March 30, 2018

Source: SMBC

# Contents

1. Introduction
2. Examples
3. How the most successful conceptual analyses become definitions

# Introduction

The point has been made often and well (Wittgenstein, Ramsey, Muehlhauser, Yudkowsky), that conceptual analysis is doomed by resting on falsified assumptions about human cognition, and a mistaken view of the nature of empirical categories.

A first problem is with necessary and sufficient conditions:

Category-membership for concepts in the human brain is not a yes/no affair, as the “necessary and sufficient conditions” approach of the classical view assumes. Instead, category membership is fuzzy. (Muehlhauser)

This first problem could be solved with a new type of conceptual analysis, one admitting of degree. However, a deeper problem arises from the requirement that an analysis admit of no intuitive counterexamples:

[…] most of our empirical concepts are not delimited in all possible directions. Suppose I come across a being that looks like a man, speaks like a man, behaves like a man, and is only one span tall – shall I say it is a man? Or what about the case of a person who is so old as to remember King Darius? Would you say he is an immortal? Is there anything like an exhaustive definition that finally and once for all sets our mind at rest? ‘But are there not exact definitions at least in science?’ Let’s see. The notion of gold seems to be defined with absolute precision, say by the spectrum of gold with its characteristic lines. Now what would you say if a substance was discovered that looked like gold, satisfied all the chemical tests for gold, whilst it emitted a new sort of radiation? ‘But such things do not happen.’ Quite so; but they might happen, and that is enough to show that we can never exclude altogether the possibility of some unforeseen situation arising in which we shall have to modify our definition. (Waismann)

Waismann called this feature of our language open texture.

Clearly these two requirements must be abandoned (there go entire literatures…).

Is all conceptual analysis therefore useless? The view has some appeal. If all we want is to dissolve philosophical confusions through clarification of ambiguities; this can be achieved by stipulating definitions that allow us to be as precise as we want, after which we can abandon other verbiage. Hence SEP tells us:

Another view, held at least in part by Gottlob Frege and Wilhelm Leibniz, is that because natural languages are fraught with vagueness and ambiguity, they should be replaced by formal languages. A similar view, held by W. V. O. Quine (e.g., [1960], [1986]), is that a natural language should be regimented, cleaned up for serious scientific and metaphysical work.

My view is the following: abandoning ambiguous terms in favour of more precise, stipulatively defined ones, i.e. regimentation, is always a legitimate philosophical move. Pragmatically, however, there are costs to doing so. Technical texts with a lot of jargon are difficult to read for a reason. It takes time to communicate the definitions of one’s terms to others. And it takes longer still until our audience gains intuitive familiarity with the new terminology, and can manipulate it with speed and accuracy.

When deciding which words to use, we face a trade-off between precision on the one hand, and agreement with intuitive terminology on the other.

Programming languages are an example of the fully regimented extreme. There is no ambiguity, but coding must be learnt the hard way. The language of small children or pre-scientific civilisations (“a whale is heavier than a bowling ball”), on the other hand, is completely intuitive.

The old view of conceptual analysis, requiring necessary and sufficient conditions, and admitting of no counter-examples, was an attempt to achieve both complete precision and complete intuitiveness. But from its failure it does not follow that all our old words should be regimented away. In some cases that may be the best we can do; some unsalvageable concepts, like what it means for a storm-cloud to be angry, are to be consigned to the dustbin of language. But for other terms, like “causation”, it’s not a foregone conclusion that the optimal way to navigate the trade-off is to abandon the word. We may do better to keep the word, along with its “good enough” definition. Conceptual analysis, on a more modest and fruitful view, is a tool that can help us to find such opportunities.

In general, therefore, I don’t find conceptual analysis particularly exciting. If the use of regimented language dissolves a controversy of analysis, it’s clear that nothing of “philosophical” importance was hanging in the balance in the first place. However, conceptual analyses can be pragmatically useful, and indeed there have been a number of examples I enjoyed. In what follows I list some intellectual phenomena I consider examples of conceptual analysis, and comment on them.

# Examples

## Knowledge

The “analysis of knowledge merry-go-round” (Weatherson 2003), has rightly been much derided.

Here’s a nice quote by Scott Sturgeon (who used to be my tutor!):

Thirty years ago this journal published the most influential paper of > modern analytic epistemology - Edmund Gettier’s ‘Is Justified True Belief > Knowledge?’. In it Gettier refuted a classic theory of propositional knowledge by constructing thought experiments to test the theory. A cottage industry was born. Each response to Gettier was quickly met by a new Gettier-style case. In turn there would be a response to the case, a further Gettier scenario, and a reiteration of the process. The industry’s output was staggering. Its literature became so complicated, its thought experiments so baroque, that commonsense was stretched beyond limit.

This is a clear example where regimentation is appropriate. Our epistemic state can be fully described by our beliefs and our evidence. What about “knowledge”? Commit it then to the flames!

## Belief

Quoting from an essay I wrote in 2017:

We want a theory of when it is rational to have an outright belief. It seems like we might easily get this from our theory of when it is rational to have a graded belief. Simply say, “it is rational to believe something simpliciter iff it is rational to believe it with a probability p>y.” Let’s call this the threshold view. We won’t be able to put an exact number on y. This merely points to the fact that outright belief-language is somewhat vague. Similarly, in “a person is bald iff they have fewer than z hairs on their head”, z is imprecisely specified, but we still understand what it means to be bald, and we know that $% $.

But the cases of preface and lottery appear to show that the threshold view is false.

Consider the lottery: “Let the threshold y required for belief be any real number less than 1. For example, let y = 0.99. Now imagine a lottery with 100 tickets, and suppose it is rational for you to believe with full confidence that the lottery is fair and that as such there will be only one winning ticket. […] So, it is rational for you to have 0.99 confidence that ticket #1 will not win, 0.99 confidence that ticket #2 will not win, and so on for each of the other tickets. According to the [threshold view], it is rational for you to believe each of these propositions, since it is rational for you to have a degree of confidence in each that is sufficient for belief. But given that rational belief is closed under conjunction, it is also rational for you to believe that (ticket #1 will not win and ticket #2 will not win . . . and ticket #100 will not win)” (Foley 1992). However, this is a contradiction with your belief that the lottery is fair, i.e., that exactly one ticket will win the lottery. Thus y cannot be 0.99. The same conclusion can be reached for any probability y<1: simply create a lottery with 1/(1-y) tickets, and argue as before. Thus the threshold cannot be any less than 1. This clearly will not do, as it violates our intuitions about everyday uses of ‘believe’, as in “I believe it will rain tomorrow”.

