The Ordinary World of the Sorites Paradox

What is the sorites paradox? Is there any satisfying way to resolve it?

There is a difference between things being general, ambiguous, and vague. If I say "Cats are cute." I'm talking about all cats, or more reasonably most cats. It's a general statement. The class of objects known as cats usually has the quality of being cute from my perspective.

If I say "Your cat is cute." and you have five cats, then you're probably not sure which one I'm talking about. My statement is ambiguous.

The concept of vagueness is different than either of these. Where is the dividing line between tall and short? When does the spectrum running from red to pink change from red to pink? When you're crossing a threshold, when are you in?

The original sorites paradox is about a heap of sand. You have a heap of sand. You remove one grain. You still have a heap of sand. You remove another grain, you still have a heap of sand. Eventually you have only one grain of sand left. One grain of sand isn't a heap. When did the heap turn into a non-heap?

Let's look at some approaches we can take.

We can give a percentage to the truth value of a statement. This approach of many-valued logic can get as detailed and specific as we want. As we approach this borderline that we're dealing with we can say that the overlapping area has a glut of truth-values. Or, we can say that there is a gap in the truth-values. We can add the opposite to the statement in question and thus it must be true because it contains both options. The thing is, the sorites paradox is a practical problem that humans have been solving since before it was articulated in ancient Greece.

Sand mining is a large industry, it's not just a theory. They don't measure sand in heaps. In the United States it's done in cubic yards. Let's say I want to make a sandbox in my yard. It's three dollars and twenty-five cents per yard near where I live in West Michigan. If I want the sand to be one foot deep and the area to be ten feet by ten feet, then I need 3.7 cubic yards of sand. That's as accurate as the calculator goes. So the actual unit of measurement is tenths of cubic yards. If they give me 3.7 cubic yards of sand, plus or minus seven grains, I don't care and they don't care. If I get 3.6 yards, they shorted me a bit. If I get 3.8 yards, then they're having a little waste on their end. But the numbers from 3.7 to 3.8 don't matter to either party because it's within an acceptable tolerance. Thus, we end up with an amount that is too little for one party, an amount that is too much for one party, and a range of tolerance in-between that is acceptable to both parties.

Outside of this range that's completely acceptable to both parties we have another gradient. Let's say they do give me 3.6 yards of sand and I can tell because my area measurements are exact and the depth is about a third of an inch short. Maybe the difference is enough for me to be slightly annoyed, but that's it. Maybe if it's a half of an inch I tell a few neighbors about it being a little short. Maybe if it's an inch short I call the company and tell them. There are these different levels that are tipping points on each side. At a certain level of waste the company is going to review the process, the personnel, and the equipment. There's tolerance to a certain level, and that level is decided by people individually or as a group depending on the situation.

Going beyond certain tolerances cause both certain perceptual and behavioral thresholds to be crossed. Below these thresholds things aren't noticed or aren't acted on. That's how the sorites paradox is solved by people every day all over the world.



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