Why More Still Isn’t Always Better and True Paralysis Barbara Gail Montero

1. Why More Still Isn’t Always Better and True Paralysis Barbara Gail Montero https://barbaramontero.wordpress.com Princeton Workshop on Infinite Value , 31 October 2015

2. The PurgatoryPuzzle

3. My Aim: Uncovering the Meaning of Utilitarianism Can a utilitarian resolve the the Purgatory puzzle? Do we really need to worry about this? Might we be living in a world with infinite utility? I aim to better understand the commitments of utilitarianism.

4. But are we living in an infinite universe? “Recent cosmological evidence suggests that the world is probably infinite” (Bostrom 2011). “Current data suggest a flat or open universe, [which implies] that it contains an infinite number of galaxies stars, and planets” (referencing Martin’s 1995, General Relativity). But this is correct only if we accept that the universe is homogeneous. With the conjecture of the accelerating universe, has the tide has been turning against homogeneity?

5. Another line of defense: “many cosmologists believe that our universe is just one in an infinite ensemble of universes” (Bostrom 2011). The support: the multiverse hypothesis hypothesis explains away the appearance of “fine-tuning.” Whether it does this is tied up in complicated way with measuring probabilities in infinite cases. Is it “definitely not reasonable to assume that we do not live in a world that is canonically infinite [a world with an infinite amount of both positive and negative value]”?

6. Perhaps we can’t assume a finite universe. Perhaps we ought to take this into account in our deliberations about how to act. But that issue is not my focus. Here I investigate infinite scenarios in order to understand which principles the utilitarian, even in the finite case, holds most dear.

7. A Comparison Hamkins and Montero (2000a), Hamkins and Montero (2000b), Fishkind, Hamkins, Montero (2002). Since then, I’ve been uncovering the commitments of another view: physicalism. For example: How does one apply physicalism to infinitely decomposable worlds? The challenge is to formulate physicalism without assuming a fundamental level.

8. Similarly: How can we formulate utilitarianism without assuming that there is only a finite amount of value in the world? This challenge can help us uncover the core commitments of the view. Aside: Infinite decomposition combined with panpsychism also suggests a way in with the world may be suffused with infinite value. When you make a person happy, must you also consider the infinite descent of conscious entities that you may (or may not) also be making happy?

9. Nonconvergent Worlds Physicalism is false if there is no fundamental level. Utilitarianism (as the view that the best action is the one that leads to a world with greatest total utility) is not false, but meaningless if utility calculations fail to converge: (1, -1, 1, -1....), or (1, -2, +3, -4...). It’s not that the incorrect action is judged morally optimal or that any action we choose results in the same utility. There is no total utility.

10. The subject of infinite value starts with the realization that the standard aggregative idea is meaningless in many infinite cases, so we must find another way to make comparisons.

11. Bostrom (2011) suggests that the central problem infinite cases pose for utilitarianism (and other aggregative ethical positions) is that it wrongly implies that that in worlds with infinitely many bearers of value (locations), that it is always “ethically indifferent what we do”: If a world has an infinite number of locations, and there is some finite value v such that an infinite number of locations have an ethical value greater than v, then that world has an infinite ethical value. This is a core commitment of aggregationism; giving it up means giving up aggregationism. (Bostrom 2011)

12. Bostrom’s claim: “If a world has an infinite number of locations, and there is some finite value v such that an infinite number of locations have an ethical value greater than v, then that world has an infinite ethical value.” But zero and negative numbers are finite. If v is zero, we could have, for example, ½, ¼, ⅛, ..., which converges to 1; if v is a negative number, the locations could all have a value of 0, which converges to 0. What he meant was not that v was finite, but that v has some positive value.

13. More significantly, if an infinite number of locations in a world have value 2 and an infinite number have value -2, then the world does not have “an infinite ethical value,” as the series does not converge. In this case, the theory would not be able to make determination at all. In such a case, the theory isn’t even false; it’s meaningless. The question: Is giving up the ability to make a determination in any situation abandoning utilitarianism?

14. Background Theory: Some Core Utilitarian Commitments In worlds with infinitely many bearers of utility, utilitarians must relinquish certain commitments, such as: The value of a world depends on the sum total of the value of all the utility bearers in that world. Does relinquishing this commitment already amount to abandoning utilitarianism?

15. If there is some way to compare the relative value of worlds, utilitarianism may be able to do without the requirement that utility sums must converge. Some commitments that I think are non-negotiable: *Self-reflexivity: Every world is at least as good as itself: U ≤ U * Transitivity: If world U is at least as good as V and V is at least as good as W, then U is at least as good as W.