“After all, what reasons do we have to be interested in an [invariantist] theory of rational belief [simpliciter] if we have an adequate [invariantist] theory of rational degrees of belief? Does the former tell us anything useful above and beyond the latter? Is it really needed for anything? It doesn’t seem to be needed for the theory of rational decision making.” (Foley 1992). The fact that our ordinary-language usage of ‘belief’ cannot fully account for the laws of probability is simply a kink of ordinary language. Ordinarily, we do not speak about things like very long conjunctions concerning lottery tickets. The shorthand word ‘belief’ deals well with most cases we do ordinarily encounter. In other cases, we can simply retreat to using the language of degrees of belief.

Yeah, we don’t need to conceptually analyse ‘belief’. It’s probably outright harfum to keep using that word.

## Species

Humans have long understood that animals come in relatively sharply delineated clusters. By using a word for, say, “pig” and another for “dog”, we are making use of these categories. More recently, modern biology has developed the concept of “species”. Wikipedia explains that “a species is often defined as the largest group of organisms in which two individuals can produce fertile offspring, typically by sexual reproduction”.

This definition can be viewed as a proposed conceptual analysis of our pre-scientific, or folk-biological, concept of “type of animal”.

This analysis does really well, on hundreds of folk biological categories! We are so used now to the concept of species that this remarkable fact may appear obvious. There are some problem cases, too: Elephants are three species; while a caterpillar and a butterfly can be the same species.

What is more, even the more regimented concept of species is too imprecise for some use cases. Wikipedia says: “For example, with hybridisation, in a species complex of hundreds of similar microspecies, or in a ring species, the boundaries between closely related species become unclear.”

## Temperature

The definition of temperature as mean molecular kinetic energy can be viewed as a conceptual analysis. Wikipedia says that temperature is “a physical quantity expressing the subjective perceptions of hot and cold”. And by and large it does excellently. However, it fails with spicy (“hot”) food.

Does this exception mean we need to regiment away common-sense notions of hot and cold? No! This illustrates how analysis that admit of exceptions can still be useful.

## Speed and acceleration

Heisenberg:

The concepts of classical physics are just a refinement of the concepts of daily life and are an essential part of the language which forms the basis of all natural science.

Speed is the first derivative of location with respect to time, and acceleration is the second derivative.

This is a conceptual analysis so successful that the definition resulting from the analysis has replaced, in most adult speakers, the intuitive notion. (Something we have already seen to some extent with species). For this reason, it’s hard to see that it was, in fact, a conceptual analysis.

Where can we find remnants of the pre-scientific, ur-intuitive notion of speed? The theories of Aristotle and small children seem like a good place to start in search of this pristine naiveté.

Per Macagno 1991, Aristotle had piecemeal correct intuitions about speed, but he did not see the more general point:

Although Aristotle discusses in detail when a motion is faster than another by considering the space traversed and the corresponding time, he never arrived at what is so elementary for us: $V = S/T$. He considers several cases; for instance, in the case $S_2=S_1$, velocity $V_2$ is larger than $V_1$ if $% $. To divide a distance by a time was not an acceptable operation, if it was considered at all […]

Similarly, 11-year olds get time, distance, and speed right in most but not all cases (Siegler and Richards 1979):

Children were shown two parallel train tracks with a locomotive on each of them. The two locomotives could start from the same or different points, could stop at the same or different points, and could go the same or different distances. They could start at the same or different times, could stop at the same or different times, and could travel for the same or different total time. Finally, they could go at the same or different speeds. […]

On the time concept, the state before full mastery seemed to be one in which time and distance were only partially differentiated. This was evident in the use of the distance rule to judge time by a large number of 11- year-olds.

Similarly, I would expect (although citation needed) that many children who have a good grasp of the difference between position and speed (i.e. they would not say that whichever train ended farther ahead on the tracks travelled for the longer time, or the faster speed, or the greater distance), still do not clearly distinguish speed from acceleration. For instance, they might say: “whoa, the car went so fast just then - I was really pressed up against my seat.”

Once we have conceptually analysed speed and acceleration as the first and second derivatives of position with respect to time, we have a powerful new formal tool. We can use this tool to create new concepts which did not exist in natural language. For example, the third time-derivative of position is jerk. Understanding jerk has many uses, for instance to build quadcopters and other drones.

Finally, here’s an analogy from the opposite direction, taken from Mori, Kojima and Tadang (1976).

Children are likely to judge the speed from temporal precedence and say, “It went faster because it arrived earlier.” In the Japanese language, the two words meaning fast in speed and early in temporal precedence, respectively, have the same pronunciation, i.e., hayai. On the other hand, in the Thai language, these two words are differentiated in their pronunciation as well as in meaning; the one that means high speed is re0 and the other one that means temporal precedence is khon. […]

The Japanese and Thai children were shown the same visual displays of moving objects and asked to compare the speed of those moving objects. The results significantly indicate that Thai children’s concept of speed is further advanced than that of Japanese children.

The Japanese children are to the Thai children like Aristotle is to a modern student armed with the formal notion of accelaration. It’s possible to go beyond ordinary English with the formal language of physics, but it’s also possible to lag behind ordinary English with (children’s understanding of) Japanese. Similarly, “the Pirahã language and culture seem to lack not only the words but also the concepts for numbers, using instead less precise terms like “small size”, “large size” and “collection”.”

## The epsilon-delta definition of a limit

See my other post on the success story of predicate logic.

## Effective calculability

See my other post on the success story of computability.

## Causation

The conceptual analysis of causation fills many a textbook. Here I’ll focus on just the counterfactual analyses, that is, analyses of causal claims in terms of counterfactual conditionals.

A first attempt might be:

Where c and e are two distinct actual events, c causes e if and only if, if c were not to occur e would not occur.

But cases of Preemption offer a counter-example (SEP):

Suppose that two crack marksmen conspire to assassinate a hated dictator, agreeing that one or other will shoot the dictator on a public occasion. Acting side-by-side, assassins A and B find a good vantage point, and, when the dictator appears, both take aim. A pulls his trigger and fires a shot that hits its mark, but B desists from firing when he sees A pull his trigger. Here assassin A’s actions are the actual cause of the dictator’s death, while B’s actions are a preempted potential cause.

To deal with Preemption, we can move to the following account:

[Lewis’s] truth condition for causal dependence becomes:

(3) Where c and e are two distinct actual events, e causally depends on c if and only if, if c were not to occur e would not occur.

He defines a causal chain as a finite sequence of actual events c, d, e,… where d causally depends on c, e on d, and so on throughout the sequence. Then causation is finally defined in these terms:

(5) c is a cause of e if and only if there exists a causal chain leading from c to e.

