# Implicit comparatives and the Sorites

*History and Philosophy of Logic*27 (1):1-8 (2006)

**Abstract**

A person with one dollar is poor. If a person with n dollars is poor, then so is a person with n + 1 dollars. Therefore, a person with a billion dollars is poor. True premises, valid reasoning, a false a conclusion. This is an instance of the Sorites-paradox. (There are infinitely many such paradoxes. A man with an IQ of 1 is unintelligent. If a man with an IQ of n is unintelligent, so is a man with an IQ of n+1. Therefore a man with an IQ of 200 is unintelligent.) Most attempts to solve this paradox reject some law of classical logic, usually the law of bivalence. I show that this paradox can be solved while holding on to all the laws of classical logic. Given any predicate that generates a Sorites-paradox, significant use of that predicate is actually elliptical for a relational statement: a significant token of "Bob is poor" means that Bob is poor compared to x, for some value of x. Once a value of x is supplied, a definite cutoff line between having and not having the paradox-generating predicate is supplied. This neutralizes the inductive step in the associated Sorites argument, and the would-be paradox is avoided.

**Keywords**

No keywords specified (fix it)

**Categories**

**ISBN(s)**

**PhilPapers/Archive ID**

JOHICA

**Revision history**

References found in this work BETA

Vagueness.Williamson, Timothy

Truth and Other Enigmas.Dummett, Michael A. E.

Vagueness, Truth and Logic.Fine, Kit

Blindspots.Sorensen, Roy A.

Concepts Without Boundaries.Sainsbury, R. M.

View all 13 references / Add more references

Citations of this work BETA

No citations found.

**Added to PP index**

2010-08-10

**Total views**

127 ( #19,677 of 39,026 )

**Recent downloads (6 months)**

13 ( #26,859 of 39,026 )

How can I increase my downloads?

**Monthly downloads since first upload**

*This graph includes both downloads from PhilArchive and clicks to external links.*