The words ‘vague’ and ‘vagueness’ are used frequently in everyday language as synonyms for ‘imprecise’ and ‘lack of precision’. In philosophical terminology, ‘vagueness’ and the adjective ‘vague’ apply to discussions of whether or not a statement is true with a slightly different or, more accurately, a more specific meaning. If the boundaries between a statement being true and it being false are not precisely defined, the statement can be said to be a vague one.
The following example will illustrate the difference between this definition used in philosophy and the more common, everyday meaning of ‘vague’- namely inexact and/or uninformative.
Suppose I attend a football match and, after the match a friend asks me how many spectators there were at this match. If I reply “More than 10 and less than 100,000,” my answer is very uninformative: my friend has little chance of accurately imagining the size of the crowd but it is not vague in the philosophical sense. A vague answer to the question would be something like:
Although much more informative from my friend’s point of view, this is a vague statement because it is unclear when this statement is true and when it is false. If the actual number was 19,000, is this reply true? What if the crowd was really 25,000? The boundaries are not well-defined.
This essay will look at some of the methods available for dealing with such cases where the boundaries between a statement being true or false are difficult or impossible to determine. The classic example, and the inspiration for all subsequent study in the area of vagueness, is known as the Sorites paradox- if we have a heap of sand and take one grain of sand away, is the statement “We still have a heap of sand” true or not?
In Norse mythology, there is a story in which the mischievous god Loki makes a bet with a group of dwarves, which he subsequently loses. Under the terms of the bet, this means that the dwarves are entitled to take Loki’s head. Loki, good loser that he is, meets the dwarves to give them his head but demands that he is allowed to keep all of his neck- the price was only the head, not the neck. The ensuing discussion over where exactly the neck stopped and the head began proved impossible to resolve and Loki kept his head.
Wittgenstein’s thought experiment
Wittgenstein first asks the reader to indulge him in a short thought experiment- the reader must provide a definition for the word ‘game’. Initially defining such a common, frequently used word appears very simple but, after a few moments thought, the reader will find himself struggling to describe concisely an idea which encompasses straight forward children’s entertainments like ‘Snap’ and ‘Catch’ as well as complex intellectual pursuits such as chess and bridge, ones which have no competitive element like ‘Patience’ and the huge range of differences in rules for different games.
His point with this experiment is twofold. Firstly, the experiment shows that the word ‘game’ is vague- there isn’t a simple one-one relation between the symbol and what is represented by the symbol. The second point to be drawn is that, despite this vagueness and the inability to define exactly what is represented by the word ‘game’, its use in language is not inhibited- if I tell someone I was playing a game yesterday, they will understand me, and if I go on to tell him that by ‘playing a game’ I mean writing this paper, he will know immediately that I have made an error in my use of the word.
None of the available methods of handling vagueness give us a perfect solution to the problem, none give us the answer as to the logical value of a statement in a borderline case so we are left with a situation of choosing the lesser of a selection of evils. Taking into account the arguments for and against each, I suggest that the epistemic view is the most sensible to adopt- others all involve throwing out or at least adapting the rules of classical logic which serve us so well and raise as many questions as they successfully answer, if not more.
The epistemic view maintains all of classical logic and simply says that there is a gap on our knowledge- cf. Godel’s incompleteness rules for mathematics – whatever system of rules and symbols we adopt, there will always be statements which are true but cannot be proven, for example the Goldbach conjecture. Changing the system may allow us to prove these things but will leave other ‘holes’. Applying a similar theorem to the system we call ‘language’, whether we have a heap or not in a borderline case, and where the border is between heap and non-heap appear to be among these unknowables.
For most people the idea of not knowing something is fairly easy to handle but the additional proviso that this information cannot be determined and will never be known is decidedly uncomfortable and many, myself included, would be reluctant to accept such an apparently defeatist conclusion. However, the evidence before us leads me to agree, for the time being at least, with those who claim that our language is inherently vague and we cannot always know for certain where the boundaries of meaning for the words we use lie.