But take the following case:

A person is walking along a mountain trail, when a boulder high above is dislodged and comes careering down the mountain slopes. The walker notices the boulder and ducks at the appropriate time. The careering boulder causes the walker to duck and this, in turn, causes his continued stride. (This second causal link involves double prevention: the duck prevents the collision between walker and boulder which, had it occurred, would have prevented the walker’s continued stride.) However, the careering boulder is the sort of thing that would prevent the walker’s continued stride and so it seems counterintuitive to say that it causes the stride.

Hence:

Some defenders of transitivity have replied that our intuitions about the intransitivity of causation in these examples are misleading. For instance, Lewis (2004a) points out that the counterexamples to transitivity typically involve a structure in which a c-type event generally prevents an e-type but in the particular case the c-event actually causes another event that counters the threat and causes the e-event. If we mix up questions of what is generally conducive to what, with questions about what caused what in this particular case, he says, we may think that it is reasonable to deny that c causes e. But if we keep the focus sharply on the particular case, we must insist that c does in fact cause e.

Aha, but we simply need to modify the marksman case to get a case of late preemption:

Billy and Suzy throw rocks at a bottle. Suzy throws first so that her rock arrives first and shatters the glass. Without Suzy’s throw, Billy’s throw would have shattered the bottle. However, Suzy’s throw is the actual cause of the shattered bottle, while Billy’s throw is merely a preempted potential cause. This is a case of late preemption because the alternative process (Billy’s throw) is cut short after the main process (Suzy’s throw) has actually brought about the effect.

Lewis’s theory cannot explain the judgement that Suzy’s throw was the actual cause of the shattering of the bottle. For there is no causal dependence between Suzy’s throw and the shattering, since even if Suzy had not thrown her rock, the bottle would have shattered due to Billy’s throw. Nor is there a chain of stepwise dependences running cause to effect, because there is no event intermediate between Suzy’s throw and the shattering that links them up into a chain of dependences. Take, for instance, Suzy’s rock in mid-trajectory. Certainly, this event depends on Suzy’s initial throw, but the problem is that the shattering of the bottle does not depend on it, because even without it the bottle would still have shattered because of Billy’s throw.

To be sure, the bottle shattering that would have occurred without Suzy’s throw would be different from the bottle shattering that actually occurred with Suzy’s throw. For a start, it would have occurred later. This observation suggests that one solution to the problem of late preemption might be to insist that the events involved should be construed as fragile events. Accordingly, it will be true rather than false that if Suzy had not thrown her rock, then the actual bottle shattering, taken as a fragile event with an essential time and manner of occurrence, would not have occurred. Lewis himself does not endorse this response on the grounds that a uniform policy of construing events as fragile would go against our usual practices, and would generate many spurious causal dependences. For example, suppose that a poison kills its victim more slowly and painfully when taken on a full stomach. Then, the victim’s eating dinner before he drinks the poison would count as a cause of his death since the time and manner of the death depend on the eating of the dinner.

Lewis then further modifies his theory:

The central notion of the new theory is that of influence.

(7) Where c and e are distinct events, c influences e if and only if there is a substantial range of c1, c2, … of different not-too-distant alterations of c (including the actual alteration of c) and there is a range of e1, e2, … of alterations of e, at least some of which differ, such that if c1 had occurred, e1 would have occurred, and if c2 had occurred, e2 would have occurred, and so on.

Where one event influences another, there is a pattern of counterfactual dependence of whether, when, and how upon whether, when, and how. As before, causation is defined as an ancestral relation.

(8) c causes e if and only if there is a chain of stepwise influence from c to e.

One of the points Lewis advances in favour of this new theory is that it handles cases of late as well as early pre-emption. (The theory is restricted to deterministic causation and so does not address the example of probabilistic preemption described in section 3.4.) Reconsider, for instance, the example of late preemption involving Billy and Suzy throwing rocks at a bottle. The theory is supposed to explain why Suzy’s throw, and not Billy’s throw, is the cause of the shattering of the bottle. If we take an alteration in which Suzy’s throw is slightly different (the rock is lighter, or she throws sooner), while holding fixed Billy’s throw, we find that the shattering is different too. But if we make similar alterations to Billy’s throw while holding Suzy’s throw fixed, we find that the shattering is unchanged.

At this point, I’m hearing distinct echoes of the knowledge merry-go-round. After over forty years of analyses of causation, it’s a good time to ask ourselves: what would be the value of success in this enterprise? What would be the use of a conceptual analysis that captured all these strange edge cases?

I think the value would be very limited. We are able to fully describe any situtation without making use of the word “causation” (see below). Why then spend all this time considering baroque thought experiments? In the case of Suzy and Billy’s bottle, I honestly haven’t got that strong an intuition of what was the cause of the shattering. I think it’s playing games with open texture.

How is it that we can eliminate1 causation from our langauge? To describe what actually happens in the world, including in the above cases, we only need to describe each counterfactual situation. Brain Tomasik describes one way of doing so:

But if we had a complete physical model of the multiverse (e.g., a giant computer program that specified how the multiverse evolved), [we could ] change the program to remove X in some way and see if Y still happens.

Alternatively, you could specify your model using a causal graph. Once the causal graph is fully specified, it’s an empty question what truly caused the bottle to shatter.

# How the most successful conceptual analyses become definitions

The analysis of limit, has become a universally accepted definition. The same thing is in the (largely completed) process of happening for the analysis of computability. Soare 1996 draws the analogy beautifully:

In the early 1800’s mathematicians were trying to make precise the intuitive notion of a continuous function, namely one with no breaks. What we might call the “Cauchy-Weierstrass Thesis” asserts that a function is intuitively continuous iff it satisfies the usual formal episilon-delta-definition found in elementary calculus books.

Similarly, what we might call the “Curve Thesis” asserts that the intuitive notion of the length of a continuous curve in 2-space is captured by the usual definition as the limit of sums of approximating line segments. [Kline 1972: “Up to about 1650 no one believed that the length of a curve could equal exactly the length of a line. In fact, in the second book of La Geometrie, Descartes says the relation between curved lines and straight lines is not nor ever can be known.”]

The “Area Thesis” asserts that the area of an appropriate continuous surface in 3-space is that given by the usual definition of the limit of the sum of the areas of appropriate approximating rectangles.

These are no longer called theses, rather they are simply taken as definitions of the underlying intuitive concept.

1. This idea has a good pedigree: in the words of Russell: “The law of causation, […] is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm. […] In the motions of mutually gravitating bodies, there is nothing that can be called a cause, and nothing that can be called an effect; there is merely a formula.” For more discussion see Stanford and Judea Pearl

# Understanding central bank loss functions

March 27, 2018

Note: this post is unlikely to be of interest if you haven’t done a basic undergraduate course in macroeconomics.

I use notation and terminology from Carlin and Soskice (2015).

What is the central bank (CB) trying to achieve? In discussing the CB’s goals, it’s important to distinguish rates of change in inflation from levels of inflation.

