Glover argues that Taurek’s math is funny.
Suppose there was one person, Able, stranded on a rock who is at risk of drowning when the tide comes in. Taurek agrees that you would be required to save Able. Here 1 > 0.
But if there were two people, Baker and Charlie, on one rock and Able alone on the other rock, Taurek thinks they should have equal chances of being rescued, provided there isn’t a special reason to favor one over the other. Here 2 = 1 or, if you like, the first 1 = 1 and the second 1 = 0.
That is not consistent with 1 > 0.
Taurek would say “Well, what do expect from someone who thinks the numbers don’t matter?” His basic point is that people aren’t like other things. Since you can’t add their value together you shouldn’t expect the mathematical operation of addition to work.
And here we have a genuine disagreement to resolve.
One thing we might do is talk about how you can treat everyone equally in cases like these.
Taurek describes it like this: we have a choice about whether to save two lives (Baker and Charlie) or one (Able). Assuming we don’t have any special reason for preferring one over the others, the fairest way to decide what to do is flip a coin, so everyone has an equal 50-50 chance of living.
But it isn’t obvious that this is the only way of counting them equally.
What if they each got one chance in three of being saved? Should that mean that there is one chance in three that no one is saved? One chance in three that only one of Baker or Charlie is saved? Or do those two go together, so that they get two chances in three?
Or what if we went through a series of one to one comparisons like this?
| line | person | person |
|---|---|---|
| 1 | Baker | Able |
| 2 | Charlie | – |
The idea is that treating people as equals means pitting equals against equals. On the first line, compare one person on one rock against one person on the other rock. Do the same on the second line. And the third, and so on. Here the greatest number will always win because that group will always have someone who isn’t matched with anyone on the other side.
These are the points from today’s class that you should know or have an opinion about.