CHAPTER 19: THE MERE ADDITION PARADOX


As we move from A+ to Divided B, the least well off improve more than the best well off lose.

If we appeal to the Valueless Level A is better than B:

Just assume lives in B are below the level at which quantity has value.

On the Lexical View, A is better than B:

Since quality is about 4/5 as high in B as in A, it cannot be both that lives in A are above the blissful level and lives in B below the mediocre level. So if B's population was large enough, B could be better than A. But B's population is only twice A's.

Hence on either view A is better than B (this is 6 below)

The Mere Addition Paradox (First Version):

'<' means "is worse than"

            1         B = divided B                Obvious

            2         A+ < Divided B             Maximin, Equality, Beneficence

So        3         A+ < B                           1,2

            4       ~(A+ < A)                         Mere addition can't hurt

So        5      ~(B < A)                             3,4

                     But      6       B < A                             Appeal to Valueless Level, Lexical View
                                                                                (Quantity does not always count)

                    So         7       Contradiction                 5,6

It may seem as if conclusion 5 iterated implies the Repugnant Conclusion, but it doesn't, because it is not the case that:

(B is not worse than A) ® (A is at least as good as B)

i.e. it is not the case that:

~(B < A) ® (B £ A)

Hence "not worse than" is not transitive and does not lead us to Repugnant Conclusion.

Mere Addition Paradox (Second Version):

Unlike the first version of the paradox, the second gets us something very much like the Repugnant Conclusion:

Iterating the move from New A to New B eventually gets us to New Z where lives are just above the bad level indicated by horizontal line. This is a form of the Repugnant Conclusion.

The assumptions here are:

        1         A+ < New A                           Improvement outweighs loss in initial worlds;
                                                                    moreoever Mere Addition can't hurt (434)

        2         New A < New B                     Maximin, Equality, Beneficence

        3         New B < New C                     Maximin, Equality, Beneficence

        4         New C < New D                     Maximin, Equality, Beneficence

            .
            .
            .

        N         New Y < New Z                     Maximin, Equality, Beneficence

So   (N+1)   A+ < New Z                           1-N

(N+1) is the:

New Repugnant Conclusion: In A+ there are two groups of 10 billion people, one of which has a quality of life far higher than anyone who has ever actually lived and the other of which has a quality even higher. In New Z there is a much larger number of people none of whom has a quality of life much above the bad level. New Z is better than A+.

 The third version of the paradox is the same idea with each block representing 1000 years.

It seems much less repugnant that way.
 
 

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