# Costs of high rates of change in inflation

## 1

The CB wants to avoid runaway inflation or deflation. If inflation is high (or low) because the labour market (WS-PS model) is out of equilibrium, then inflation may increase (or decrease) without bound. The CB wants to set employment and output to the level consistent with a WS-PS equilibrium, where inflation will be constant.

The goal of constant inflation could in theory be achieved at any level of inflation.

## 2

There is another, conceptually distinct cost of volatile inflation. Volatile inflation interferes with the ability of prices to convey information. It masks relative price changes.

# Levels of inflation, and their costs and benefits

## 1

There are costs to high absolute values of $\pi$:

• High inflation incentivises making purchases quickly and holding no cash, while large deflation incentivises delaying purchases and holding cash.

## 2

There are also benefits to higher levels of inflation. Workers are particularly resistant to nominal wage cuts. So inflation oils the wheels of the labour market.

# Which level?

As we said above, the bank’s primary concern is to avoid runaway inflation or delfation. But what level of inflation should the CB target? Inflation has costs and benefits. So it might not seem unreasonable to target $\pi=0$ or even $% $. But there is a good reason to aim for a positive level of inflation. Because of the zero lower bound on $i$, it’s more prudent to stay away from low or negative $\pi$. Suppose aggregate demand falls when $\pi = -x$. Then $r=i-\pi$ has a lower bound of $x$ and cannot be lowered enough to bring the WS-PS market into equilibrium. The result is a deflationary spiral.

This argument works for both positive $x$ and $x=0$.

Even if $i$ is not currently at the ZLB, there could be measurement error or forecasting failures, so that $i$ could unexpectedly hit the ZLB. The CB uses a target $\pi>0$ to stay safely away from the ZLB.

In fact, the target rate of $\pi^T=2\%$ is typically used. Why 2%? We have seen that the ZLB provides a good reason to avoid levels of inflation very close to zero. But why not target higher inflation? The qualitative considerations discussed above could go either way, and provide no particular justification for the specific choice of $\pi^T=2\%$. Choosing the optimal level of inflation is a very difficult empirical and moral question.

# A typical loss function

The CB is conventionally taken to be minimising, at each time $t$:

This loss function makes no sense from the point of view of the considerations we discussed above.

First, the loss function tells us that the CB does not care about rates of change in inflation at all. It is perfectly myopic, and never looks beyond the current period. But runaway inflation and deflation are catastrophic, and avoiding them should arguably by the CB’s primary goal.

Second, when $y_t>y_e$, the loss function penalises higher output. But getting richer is usually taken to be a good thing.

I think there’s a confusion here between final and instrumental goals. Minimising $L$ makes no sense as a final goal. But in practise, $L$ is a good rule of thumb for avoiding runaway inflation or deflation. Penalising output above $y_e$ while ignoring future inflation may lead to policies which approximate the CB’s true final goals.

Carlin and Soskice write: “The policy maker is modelled as an inflation-targeting central bank not because this is necessarily the best policy-making arrangement, but because it most closely resembles hoe modern stabilisation policy is undertaken”. They also say: “Note that this loss function […] assumes a symmetrical attitude to positive and negative deviations […] from the equilibrium level of output. The most straightforward way of thinking about this is that the central bank understands the model and realises that inflation is only constant at $y_t=y_e$. If $% $ then this represents unnecessary unemployment that should be eliminated. If $y_t> y_e$, this is unsustainable and will require costly increases in unemployment to bring the associated inflation back down”.

Unfortunately, I think this confuses rather than clarifies matters. According to the WS-PS model, $% $ will lead to runaway deflation, and $y_t>y_e$ will lead to runaway inflation. In the same breath, the authors mix instrumental goals (“If $y_t > y_e$, this is unsustainable and will require costly increases in unemployment…”) and final goals (“If $% $ then this represents unnecessary unemployment”).

Instead, I think the (final) loss function of the CB should be something like:

$L = \sum_{t=0}^\infty \delta^t (\beta y_t - \gamma(\pi_t-\pi^T)^2 -\theta(\pi_t - \pi_{t-1})^2)$,

where $\delta$ is the discount factor, $\beta y_t$ represents the fact that more output is good, $\gamma(\pi_t-\pi^T)^2$ reflects the fact that inflation has costs and benefits, so we want to aim for an optimal rate $\pi^T$, and $\theta(\pi_t - \pi_{t-1})^2$ is present because volatile inflation is costly.

# The definition of effective altruism

March 20, 2018

William MacAskill proposes a definition of effective altruism (EA). I think having a definition is useful. It could allow effective altruists (and their critics) to have better, clearer conversations, and to avoid misconceptions.

# A definition

In MacAskill’s quote below, I have emphasised in bold some notable features of the definition.

As I and the Centre for Effective Altruism define it, effective altruism is the project of using evidence and reason to figure out how to benefit others as much as possible, and taking action on that basis.

On this definition, effective altruism is an intellectual and practical project rather than a normative claim, in the same way that science is an intellectual and practical project rather than a body of any particular normative and empirical claims. Its aims are welfarist, impartial, and maximising: effective altruists aim to maximise the wellbeing of all, where (on some interpretation) everyone counts for one, and no-one for more than one. But it is not a mere restatement of consequentialism: it does not claim that one is always obligated to maximise the good, impartially considered, with no room for one’s personal projects; and it does not claim that one is permitted to violate side-constraints for the greater good.

Effective altruism is an idea with a community built around it. That community champions certain values that aren’t part of the definition of effective altruism per se. These include serious commitment to benefiting others, with many members of the community pledging to donate at least 10% of their income to charity; scientific mindset, and willingness to change one’s mind in light of new evidence or argument; openness to many different cause-areas, such as extreme poverty, farm animal welfare, and risks of human extinction; integrity, with a strong commitment to honesty and transparency; and a collaborative spirit, with an unusual level of cooperation between people with different moral projects.

Effective Altruism: Introduction”, Essays in Philosophy: Vol. 18: Iss. 1, Article 1, doi:10.7710/1526-0569.1580

In what follows, I quote or paraphrase extensively from a presentation given by William MacAskill at the Oxford workshop on the philosophical foundations of EA, 2017.

# Common misconceptions

There are a number of common misconceptions about EA.

