The Impact of Using Multi-Dimensional and Combinatory Vague Terms on the Possibility of Formulating Sorites Paradoxes - Jan Štěpánek (Organon F, 2014)
We cannot definitely determine precise boundaries of application of vague terms like “tall”. Since it is only a height of a person that determines whether that person is tall or not, we can count “tall” as an example of a linear vague term. That means that all objects in a range of significance of “tall” can be linearly ordered. Linear vague terms can be used to formulate three basic versions of the sorites paradox – the conditional sorites, the mathematical induction sorites, and the line-drawing sorites. In this paper I would like to explore a possibility of formulating sorites paradoxes with so called multi-dimensional and combinatory vague terms – terms for which it is impossible to create a linear ordering of all objects in their range of significance. Therefore, I will show which adjustments must be made and which simplifications we must accede to in order to formulate any version of the sorites paradox with multi-dimensional or combinatory vague terms. I will also show that only the conditional version of the sorites paradox can be construed with all three kinds of vague terms.
Keywords: Combinatory vagueness; linear vagueness; multi-dimensional vagueness; paradox; Paradox of the Heap; sorites; vagueness