Pairs

As a warmup to his arguments against the existence of ordinary objects, Trenton Merricks argues against the existence of pairs of gloves.

Here’s another argument against pairs of gloves. I recently bought a pack of 200 nitrile gloves. How many pairs am I buying? Intuitively, there were a hundred pairs in the box. But if so, then we have have an odd question: For which distinct gloves of x and y in the box, do x and y in the box constitute a pair? If they all do, then there are 200⋅199/2 = 19,900 pairs in the box, while sure we would feel ripped off if the box said “19,900 pairs”.

Well, we might say this, starting at the top of the box: the first and second gloves are a pair, the third and fourth are a pair, and so on. But now suppose that something went wrong in the packing, and only 199 gloves went into the box (maybe that actually happened—I didn’t count). Then the box has 49 pairs, plus one more glove. But which of the gloves is the extra? Is it the bottom one, the top one, or some one in the middle? There seems to be no answer here.

Moreover, sometimes I only use one glove at a time. If so, then there is a 50% chance that at this point the next two gloves from the box that I put on aren’t actually a pair, and so when I put them on, I am not actually putting on a pair of gloves.

Perhaps, you say, all these difficulties stem from the fact that nitrile gloves do not have a left and right distinction. But suppose they did, and I got sent a messy box with 100 left gloves and 100 right gloves. Now, if every left glove and every right glove make a pair, there are 100⋅100 = 10,000 pairs, but it would be clearly a rip-off to label the box “10,000 pairs”: clearly, there would be 100 pairs. But now we would once again have the insuperable question of which left glove with which right glove makes a pair.

Maybe the problem disappears if one buys things by the single pair, as the “true pairs” are the ones one buys? I doubt it. If you saw me walking around today, you’d have said I was wearing a pair of black running shoes. But what happened was this: Some years back, I bought a pair of running shoes. The stitching on the right shoe gave out all too soon, and I patched it with a punctured bike inner tube (I save inner tubes that are themselves too far gone to keep patching, as they are useful for various projects), and wore it for another couple of months, but eventually gave in and got a second pair of the same make, model, size and color. After a year or two, I noticed that the left shoe on my newer pair was now more worn than the left shoe on my older pair (I didn’t throw the first pair out). And you can guess what I did: I started wearing the right shoe from the newer pair with the left shoe from the older pair. And that’s what I was wearing today. So, if the true pairs are as purchased, you would have been objectively wrong if you thought you saw me wearing a pair of shoes today: I was wearing two half-pairs. But this is absurd.

One might say: shoes become a pair when customarily worn together. But how many days do I need to wear them together for them to become a pair? And what if I bought two pairs of shoes of the same sort, and every morning randomly chose which left one and which right one to wear?

Perhaps the problems afflicting pairs don’t afflict more tightly bound artifacts. But I suspect it’s largely just a difference in vividness of the problem.