• Misconception #1: EA is just about poverty. This is misguided both in principle and in practice. In principle, EA is open to any cause. In practice, different EAs support different causes, including animal suffering reduction, existential risk mitigation, criminal justice reform, science and tech progress, and more.
• Misconception #2: EA is just utilitarianism or consequentialism. EA is a project, not a normative claim. Any normative claims would have to be about someone’s obligations to engage in that project. EA doesn’t require doing the most good possible with all your resources; EA doesn’t condone rights violations. Utilitarianism might entail effective altruism, but so do many other moral views
• Misconception #3: EA neglects systemic change. EA supports systemic change in principle and in practice.
• The Open Philanthropy Project is funding projects in immigration reform, criminal justice reform, and macroeconomic policy.
• One of GiveWell’s main goals from the beginning, perhaps its primary goal, has been to change the cultural norms within the non-profit sector, and the standards by which they are judged by donors.
• Giving What We Can representatives have met with people in the UK government about options for improving aid effectiveness. One of its first and most popular content pages debunks myths people cite when opposing development aid. One of the first things MacAskill wrote when employed by Giving What We Can was on the appropriate use of discounts rates by governments delivering health services. Rachel Glennerster, a self-identified effective altruist, is currently the chief economist of DfID.
• Some 80,000 Hours alumni are going into politics, think-tanks, setting up a labour mobility organisations or businesses that facilitate remittance flows to the developing world.
• Several organisations focussed on existential risk (e.g. the Future of Humanity Institute, the Centre for the Study of Existential Risk and the Future of Life Institute) take a big interest in government policies, especially those around the regulation of new technologies, or institutions that can improve inter-state cooperation and prevent conflict.
• Many effective altruists work on or donate to lobbying efforts to improve animal welfare regulation, for example with the Humane Society of the United States. Other activists are working for dramatic society-wide changes in how society views the moral importance of non-human animals.
• Misconception #4: EA is mainly about earning to give. According to 80,000 Hours, only ~15% of EAs should earn to give. At the most recent EA Global conference, only 10% of attendees were planning to earn to give long-term. (Rather than, for example, doing so temporarily as a means of building skills.)

# Why this definition

MacAskill considers the following desiderata for a definition of EA:

1. Stated views on the definition by EA leaders
2. Faithfulness to the actual practice of those in the effective altruism community
3. Philosophical justification
4. Ecumenism with respect to different moral views
5. Practical value of public concept: how valuable it is to have the concept, so defined, discussed in the public sphere.

And he notes that different definitions proposed so far have varied insofar as they sometimes do, and sometimes do not:

1. Build in some theory of value
2. Include a prohibition against violating side-constraints
3. Include a sacrifice component
4. State the view as a normative claim

Within this framework, we may note that in MacAskill’s definition:

• EA is an intellectual and practical project, not a normative claim
• According to a survey of EA leaders, a large majority believe the definition should not be a normative claim and should not include a sacrifice component.
• The definition is compatible with practising EA being supererogatory, and with the view that there are no normative claims at all. (Both are common views among EAs).
• Most EAs want to get on with the project of figuring out how to maximise welfare, rather than asking how much is required of one.
• A project is more appealing as a public concept than a normative claim.
• Any normative claim risks being inflexible. By analogy: it’s a good thing that science was not defined as some specific empirical claims believed by Galileo or Bacon.
• This project’s aims are welfarist, impartial, and maximising. (Some values should be immediately emphasised, but aren’t part of the definition, such as: cause-neutrality, epistemic humility, good conduct (including respect for rights and co-operation), moral commitment, excitement.)
• To be philosophically well-supported, it can’t just be ‘doing good’, given whatever conception of the good. What about Neonazis?
• A majority of EA leaders surveyed believe the definition should include welfarism and the equal consideration of interests.
• Compatibility with current practice:
• All current projects within the effective altruism community are focused on promoting welfare.
• Most members of the community state that they identify as, or are sympathetic to, utilitarianism.
• Ecumenism: Promoting welfare (within constraints) is at least permissible on almost all moral views (given the way the world is) and is very important on many moral views.
• This definition avoids EA losing all of its value by becoming so diluted as to be meaningless, or falling into relativism.
• A prohibition against violating side-constraints is not included in the definition
• EA leaders in the survey were evenly split on whether the definition should include respect for common-sense ethical prohibitions.
• Science is the use of evidence and reason to discover truths. It would seem strange to include a “without killing anyone” clause, even though it’s true.
• Defining EA as a project, not a normative claim, escapes ‘the end justifies the means’ worries.

# The formal structure of ethical theories

March 13, 2018

This diagram illustrates some popular theories of normative ethics, with a particular focus on consequentialist theories and their internal structure.

Theories of normative ethics, and the structure of consequentialist theories. Here’s the same diagram as a .png and an .xml.

# Contents

1. What is consequentialism?
2. Comparing consequentialist and non-consequentialist theories

# What is consequentialism?

The term “consequentialism” has been used in many different senses. Of course, what matters are not the words, but to clearly distinguish different distinctions. What’s important about the diagram above is how it carves up the space of possible theories, not what the theories are called. Let me just clarify how I use the terms.

SEP tells us that consequentialism is the view that moral rightness depends only on consequences. I’ll take a slightly broader definition and say that consequentialism is the view that moral properties depend only on consequences.

John Broome (1991, Chapter 1) calls this the distinction between teleological and non-teleological theories.1

Broome proposes the following case to summarise the crux of the disagreement between consequentialism and non-consequentialism:

[Suppose that] by breaking a promise now I can bring it about that I shall, in the future, keep five promises that otherwise I would have broken. Suppose, say, that if I break a promise now, the experience of guilt at my present tender age will stiffen my resolve in future life.

In this case, any theory that says I ought to keep my current promise would have to be non-consequentialist.

Any consequentialist theory combines a cardinal axiology and a decision rule that depends only on this axiology in order to compare evaluands.

The issue of agent-neutrality vs agent-relativity is completely separate from that of consequentialism. There can be agent-relative consequentialist theories, and vice-versa. Agent-relative consequentialist theories will simply specify an axiology (and optionally also a decision rule and evaluands) for each agent. The Cambridge Dictionary of Philosophy says:

A few versions of consequentialism are agent- relative: that is, they give each agent different aims, so that different agents’ aims may conflict. For instance, egoistic consequentialism holds that the moral rightness of an act for an agent depends solely on the goodness of its consequences for him or her. However, the vast majority of consequentialist theories have been agent-neutral (and consequentialism is often defined in a more restrictive way so that agentrelative versions do not count as consequentialist). A doctrine is agent-neutral when it gives to each agent the same ultimate aims, so that different agents’ aims cannot conflict.

## Axiology

An axiology is a ranking of states of affairs in terms of better and worse overall. A cardinal axiology assigns numerical values to states of affairs. The axiology used by a consequentialist theory must be cardinal in order to be able to apply expected utility theory when there is uncertainty.

An axiology is welfarist if it’s about what makes the life of persons (moral patients) go best. Non-welfarist axiologies might care about other features of states of affairs, like complexity or beauty in the universe, independently of what is good for any person. “Go best” is here intended to encompass a wide range of theories of well-being. Three common theories of well-being are the hedonistic, desire fulfilment, and objective list theories discussed by Parfit (1984, Appendix i).

