 Transitivity is a controversial property, and many examples have been offered to show that it does not hold in general. A classic type of counterexample to transitivity is the so-called Sorites Paradox. It employs a series of objects that are so arranged that we cannot distinguish between two adjacent members of the series, whereas we can distinguish between members at greater distance (Armstrong 1939, Armstrong 1948, Luce 1956). Consider 1000 cups of coffee, numbered \(C_0, C_1, C_2,\ldots\) up to \(C_{999}\). Cup \(C_0\) contains no sugar, cup \(C_1\) one grain of sugar, cup \(C_2\) two grains etc. Since one cannot taste the difference between \(C_{999}\) and \(C_{998}\), one might consider them to be equally good (of equal value), \(C_{999}\sim C_{998}\). For the same reason, we have \(C_{998}\sim C_{997}\), etc. all the way to \(C_1\sim C_0\), but clearly \(C_0 \succ C_{999}\). This contradicts transitivity of indifference, and therefore also transitivity of weak preference.