16. A couple more non-negotiables: *Aggregation Principle: When the sum of goodness over individual locations of a world does exist, then the overall goodness of a world is equal to this sum and we can compare worlds by comparing these sums. *Pareto Principle: If two worlds U and V and have same locations and every location has at least as much goodness in U as it does in V, then U is at least as good as V. Roughly: if everyone is made at least as well off, then the world as a whole is at least as good.

17. Several Stronger Principles I take the background theory to be necessary for a view to capture the spirit of utilitarianism. But it obviously isn’t sufficient. It doesn’t offer a ruling on numerous situations. For example: U: ...1, 1, 1, 1, 1, 1, V: ...1, 2, 1, -1, 1, 1, 1...

18. Further principles with at least prima facie appeal. The first captures the idea that the value of a world is determined by the pattern of utility in that world and does not depend on the particular identities of the locations of that world. Isomorphism Principle: If world U and world V are isomorphic copies, then U and V are equally good. Worlds U and V are isomorphic copies if there is a one-to-one correspondence between the locations of U and the locations of V such that the goodness of any locations of U is exactly the same as its counterpart in V (and if any structure, such as the order to time, is deemed relevant to one’s calculations, this is preserved too.)

19. Isomorphic copies, by definition, share all that is determined relevant in determining their value, so it seems to follow almost tautologically that any world is as good as its isomorphic copies. I don’t take it as part of the background theory since it is controversial. Vallentyne and Kagan’s Basic Idea is incompatible with Isomorphism: Basic Idea: If every location has greater goodness in U than in V, then U is better than V.

20. In Hamkins and Montero (2000) we argued against the Basic Idea: Imagine Dan and Daniela on an infinite voyage from Hell to Heaven: M T W TH F S Su Dan: . . . -3 -2 -1 0 1 2 3 . . . Daniela: . . . -3 -2 -1 0 1 2 3 . . . The Isomorphism Principle judges Dan and Daniela’s world as equally good. The Basic Idea says that Daniela’s world is better. What is the justification for this?

21. Bostrom (2011) defends the intuition behind the Basic idea (though does not ultimately accept it) by considering W1 and W2, each containing one immortal person: W1: 2, 2, 2, 2, ... W2: 1, 1, 1, 1, ... “Clearly,” he says, “most people would prefer to live in w1.”

22. However, this is the wrong question to ask for a Utilitarian, even in the finite case. • The classical utilitarian ranks w3 and w4 as equivalent • W3: 2, 2, 2, 2, 2 • W4: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 • But most people would prefer to live in W3.

23. The expanding sphere of happiness or misery illustrates (Cain 1995) Illustrates a similar point: A world with infinitely many miserable people in which there is an expanding sphere of happiness. A world with infinitely many happy people in which there is an expanding sphere of misery Most prefer to live in the former (after some finite period of time, you become happy). But on a utilitarian calculus, the latter is preferable (at any time there are only finitely many miserable people and infinitely many happy people).

24. Other principles that would seem to at least have prima facie appeal for a utilitarian are: *Addition Principle: If a world U is at least as good as another world V, and we add (at new locations) at least as much goodness to U as we do to V, thereby obtaining World U′  and V′ , then U′  is at least as good as V′ 

25. The next principle expresses a relation between “complementary worlds” where U and U* are complements just in case all the happiness values in U becomes are reversed U*. For example, if U is the world of all 2’s, U* becomes the world of all -2s. The all zero world is its own complement. Complement Principle: If a world U is at least as good as another world V, then the complementary world U* is at least as bad as V*. That is, V ≤U implies U*≤ V*. For example, if 2 2 2 2... is at least as good as 1 1 1 1... then -2 -2 -2 -2... is at least as bad as -1 -1 -1 -1... Completeness: Any two worlds are comparable. That is, for any two worlds U and V, either U ≤ V or V ≤ U, or both.

26. Bostrom (2011) asks for more: “It must not be the case that all humanly possible acts come out as ethically equivalent.” But shouldn’t whether all humanly possible acts are ethically equivalent depend on the world you are in? Perhaps Heaven is infinitely good and your actions can make it neither better nor worse; in Heaven, you can do whatever you want and it will still be Heaven. Here the utilitarian/aggregative consequentialist ought to judge that all humanly possible acts do come out as ethically equivalent. It does seem that a theory of ethics ought not to imply that necessarily all humanly possible acts are morally equivalent.