In a universe with more than one person, a welfarist also has to give an account of how to aggregate welfare across persons. This is population ethics. Again there are many different views of population ethics, I depict only three in the diagram. Totalism is the view that the value of a state of affairs is equal to the sum (as opposed to, say, the average) of the welfare of all persons.

## Evaluands

An evaluand is anything that could make states of affairs better or worse. Evaluands could include acts, desires, dispositions, beliefs, emotions, the colour of our eyes, the climate, etc.

The most widely discussed evaluands are acts. For instance, act-consequentialism is consequentialism applied only to acts.

In almost all cases, an evaluand combined with an axiology in the following direct way. Within a set of mutually exclusive evaluands, each evaluand is given the cardinal value of the state of the world that would result if the evaluand were to obtain.

In theory it’s also possible to assign a value to an evaluand indirectly. I only discuss this possibility because it has been the source of confusion. The name “rule consequentialism” has been applied to both a direct and an indirect theory. Direct rule-consequentialism is consequentialism applied only to rules, and has the same structure as act-consequentialism. Indirect rule-consequentilism assings values to acts according to the goodness of the state of affairs in which the rule obtains. For both theories, a bit of additional precisification is needed to explain what it means for a rule to “obtain”. Does it mean that the rule is widely or universally followed? That people intend to follow it?

The result of combining an axiology with a set of evaluands is an assignment of values to evaluands, which is what the blue box depicts.

## Decision rule

A decision rule, for our purposes, is a procedure that classifies evaluands into right, wrong, or neither. The decision rule is what gives rise to a theory’s normative pronouncements: its “ought” and “ought not”-statements (much more on this below). A maximising decision rule says that the object which makes states of affairs best (according to some axiology) is right, and all others are wrong. An example of a non-maximising decision rule is satisficing: everything that makes states of affairs better than some threshold is right (or at least not wrong).

Combining consequentialism with a maximising decision rule gives theory C2. theory C roughly says: “There is one ultimate moral aim: that outcomes be as good as possible” (Parfit p.24). More precisely, for any evaluand X, it says: “The right X is the X such that if it were to obtain, outcomes would be as good as possible. All others are wrong”.

## What is utilitarianism?

Utilitarians claim that each of us has one ultimate moral aim: to maximise everybody’s happiness. There are many ways to precisify this slogan, and hence many flavours of utilitarianism. The simplest one is hedonistic total utilitarianism. Hedonistic total utilitarianism is theory C combined with a hedonistic, totalist axiology. Hedonistic total act-utilitarianism is hedonistic total utilitarianism applied only to acts.

# Comparing consequentialist and non-consequentialist theories

## Older theories

Older theories of ethics, like, say, the ten commandments or Kantianism, were built entirely around a list of prohibitions. They are essentially just a decision rule, and they only apply to acts. These decision rules pronounce some acts right (and mandatory), some wrong (and forbidden), and make no normative statements about the majority of acts, calling them neither right nor wrong, and permissible. They do not involve an axiology.

This is not to say that these decision rules are chosen by mere intuition (what Will MacAskill would call “no-theory deontology”). Philosophers (famously, Kant) have developed intricate justifications for their decision rules. But these justifications do not involve axiologies, or degrees of goodness which are then compressed down by a decision rule.

The structure of older theories

## Theory C applied to acts vs the spirit of consequentialism

I must here make a point that may appear somewhat technical and pedantic. But it actually has some importance (especially if you’re interested in understanding how academic philosophers talk about consequentialism).

Let’s consider the intersection of theory C and act-consequentialism, or, equivalently, theory C applied only to acts. That is, let us consider a consequentialism that is maximising and applied only to acts. Call this theory Act-C. Act-C claims only that the unique right act is the act which would make outcomes as good as possible. It picks out just one mandatory act and makes all other acts impermissible.

The technical point is: Act-C has the same formal shape as these older theories. Of course, what is really of interest to consequentialists is something much richer than Act-C. It is richer in two ways. First, consequentialists care about all evaluands, not just acts; they see no reason to focus the particular subset Act-C of C. Second, what animates them is not even really C itself, but rather the assignment of cardinal values to evaluands (blue box), which, when combined with maximisation, produces theory C as its output.

On the first point: consequentialists have no particular hang-up about acts. They endorse the evaluation of all evaluands according to their consequences, and use whatever evaluand is appropriate.

On the second point: the motivating idea of consequentialism is not to pick out one act as the right one. It’s to assign cardinal values to acts (and to motives, dispositions, or anything else you might be able to affect) and to say: “that’s how good it is!”. That is what we find in the blue box. The move from the blue box to the red box is an act of lossy compression, throwing out almost all the information and retaining only a ternary3 classification4. That is why I call the red box only the “normative output” of consequentialism. It’s what a consequentialist will say if forced to make “right/wrong”-statements.

In sum, Act-C is a doubly watered down of the real idea behind consequentialism.

## Why Act-C has received so much attention

What I’ve said is very obvious. Discussing the definition of Act-C as I did may seem rather like philosophic pedantry. I share that sentiment.

Yet Act-C has received most of the philosophical attention devoted to consequentialist theories.

The reason for this strange practice has to do with the order in which ethics has progressed. When consequentialist theories were first developed, they were discussed in terms of how they disagreed with the older theories. This affected the discussion in two ways. First, consequentialist theories were shoehorned into the ternary mould of the older theories, this de-emphasised their distinctive structure. Second, they were applied only to acts, like the older theories.

## Why it matters

I haven’t delved into this pedantic distinction just because I’m interested in history of philosophy for its own sake. I think it can actually teach us something. Two common objections to consequentialism are (i) that it’s too demanding and (ii) that it’s self-defeating in a damaging way. The demandingness objection is narrowly targeted at theory C rather than at the spirit of consequentialism, so it is revealed to misconstrue that spirit. The self-defeat objection is aimed even more narrowly at those who (naively) would apply C only to acts rather than to everything. Hence both objections lose much of their force.

In a sense, the order in which ethics has developed has given an unfair incumbency advantage to the older theories. Those theories shaped the terms of the debate, allowing attention to be focused on strange, shoehorned versions of consequentialism, rather than letting consequentialism shine in its natural form.

### Demandingness

Theory C is sometimes said to be too demanding, constantly requiring us to do the very best thing, lest we be hit with the moral opprobrium of the theory. To indulge in caricature: deontologists think of morality as a matter of whether or not the heavens will part and god will thunder down at you: “WRONG!”. And it does seem a bit excessive to be thundered down at every time you don’t do literally the most altruistic thing possible.

