Mere Addition
February 13, 2015 — 11:35

Author: Michael Almeida  Category: Existence of God General Uncategorized  Tags: , , , ,   Comments: 0

Stephen Grover offers an interesting version of the Mere Addition Paradox (‘Mere Addition and the Best of all Possible Worlds’, Religious Studies, 1999) against Swinburne’s brief argument (The Existence of God, Oxford, 1979, 114 ff.) that there is no best world. Swinburne’s argument goes this way.

… take any world W . Presumably the goodness of such a world.will consist in part in it containing a finite or infinite number of conscious beings who will enjoy it. But if the enjoyment of the world by each is a valuable thing, surely a world with a few more conscious beings in it would be a yet more valuable world W’ . . .  I conclude that it is not, for conceptual reasons, plausible to suppose that there could be a best of all possible worlds, and in consequence God could not have overriding reason to create one.

There are good reasons to deny that Swinburne’s argument shows anything like there is no best world. Still, the argument does not suffer from the Mere Addition Paradox (MAP).

The MAP, adapted for Swinburne’s argument, goes this way. Let W be a world in which a group G of conscious beings enjoy very good lives. According to Swinburne, there is another world W+, which includes G and larger group G’. The larger group all live lives that are worth living, but definitely do not live very good lives. The mere addition of the individuals in G’ does not make W+ worse than W. Indeed, for Swinburne, W+ is better than W. Now consider W*. In W*, G is worse off than it is in W and G’ is better off than it is in W+. The average level of well being in W* is higher than it is in W+, but lower than it is in W. And the total quantity of hedons enjoyed in W* is greater than in either W or W+. So, W* is better than W. Grover writes,

But this implies that a significant lowering of the quality of all the lives that are lived does not make an outcome worse, provided that the increase in the quantity of lives is substantial enough. Many people reject this claim. . .(175)

I’m not sure how this is a problem for Swinburne’s argument. Suppose we grant that for every good world W0, there is another world W1, that is both better than W0 (according to Swinburne’s criteria) and has a lower average quality of life than W0. Swinburne should reply that, first this does not affect his argument at all. Note that, for every world W1 in which there is an average quality of life that is low, there is a better world W2 which is clearly better than W0 and W1. In W2 there are many more people than in W0, and they are all enjoying lives that are very good. Swinburne’s argument might well go this way: W0 < W2 < W6 < W10 < . . . < Wn. For his argument to succeed, Swinburne does not need every positive addition to a world to uncontroversially yield a better world. He just needs some positive addition to a world to uncontroversially yield a better world, no matter how good the world is.

But second, Swinburne should argue that he has an argument that W0 really is worse than W1. Let W1 = {A2, B2, C2, D2, E2}, where A – E are each enjoying 2 hedons. Let W0 = {F5}. W0 is worse than W2 = {A4, B4}. W2 is worse than W3 = {A3, B3, C3}. And W3 is worse than W1. So, by transitivity, W0 is worse than W1. It should be obvious that we could make the differences in average well being between these worlds much less significant–we can make it nearly insignificant while increasing the numbers of conscious beings enjoying them–and the argument will be that much stronger.

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