27. So we have a bunch of principles: *Self-reflexivity * Transitivity *Aggregation Principle *Pareto Principle *Isomorphism Principe *Addition Principle *Complement Principle *Completeness All are true of utilitarianism in finite worlds. But, as I shall argue, you cannot hold them all consistently in infinite worlds.

28. Weakening and Combining some of these principles For ease of exposition, I rely on a less ambitious special case of Completeness, namely, that we can compare any world to a world with zero utility: Neutrality: Every world is good, bad or neutral In other words, every world is better than the all-zero world (good), worse than the all-zero world (bad) or equally good as the all-zero world (neutral).

29. To simply further, let me weaken and combine several other principles into: Balance Principle: Every balanced world has zero goodness overall. A “balanced” world is one where each location with nonzero goodness is paired with a complementary location. For example, the all picnic world where each sunny, festive picnic is offset by a rainy, ant-infested one is balanced is equivalent to living in a world where every picnic is overcast and the spiked lemonade has, rather than being balanced with pure lemon juice is replaced with water.

30. The Balance Principle is easily derived from Neutrality, Complement and Isomorphism. The Neutrality Principle asserts that U is at least as good as or at least as bad as an all 0 world (or both). If U is at least as good as 0, then by Complement, U* is at least as bad as 0. But if U is balanced, then U and U* are isomorphic and thus equally good. So if U is balanced and at least as good as 0, it follows that U and U* are equally as good as 0. A similar argument shows that when U is balanced and at least as bad as 0, then both U and U* are equally as good as 0. Thus U is equally good as 0.

31. Finally, as it will be useful in the argument, let me unify the Pareto Principle with the Isomorphism principle into: The Modified Pareto Principle: If there is a one to one correspondence between the locations of world U with those of V and every location in U has at least as much goodness as its counterpart in V, then U is at least as good as V. This principle follows from Pareto and Isomorphism and from the Modified Pareto Principle one can derive Pareto and Isomorphism.

32. The Inconsistency Argument Consider world U: U= ... -3 -2 -1 0 1 2 3 ... For the sake of argument, let us suppose that U has no essential natural structure. Since U is balanced, it follows by the Balance Principle that world U has zero goodness overall and is therefore equally good as world Z, which has the same locations but with zero goodness at each location: Z=... 0 0 0 0 0 0 0 ...

33. Now let U+ and Z+ be the worlds obtained by adding a new location bearing goodness 2 to each of U and Z respectively: U= ... -3 -2 -1 0 1 2 3 ... U+= ... -3 -2 -1 0 1 2 2 3 ... Z= ... 0 0 0 0 0 0 0 ... Z+= ... 0 0 0 0 0 2 0 0 ... Since U is at least as good as Z (by Balance), it follows by the Addition principle that U+ is at least as good as Z+. But, by the Modified Pareto principle, U is also at least as good as U+. For, as you can see, every location in U has at least as much goodness as its counterpart in U+.

34. U= ... -3 -2 -1 0 1 2 3 ... U+= ... -3 -2 -1 0 1 2 2 3 ... Z= ... 0 0 0 0 0 0 0 ... Z+= ... 0 0 0 0 0 2 0 0 ... Putting everything together, Z is equally good as U and U is at least as good as U+ and that U+ is at least as good as Z+. Thus, by Transitivity, Z is equally good as Z+. But by Aggregation, they cannot be since the overall value of Z is zero, while the value of Z+ is 2. Thus we have a contradiction. This means that over the background theory, the Isomorphism Principle, the Addition Principle and the Balance Principle are inconsistent.

35. The Utilitarian Response How should a utilitarian respond to this inconsistency? The Addition Principle is unassailable; adding equal amounts of goodness to duplicate worlds, it seems, should not change the relative value of those worlds. The Isomorphism Principle has been challenged. As I said, it is inconsistent with Vallentyne and Kagen’s Basic Idea, which captures the intuition that adding value to an infinitely good world, makes for a better world. Many people seem to have this intuition. As well as the complementary intuition that taking utility away from an infinitely good world makes a world strictly worse.

36. Tim Maudlin’s comment: “So it’s OK to kick a dog, if there are infinitely many dogs?” Probably there are many people who feel that: Whether you have infinitely many happy dogs or just some finite number merrily wagging their tails, it is never OK to kick an innocent dog.