But if we look at the blue box, we can see that this is not what consequentialists have in mind. It’s more like: if you donate $3000 to the Against Malaria Foundation, the heavens will part and god will say: “30 quality-adjusted life-years added in expectation”; if you donate$6000, the heavens will part and god will say: “60 quality-adjusted life-years added in expectation”, and so on.

Consequentialism needs to be thought of more like a general injunction to maximise good consequences, rather than a god who rains lightning on you if you don’t attain the exact global maximum.5

Some might find even that too demanding6. But at least the basic form of the demandingness objection is deflected.

### Self-defeat, decision-making and motivation

Consequentialism is often said to be self-defeating in some damaging way. For example: making decisions by means of consequentialist calculation might lead to a sort of “alienation” between one’s affections and one’s deliberative self – one that in turn leads to a sense of loneliness and emptiness, and is destructive to valuable relationships. Hence even a consequentialist should not, by his own lights, desire that people make decisions by explicit appeal to consequentialist reasoning. Hence Bernard Williams writes “Utilitarianism’s fate is to usher itself from the scene” (‘A critique of utilitarianism’, p.134)7.

In part I of Reasons and Persons, Parfit painstakingly shows the mistakes in these objections. But the solution to the purported puzzle would have been more obvious, I claim, if the focus had been from the start on theory C rather than only on Act-C. Act-C may be viewed as a historical accident which led us into thickets of confusion. Theory C (Ord’s ‘global’ consequentialism8) is simpler and more general. It just says: “The right explicit moral reasoning is that which makes things best”, “the right motive is that which makes things best”, “the right act is that which makes things best”, and so on.

These statements do not contradict each other. Hence there is nothing self-defeating about C when applied to decision-making and motivation. There is no logical contradiction. It is somewhat counter-intuitive that the act recommended by C may fail to coincide with the act that would be chosen given the decision procedure or character trait recommended by the same theory. But it actually fits perfectly with our picture of human psychology.

Theory C takes no view on the question of whether homo sapiens are best thought of as “choosing” acts, policies, entire sets of motives, or something else. It’s a topic for decision theory and psychology. It may have great practical importance, but in the realm of evaluating C, it is not relevant.

In this context, the self-defeat objection could be rephrased as: “Humans shouldn’t be thought of as really choosing acts. Rather, the proper evaluand of human moral theorising is motive or character.” The consequentialist may well agree. She might reply: “this claim seems to have some truth to it, but is certainly not an objection to C. It’s a claim about which parts of C are most useful for humans.”

1. Weighing Goods, p.3:

The idea is, then, that teleology insists acts are to be valued by their consequences alone, and that this is how it should be distinguished from other theories. This is the source of the term ‘consequentialism’. ‘Consequentialism’ is these days used more often than ‘teleology’, but it means the same, except that some authors narrow its meaning in a way I shall be explaining. I prefer the older term for two reasons that will soon appear.

2. Some, like Parfit, define consequentialism as theory C. In other words, they bake a maximising decision rule into the definition of consequentialism. That is a merely verbal issue which need not distract us.

3. In consequentialism, the resulting classification is actually just binary, since no acts are merely permissible.

4. It’s as if you had a .docx file and needed to convert it to a .doc to run on your antiquated office computer, and all tables showed up as uneditable images. Another analogy: asking a consequentialist whether something is right or wrong is like a chimpanzee asking a Labour MP whether a Green MP is a glorious fellow tribesmember who must be protected no matter what, or a filthy outsider who should be killed at the earliest opportunity. It’s shoehorning the nuance of modern politics into old categories. I am also reminded of the lottery and preface “paradoxes” in epistemology, about which I’ll simply quote David Christensen (Putting Logic In Its Place, 2004, p. 97-98.):

Kaplan, for example, considers a case in which you’ve just reported exactly how confident you are that a certain suspect committed a crime:

One of your colleagues turns to you and says, “I know you’ve already told us how confident you are that the lawyer did it. But tell us, do you believe she did it?” (Kaplan 1996, 89)

For Kaplan, there is something epistemically important left out when we give a description of a person’s degrees of confidence. or my own part, the colleague’s question feels a lot like the question “I know you’ve told us that the dog weighs 79 pounds and is 21 inches high at the shoulder. But tell us: is it big?”

5. This is very similar to Peter Railton’s idea, who “abandons normative terms altogether in the consequentialist part of his theory, arguing that the consequentialist account of wrongness as suboptimality is too much at odds with the pre-philosophic conception of wrongness as truly unacceptable behaviour” (Ord p. 115). Railton “proposed a theory that he called valoric utilitarianism. This theory differs from act-utilitarianism in two ways. The first is that it is not directly concerned with either rightness or goodness. Instead, Railton defines an act to be more morally fortunate than another if it leads to the promotion of more non-moral value. To this, one could add a theory of rightness and goodness which need not be a maximising theory. The idea is that the combined theory might be able to make consequentialist-style judgments concerning the need for maximization (using the language of moral fortunateness), and yet reserve the everyday terms rightness, wrongness, blameworthiness to bear meanings closer to their commonsense use.” (Ord p. 33)

6. But they might have a hard time finding a plausible theory that is less demanding. In “Global poverty and the demands of morality”, Ord writes:

The third variant was that the level of the demand is unintuitively high, and that morality cannot demand so much of us. However, many widely accepted moral principles demand more than this. For example, it wrong to kill the innocent. Suppose you are framed for murder in the United States, and are likely to be executed if brought to trial. The only way to escape is to kill the arresting officer, but since he is innocent, it is wrong to do so. Morality thus requires that you allow yourself to be executed in order to meet its demands. This is a much higher demand than that of donating much of your income, yet we (rightly) accept it. Similarly, it is wrong to keep slaves, and morality demanded that slave owners free their slaves even if it meant financial ruin. There are many similar cases in which morality demands a very high sacrifice and yet we find it acceptable. Most of these are extreme life-or-death cases, but so is global poverty

7. I take this from Ethics lecture notes by Hilary Greaves.

8. The abstract of his thesis:

It is often said that there are three great traditions of normative ethics: consequentialism, deontology, and virtue ethics. Each is based around a compelling intuition about the nature of ethics: that what is ultimately important is that we produce the best possible outcome, that ethics is a system of rules which govern our behaviour, and that ethics is about living a life that instantiates the virtues, such as honesty, compassion and loyalty. This essay is about how best to interpret consequentialism. I show that if we take consequentialism beyond the assessment of acts, using a consequentialist criterion to assess decision making, motivation, and character, then the resulting theory can also capture many of the intuitions about systems of moral rules and excellences of character that lead people to deontology and virtue ethics.

