The philosophical problem of vagueness usually starts with the ‘sorites paradox’ (‘sorites’ is the Greek word for ‘heap’). Consider a large heap of sand, one that is undoubtedly a ‘heap’ as it contains many grains. Then consider a second premise along the lines of: if n grains of sand is a heap, then n – 1 grains of sand is also a heap (that is, taking away one grain of sand does not make any difference). However, if we apply both premises strictly, we are left with the conclusion that one grain of sand (or even no grains of sand) is still a heap.
We are left with a paradox, two apparently true premises that lead us to a false conclusion:
- A heap is defined as 1000 grains of sand
- Taking away one grain from a heap does not make any difference. You still have a heap
- Therefore, a heap can consist of one grain of sand
The problem arises due to vagueness. The word ‘heap’ lacks a precise meaning. We have no way of knowing exactly what it means for something to be a heap. Many words in English have the same problem: ‘tall’, ‘red’, ‘close’, ‘person’, ‘conscious’, ‘overweight’. For instance, if we were to paint a wall in varying degrees of shades from red to orange, any one patch of wall viewed in isolation might look entirely uniform, with no change of colour noticeable. And yet, when you look at the entire wall, both ends have two distinct colours.
We can specify a word as vague if it has borderline cases: examples that could fit the word’s normal meaning, but also could not fit the meaning. For instance a man of 1.8 metres might be ‘tall’ in Japan, but not ‘tall’ in the Netherlands. Furthermore, for genuine cases of vagueness, there is no way to resolve the question. No amount of research or investigation is going to answer the question whether 100 grains of sand is enough to constitute a heap.
In addition, philosophers speak of ‘higher order vagueness’, in that the word ‘vague’ itself is vague. As soon as you try to introduce categories or provide more precise meanings, you are often just shifting the vagueness from one area to another. For instance, using the ‘tall’ example from the last paragraph, if you decide that tall will be based on the person’s country of origin, how then do you deal with someone of mixed heritage? We end up with borderline cases of borderline cases, which could result in an infinite regress.
Vagueness should also be contrasted with ambiguity. A vague word is vague by definition, whereas an ambiguous word might be perfectly understood, but there is more than one possible meaning. Consider the conversation: ‘Should I turn left?’. ‘Right’. An ambiguous word can be clarified immediately by the speaker (‘I meant turn right’), whereas no amount of explanation will clarify a vague word, as this is vague by definition. To put it another way, a vague word has borderline cases, whereas an ambiguous word does not.Consider the word ‘child’. This is both vague and ambiguous. Firstly, it is ambiguous in that the word has multiple things: a child is someone under a certain age; or a child is someone who stands in a relationship of parent-and-child, irrespective of age. Secondly, the word ‘child’ is vague because the definition of ‘under a certain age’ is impossible to define precisely. Is that age 18, 16 or some other pre-defined cut-off? There is no clear answer. In normal language, words need to be read in context to understand their meaning. With classical logic however this can be difficult as the context isn’t always apparent.
Does Vagueness Exist?
A related philosophical problem is whether vagueness is an actual feature of the world (a ‘metaphysical’ state), or whether everything can be precisely determined, so there is no such thing as vagueness. Proponents of vagueness as an actual feature will point out that it is impossible for words to be defined to such precision that they rule out all borderline cases. Consider an example such as ‘rain’. Although most people understand what we mean by ‘it’s raining’ and ‘it’s not raining’, there are scenarios in the middle that could fall into either category (such as a few drops of rain). And what if one person receives twenty drops of rain, while the other only receives one? This suggests that vagueness cannot be avoided.
The opposing view is that vagueness does not exist given that properties either exist or they don’t exist. You can’t say that a property ‘maybe exists’ or ‘half exists’. If we have borderline cases, the critic of vagueness would argue that the problem is not the real world (where everything is determinate and can be precisely measured), but rather the fact that language is imprecise. We have not done enough to be specific with defining words.