37. Perhaps so, but it’s not the utilitarian response. Whether the kick is OK depends on the consequences of the kick when considering the world as a whole. And it is not clear that adding misery in an already infinitely good world makes the world worse, though of course it doesn’t make it better. With infinite value, more isn’t always more and less isn’t always less. The Isomorphism Principle allows for this.

38. If not based on a rejection of utilitarianism, the intuition that the world is strictly worse after the kick than before, might be explained away by pointing out that it is analogous to the mistaken intuitive appeal of the view that if you add elements to an infinite set, you’ve made it strictly larger. Galileo felt the pull of this intuition. But Cantor argued that there are not more natural numbers than perfect squares and now it is universally accepted among mathematicians that placing sets in a one to one correspondence suffices for showing that the two sets are the same size.

39. Of course, one might think that when comparing the relative value of worlds, our reasoning need not be governed by mathematical principles. Even if God is a mathematician, goodness isn’t a mathematical quantity. Nonetheless, utilitarians want to turn it into one as much as possible and thus the ethical calculus that would seem to uphold their principles best would be one in which one compares the relative goodness of worlds in a way that is analogous to how mathematicians compare the relative size of sets. For these reasons, I also take the Isomorphism Principle as unassailable.

40. This means that the Balance Principle that must be abandoned. Balance is derived from Neutrality, Complement and Isomorphism. Complement seems non-negotiable: if U is just as good as V, then it would see that a world with opposite goodness values as U would be just as bad as a world with opposite goodness values as V. I have just argued for a committed to the Isomorphism Principle. We are thus left with giving up the Neutrality principle, and also the Completeness Principle, of which it is a special case.

41. Toil and Trouble for the Utilitarian If completeness is false there are worlds about which it is wrong to say that one is better than the other and also wrong to say that they are equally good. One can’t even be indifferent between the two worlds, if indifference means that it is permissible to substitute one world for another without objection.

42. Indifference is a transitive relation, but incomparability is not generally a transitive relation. If A is strictly better than C and both are incomparable to B than A is incomparable to B and B is incomparable to C, but A is not incomparable to C. A | B C

43. Incomparability is not mere silence about the relative worth of various worlds. Incomparability means it is wrong to say that one world is better than the other and wrong to say that they are equally good. Making no determination (silence) is not the same as judging that all options are incorrect. And so returning to your afterlife choice between Purgatory and the superposition of fates in Heaven and Hell, the response we have been led to is that there can be no Utilitarian reason to prefer once choice over the other, or even to be indifferent between them. It is wrong to choose and also wrong to flip a coin.

44. This isn’t the type of paralysis that Bostrom (2011) identifies according to which “it is always ethically indifferent what we do.” It is worse than being in the position of ofBuridan’s ass, worse than being Aristotle’s equally hungry and thirsty individual who, when placed in between food and drink, must necessarily remain where he is and starve to death” (Aristotle, On the Heavens) Rather, it’s an entirely devastating, paralysis, what I am tempted to call a “paralyzing paralysis.”

45. Similar to Sartre’s individual who needs to decide whether to go off to war to defend his country or to remain with ailing mother? He does not weigh each, see that he is just as morally bound to do one as to do the other. The duties are incomparable and so one needs to simply choose. This is a profoundly anti-utilitarian approach.

46. I’ve argued that a utilitarian must accept the possibility of incomparabilities. The incomparability I identified between the is just one of an infinite number of incomparabilities—a topic for another paper. In the meantime, a utilitarian can consistently commit to the background theory, the Isomorphism Principle, the Complement Principle and the Addition principle.

47. And for Halloween: I claim these principles are all consistent. Try to refute me, if you DARE..... THANK YOU References Bostrom, N. (2011), “Infinite Ethics,” Analysis and Metaphysics, V. 10 , 9-59. Cain, J. (1995) “Infinite Utility,” Australasian Journal of Philosophy , 73: 3. Fishkind, D., Hamkins, J. and Montero, B. (2002), “New Inconsistencies in Infinite Utility: Is Every World Good, Bad or Neutral?” Australasian Journal of Philosophy,80:2, pp. 178-190. Hamkins, J. and Montero, B. (2000 a), “With Infinite Utility, More Needn’t be Better,” Australasian Journal of Philosophy, 78:2, pp. 231-240. Hamkins, J. and Montero, B. (2000), “Utilitarianism in Infinite Worlds,” Utilitas, 12:1, pp. 91-96. Vallentyne, P. (1997), "Infinite Utility and Finitely Additive Value Theory," (with Shelly Kagan), Journal of Philosophy 94 : 5-26.