I begin by considering the argument that consequentialism is self-defeating because its adoption would produce bad outcomes. I take up the response offered by the classical utilitarians: when properly construed, consequentialism does not require us to make our decisions by a form of naïve calculation, or to be motivated purely by universal benevolence. Instead it requires us to use the decision procedure that will produce the best outcome and to have the motives that lead to the best outcome. I take this idea as my starting point, and spend the thesis developing it and considering its implications.

# Ontology and personal identity

January 31, 2018

ONTOLOGY AND PERSONAL IDENTITY, a play in one act and two scenes

ACT I

SCENE I. The Ruskin School of Art.

Enter ARTHUR and MEREOLOGIST

Arthur: I love art. I collect clay sculptures.

Mereologist: Aha, look at all my clever mereological paradoxes involving lumps of clay1. We are led to the conclusion that two objects can share the exact same matter at the same time (or somesuch).

Enter NIHILIST

Nihilist [in an evil nihilistic voice]: All the purported puzzles of mereology dissolve if we make no existence claims about ordinary objects2. When we speak of the statue existing, we are speaking loosely. If a clever mereologist presses the point, we should concede that we really mean “there is matter arranged statue-wise” and not “there is a statue”.

Mereologist [clutching his pearls]: No objects! What an extreme, radical view.

Nihilist: Not so. The view has no practical consequences. In everyday life, we can keep speaking loosely and be prefecly well understood. In ordinary life, no-one cares about this weird, ghostly “existence” property. It’s only in the presence of metaphysicians that we have to retreat to the more cumbersome language to be perfectly exact.

Arthur: Yes, I agree. When I sell a sculpture at an auction, all anyone cares about is that they will get the statue (or the matter arranged statue-wise), and that I will get the money. No one will ask “but does the statue really exist?”. Similarly, if I am admiring the “statue” in my own home, I am perfectly indifferent one way or another to whether it “exists” as a statue. “It” is there for my eyes to look at, and that is all I care about.

Mereologist: But then you live a life of self-deception, for in truth you believe you have no statues in your collection at all!

Arthur: I hate philosophy. I’m going to leave you two and go look at my clay arranged statue-wise.

Exeunt

SCENE II3. All Souls College basement, at night.

Enter ROB and DEREK PARFIT’S EVIL TWIN

Rob: I care a lot about being rational.

Derek Parfit’s evil twin (DPET): You do? Let me try to help you with this goal.

Rob: Sure.

DPET: In ten years I will either torture you, or torture a random stranger. Which would you prefer?

Rob: I would prefer that it be the stranger, obviously.

DPET: What is your reason for that?

Rob: Rob+10 will be identical to me. It’s rational for me to care about people that are me.

DPET: You would say you have a rational reason to care about future people if and only if they are identical to you? (The identity matters (IM) view)

Rob: Yes.

DPET: Take the fission case4. You could take multiple occupancy view.5

Rob: No, I find it absurd.

DPET: You could take the no-branching view.6

Rob: No, it is a silly view. It means that neither Lefty nor Righty is you. They both come into existence when your cerebrum is divided. If both your cerebral hemispheres are transplanted, you cease to exist—though you would survive if only one were transplanted and the other destroyed. Fission is death. You can survive hemispherectomy only if the hemisphere to be removed is first destroyed. This is absurd.

DPET: We have found no plausible defence for the IM view. Hence you must abandon it, and with it your justification to prefer that the random stranger be tortured.

Rob: Oh no. This is a horrible bind, I must accept either torture or irrationality! But wait, could this be a mere sophistical trickery like that of the mereologist? I shall simply replace the IM view with the relation-R-matters 7 (RM) view. Since I stand in relation R with Rob+10 and not the stranger, the RM view justifies preferring that the stranger be tortured.

DPET: You are quite right that you should take the RM view. But unlike in the case of mereological nihilism, this has real consequences. Let us say a bit more about relation R. What are the relative contributions of connectedness and continuity to what matters? On one view, connectedness does not matter. Only continuity matters. Suppose I know that, two days from now, my only experience-memories will be of experiences that I shall have tomorrow. On the view just stated, since there shall be continuity of memory, this is all that matters. (Parfit section 100, p. 301)

Rob: I would strongly disagree. Losing all such memories would be something I would deeply regret.

DPET: Hence you must reject the view that only continuity matters. Connectedness matters to some degree.

Rob: I suppose.

DPET: Psychological connectedness comes in degrees. For example, a toddler and an old man are less connected (by shared memories, say) than a toddler and a slightly older toddler. To take another example: immediately after the operation, Lefty and Righty are very connected, over time, they become less so. Psychological connectedness comes in degrees, and hence your reasons to care about future Robs come in degrees.

Rob: The reasons that make it rational for me to care about what happens to Rob+10 also make it rational to care (to a degree) about what happens to strangers. It’s actually irrational to be an pure egoist who nonetheless cares about his future self. This is a big deal, thanks Derek!

Exeunt

THE END

Praise for ONTOLOGY AND PERSONAL IDENTITY

A work of great literary subtletly and not at all a hackneyed morality play.

— Oxford University Press

ONTOLOGY AND PERSONAL IDENTITY is of uncommon moral depth, […] a play that pushes the boundaries of the genre with vivid, believeable characters.

— Cherwell

My new favourite book.

— My grandmum

1. See Stanford on mereology.

2. See Stanford on Eliminativism about material consitution, Wikipedia on Mereological nihilism

3. Much of this scene is plagiarised from Stanford on personal identity

4. Fission is easiest to understand by first considering two other cases, Hemispherectomy and Transplant

1. Hemispherectomy: We destroy your left hemisphere (L). The result is you. (Hemispherectomy is considered a drastic but acceptable treatment for otherwise-inoperable brain tumors.)
2. Transplant: We destroy L, and transplant your right hemisphere (R). She who received the transplant would be you.
3. Fission: We transplant both L and R, each into a different empty head. The two recipients —call them Lefty and Righty— will each be psychologically continuous with you. However, Lefty and Righty cannot be identical. (Suppose Lefty is hungry at a time when Righty isn’t. If you are Lefty, you are hungry at that time. If you are Righty, you aren’t. If you are Lefty and Righty, you are both hungry and not hungry at once: a contradiction.)

5. The “multiple-occupancy view”, says that if there is fission in your future, then there are two of you, so to speak, even now. What we think of as you is really two people, Lefty and Righty, who are now exactly similar and located in the same place, doing the same things and thinking the same thoughts.

6. The no-branching view says that a past or future being is you only if she is then psychologically continuous with you and no other being is

7. On this view, what matters when it comes to persistence over time is Relation R: some mixture of psychological connectedness and psychological continuity (Parfit section 79, p. 215). Psychological connectedness is the holding of particular direct psychological connections (such as beliefs, memories, preferences). Psychological continuity is the holding of overlapping chains of strong connectedness. (Parfit section 78, p. 206).