If I gave you one grain of sand—and then another, I think we’d both agree that I haven’t given you a heap.

If I added one more, then still; no heap.

Even if I had given you a small pile of sand, it would be fair to say that just one grain of sand will never be the difference between a small pile and a massive heap.

But at some point—if I kept on adding one grain of sand at a time—we would eventually end up with a heap.

This paradox isn’t new. You may not be surprised when I say that it goes back 2,700 years to Ancient Greece, as so many things do.

But there’s more to this puzzle than a quibble about semantics—if this was a problem that could be solved by just setting a firm number on exactly how many grains of sand make a pile versus a heap, then it we wouldn’t still be talking about this now.

You see, the Sorites Paradox is just one instantiation of a phenomenon that we experience in many different aspects of our lives. Sitting back for just five minutes more when there are things to be done won’t push you for time. Even when money is tight, buying a morning coffee won’t break the bank. When spending an evening at the pub, it’s not like a single drink will tip you over from being merely tipsy to paralytic.

It’s quite easy to see where this is going. Say five more minutes enough and you’ll run out of time. Do you really have £50 spare for the total of a month’s morning coffees? Contrary to the music-hall ditty—enough little drinks really will do us harm.

Obvious—when it’s laid out plainly in front of us. A few days of me continually giving you grains of sand and there’ll be no question that I’ve made a heap.

But it doesn’t make things any clearer when we are there in the moment. It remains true that five more minutes, a morning coffee or a single drink won’t make the difference—and it is true for each single iteration. Just one grain of sand won’t transform a pile into a heap.

The hypothetical, ‘if you kept on doing that, it would make a difference’ doesn’t help because there is no contradiction in accepting that and still just adding one grain of sand.

So how can we proceed from here? We know that if we iterate our actions, we will end up with a result which we would rather avoid. But for each iteration, we can’t provide a good reason not to listen to the little devil on our shoulder—if one more won’t make a difference, why not do it?

We might try setting a firm cut-off point; five more minutes won’t make a difference but wasting more than half an hour—that’s really unacceptable. However, when the half hour’s up, it’s still going to be true that five more minutes won’t make a difference. So, what good reason do you have for getting up?

Perhaps that is the problem, the commitment to a good reason. We can circumvent the bad outcomes of this paradox by having a firm cut-off point—and sticking to it. However, the price of this is our rationality.

What do we say to the devil on our shoulder? ‘I accept that one coffee won’t break the bank but—although I would like it—I’m still not going to have it.’ This isn’t justified; the hypothetical doesn’t work. We have just set our arbitrary limit and dug our heels in.

Maybe there is a higher order ‘goal-oriented’ rationality we can try and claim here. If we want to achieve our goals, then perhaps we can say that the rational thing to do is to set an arbitrary limit and thereby avoid being sucked in by the Sorites Paradox. But we won’t be able to rationally justify where we’ve set that limit—why not just have it one grain higher? It really won’t make a difference!

We can get ourselves in a muddle over so many things if we attempt to give a reasoned explanation. Try justifying or questioning someone’s interest in a subject—it won’t take long before reasons give way to ‘just-so’ assertations.

It is so easy to give in to a fetishism of rationality. When challenged, we feel such pressure to reply with a reason—failure to do is seen as a tacit admission of error.

But this is not always the case. There are times when trying to be rational can actually hinder us in our goals and stick us in quagmires we would be better to avoid. Although there is undoubtably a place for rationality, we should not think of it as ubiquitous.

We do not need to know how many grains of sand make a heap to stop it from piling up.

 

How many grains of sand make a heap?