Monday, April 7, 2008

Vagueness and Uncertainty

Halfway down the stairs
Is a stair where I sit.
There isn't any other stair
Quite like it.

I'm not at the bottom,
I'm not at the top;
So this is the stair
Where I always stop.

Halfway up the stairs
Isn't up and it isn't down.
It isn't in the nursery,
It isn't in the town.

And all sorts of funny thoughts
Run round my head.
It isn't really anywhere!
It's somewhere else instead!
-- "Halfway Down the Stairs", a poem by A. A. Milne, author of "Winnie the Pooh".
Why are moral and political issues so difficult? Why isn't it easy to find answers to them that everyone can agree on?

There are certain terms and concepts we use a lot when we talk about moral and political issues: right and wrong, good and bad, better and worse, respectful and disrespectful, beneficial and harmful, and so forth. Basically, we make judgments about things being morally acceptable or unacceptable.

However, these concepts are vague, which is why moral and political issues present so much difficulty.

What is Vagueness?

Vagueness is a property had by many terms and concepts that we use to talk about the world and life, not just the ones we use to discuss moral and political issues.

A concept or a term is vague if there are occasions where we are uncertain as to whether or not the concept or term applies or doesn't apply. There are "borderline cases" where we're not sure what to say.

As in Milne's poem above, it's not clear where exactly to draw the line on the staircase between being in the nursery upstairs and in the town downstairs.

Examples of Vagueness

Some examples should help explain this definition.

For instance, is 4AM morning? Or not morning? Is it nighttime, or not nighttime? How about 4:30AM?

Is someone who is 17 years old a child or not? Are they and adult or not?

Is pudding a solid or not? Is it a liquid or not?

The Paradox of the Heap

Perhaps the most classic example comes from ancient Greek philosophy, and is called "the Sorites paradox" or "the paradox of the heap".

We use the term "heap" regularly and meaningfully. For instance, we talk about a heap of sand at construction site, a heap of dirty clothes at home waiting to be washed, a heap of rice on our dinner plate, or a compost heap in the back yard. So we have a good idea of what can correctly be called a heap.

We also have a good idea of what cannot correctly be referred to as a heap. A single grain of sand or rice is not a heap, nor is a lone dirty sock lying on the floor. A teaspoon worth of mulch is also not a heap.

But what about in between? One grain of sand is not a heap, fine. But what if I add another grain to it, is that a heap? No? Then what if I add another grain, for a grand total of three, is that a heap? No? What if I add one more grain? Is it a heap yet? What's the cutoff? At what point does adding one more grain transform some collection of sand into a heap of sand?

Obviously, there's no clear answer. There's a big "gray area" regarding what is or isn't a heap. This blurry, fuzzy area exists even though we have many clear, paradigm examples of what is a heap (the sand at the construction site, the clothes in my room) and of what isn't (the lone grain of rice on a plate, the teaspoon of mulch).

Moral concepts are like this, too. They are vague. Even though there are certain things that are clearly right (helping somebody who is having a heart attack get to the hospital) and certain things that are clearly wrong (torturing people simply for fun), there are plenty of things where it is unclear whether they should be called right or wrong.

More Examples of Vagueness

Some more examples might prove helpful:


Colors are often argued about due to vagueness. (It's no surprise that people often talk about "gray areas" in morality, where "things aren't black and white"). "Was that hat pink or purple? Is this shirt more green or blue?" Take a look at these color spectrums: it's pretty easy to pick out green, red, and blue. But can you pick out the point where the spectrum stops being blue and starts being purple? Or where it stops being green and starts being yellow (or whatever color the spectrum starts to be when it stops being green)?


Baldness is another hot topic when it comes to vagueness. Patrick Stewart and Telly Savalas are bald. David Coverdale and Jon Bon Jovi are not. But, in between these paradigm cases, there's a lot of people about whom it's difficult to say whether they're bald or not bald, particularly when it comes to people who are losing their hair. (Sometimes people try to hedge their way out of the dilemma by proposing a middle ground or third option: "Well, he's not bald, yet, but he's not not bald, either. He's balding." But this just invites the question: at what point does someone go from being balding to just bald, or from not-not bald to balding? So, vagueness pops up again.)

Scientific Reasoning

Vagueness is also an issue in science, a discipline in which we make observations of the world in order to come up with laws of behavior. That is, we look at how the world behaves at certain times and certain places (we're selective only because we can't be everywhere all the time) and from those observations we derive laws about how the world behaves all the time and every place. (This is called inductive reasoning.) But how many observations, under how many different circumstances, must we make in order to be justified in believing in that we have uncovered a universal law of nature?

For a more particular scientific example, how much evidence is required in order to conclude that global warming occurring and that skepticism is unjustified?

The Ship of Theseus and More

There's even vagueness infecting our use of the word "same". Theseus, the ancient Greek hero, sails around the Agean Sea having various adventures. As he goes about, bits of the ship – planks, nails, ropes, canvas – are damaged and replaced, until none of the original parts remains. Is the ship Theseus is now sailing the same ship as he started out on?

Similarly, is the flame lit at the Olympic games every four years the same flame that lit the Olympic torch at the beginning of the run to the games?

If we ever develop teleportation or transporter technology, will the person who comes out of the teleporter be the same person as the one who went in?

Finally, the Hindu story of how Narasimha kills Hiranyakashipu – who could not be killed by man or beast, day or night, indoors or outdoors – employs vagueness to literary effect.


Vagueness has long been an issue that philosophers have struggled with (notice that some of the best examples of it – the Sorites paradox, the ship of Theseus, and the story of Hiranyakashipu – date all the way back to ancient times). Philosophers and logicians today still address the issue, often under the names "indeterminacy", "fuzzy logic" or "multi-valued logic".

Because there is vagueness in our knowledge of moral priorities and the empirical world, there is vagueness in our knowledge of morality and ethics.

That is why we face moral dilemmas.

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