Many philosophers and logicians (better prepared than I) 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 is not really a Sorites argument in my opinion). |
Many philosophers and logicians (better prepared than I) 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 is not really a Sorites argument in my opinion). |
Ordinary folk need imprecise language much more than the precise language used by philosophers and scientists. The following is an article which bears on this as it reflects on the Sorites argument. It leans heavily on what I learned from [Max Black]'s Margins of Precision.
The standard form of this disturbing argument goes something like this.
My 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, We could define a p-heap which has at least p grains of sand. We 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.
And consider this
The Sorites merely illustrates that the growth and destruction of consensus is a required element in the logical analysis of how we use vague language. It is a fallacy to treat a vague term as if everyone agreed with its definition. We may agree in its application to some but not all members of the universe of discourse.