Imprecise language
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Regular people use imprecise language much more than the precise language used by philosophers and scientists. Consider the following, which is based on Max Black's Margins of Precision, and is called a Sorites argument. The Sorites is a form of argument in which the concept of consensus can dispose of a long standing confusion.
The Argument
- A million grains of sand makes a heap.
- Removing a single grain of sand from a heap doesn't destroy the heap.
- A single grain of sand makes a heap.
Many philosophers and logicians have confronted this argument and registered their analysis. Some, like Bertrand Russell, simply deny that logic works with vague concepts. Others go so far as destruction of all arguments of this form, including mathematical induction (which may or may not be a Sorites argument).
An attempt to clarify matters goes as follows:
Many of the examples of this argument use words which refer to members of a vaguely defined set with an underlying quantitative scale which can be used to make precise analogs. For example, one could define a p-heap which has at least p grains of sand. One would then have a precise analog for which the Sorites argument would clearly fail because statement 2 above could not be applied to all p-heaps. There would be a "least p-heap" to which the item could be applied.
Consider the height form of the argument.
- A man whose height is seven feet is tall.
- Reducing the height of a tall man by one inch leaves him still tall.
- A man whose height is four feet is tall.
And consider this
- A man whose height is seven feet is considered tall by everyone.
- Reducing the height of a man considered tall by consensus may change the consensus or not. If the reduction is small, then the consensus may only change slightly.
- A man whose height is four feet is considered tall by very few human people.
The usefulness of language is the consensus we share on the definitions of terms. Precise terms have a mechanism by which one can persuade others that a specific application of the term is valid. Vague terms have no such mechanism. If a person insists on calling a seven foot man short, one might suspect that its reference set includes many professional basketball players who play the center position, but we would hardly accuse it of a logic error. Vague terms are useful to the extent that we have consensus, but when used them out of context, they generally confuse.
Some languages have been created to avoid the logical fuzziness in common languages. Lojban and loglan are two nearly identical languages which have been created with the intention of being clear and impossible to misunderstand. The languages can be both spoken and written. They can also be easily interpreted by computers.
The Sorites merely illustrates logical analysis of how one uses vague language. It is a fallacy to assume that everybody agrees on the definition of a vague term. Some people may agree in its application to but not all members of the universe of discourse will as a matter of course.
See also: Logic, definition, extension (semantics), intension, ambiguity, fuzzy logic and vagueness.