that have gotten a foothold in academia already. The frequency of agreement between experts is a major reason why people want to trust science, but it is a contingent feature of it, and efforts to undermine it can be successful.

If you hate a certain discipline, study more variants of it than its practitioners do.

Qualification as Proportionality

There are different views on how to formalize qualifications, which can be made as, “A is B qua C”, but are also commonly made with English glosses like “A is B insofar as A is C”, or “A is B, when A is considered in its respect of being C”. They are reviewed in Hennig (2024). The following are some examples of qualification adapted from the paper:

• Descartes claims that, insofar as he is a thinking being, he is not made of matter.
• Kant claims that we can know things as appearances, but not as they are in themselves.
• Aristotle claims that an isosceles triangle has internal angles that add up to two right angles, but it has this property qua triangle, not qua isosceles.
• Suppose “Jane is a corrupt judge, but an honest merchant”, which is to say, “Jane is corrupt qua judge, but honest qua merchant”.

The paper reviews many proposals for translating such qualifications into formal languages. It does not review the one I propose here, because it wasn’t in the literature. My proposal relies on “degree-theoretic semantics”, which is the theory that sentences have “degrees of truth” instead of just being either true or false. This semantics arises in the philosophical theory of vagueness, which is concerned largely with solving the well-known sorites paradox:

• how many grains of sand does it take for you to have a heap of sand?
• at what precise instant does a child become an adult?
• how many hairs on his head does it take for a man to no longer be bald?

Degree-theoretic semantics approaches this problem by saying that there is no such number, but rather that the truth-value of, “x is a heap of sand”, “x is not bald”, or “x is an adult”, moves continuously from “less true” to “more true” as more grains of sand, hairs on the head, or years of age are added to x. Its oldest version seems to come from this 1976 paper by Kenton F. Machina, but probably its most famous version came from Dorothy Edgington in 1996.

My proposal, then, is to translate “A is B qua C” into “the degree of truth of ‘A is B’ is proportional to the degree of truth of ‘A is C’”. If we take the properties B and C as predicates \( B \) and \( C \), the object A as a constant \( a \), and \( \mathcal{I} \) as the interpretation function that assigns degrees of truth to statements, then formally, \( \mathcal{I}(\ulcorner Ba \urcorner) \propto \mathcal{I}(\ulcorner Ca \urcorner) \).

That’s the entire proposal, and it seems easy enough to apply to the examples:

• Descartes claims that the degree to which he is a thinking being is proportional to the degree to which he is not made of matter. With \( T \) for being a thinking being, \( d \) for Descartes, and \( M \) for being made of matter, we have \( \mathcal{I}(\ulcorner Td \urcorner) \propto \mathcal{I}(\ulcorner \neg Md \urcorner) \).
• Kant claims that the degree to which something is knowable is not proportional to the degree to which it is itself, but it is proportional to the degree to which it is an appearance. With \( I \) for a thing’s being itself, \( K \) for a thing’s being knowable, and \( A \) for a thing’s being an appearance, we have \( \forall t [\mathcal{I}(\ulcorner Kt \urcorner) \not\propto \mathcal{I}(\ulcorner It \urcorner)] \), and \( \forall t [\mathcal{I}(\ulcorner Kt \urcorner) \propto \mathcal{I}(\ulcorner At \urcorner)] \).
• Aristotle claims that the truth of something’s having angles summing to two right angles is proportional to the truth of its being a triangle, but not proportional to the truth of its being isosceles. With \( A \) for the property of having angles that add up to two right angles, \( I \) for the property of being isosceles, and \( T \) for the property of being a triangle, we have \( \forall t [ \mathcal{I}(\ulcorner At \urcorner) \propto \mathcal{I}(\ulcorner Tt \urcorner) ] \), and \( \forall t [ \mathcal{I}(\ulcorner At \urcorner) \not\propto \mathcal{I}(\ulcorner It \urcorner) ] \).
• The degree to which Jane is honest is proportional to the degree to which she is a merchant, while the degree to which she is corrupt is proportional to the degree to which she is a judge. Let’s use \( H \) for the property of being honest, and let’s assume being corrupt just means not being honest, i.e., \( \neg H \). With \( j \) for Jane, we have \( \mathcal{I}(\ulcorner Hj \urcorner) \propto \mathcal{I}(\ulcorner Mj \urcorner) \), and \( \mathcal{I}(\ulcorner \neg Hj \urcorner) \propto \mathcal{I}(\ulcorner Jj \urcorner) \).

I don’t know any objections to this, as of yet. If I knew of any, I would try to answer them, which would give me enough material to try to publish this as a paper instead of a blog post.

This came up in conversation earlier due to my further view that statements involving higher-order properties should be interpreted as qualified general statements about properties. For instance, “honesty is desirable” should be interpreted as “for any x, x is desirable insofar as x is honest”, which in turn means that “for any x, the degree to which x is desirable is proportional to the degree to which x is honest”, i.e., \( \forall x [ \mathcal{I}(\ulcorner Dx \urcorner) \propto \mathcal{I}(\ulcorner Hx \urcorner) ] \). In my view, this makes higher-order properties unnecessary. This is motivated by my view that the reason we can use properties to understand things is because properties are intrinsically understandable in themselves – if this is so, then properties don’t need further ‘metaproperties’ to be understood.