Final answer:
The set of all good things cannot be compared to numerical sets because moral or value-based judgments have no common standard of measurement, unlike physical quantities. The concept of incommensurability illustrates the distinction between quantifiable properties and qualitative values.
Step-by-step explanation:
The set of all good things is incommensurable with the sets we use natural/related numbers for because the standard of evaluation in moral or value-based judgments cannot be quantified the same way as physical measurements or counts. Pluralism leverages the notion of incommensurability to articulate this difference, emphasizing that while physical quantities can be compared using a common metric after conversion (feet to centimeters), there is no similar standard for comparing different goods or values, such as the speed of a cheetah to the grandeur of the Taj Mahal.
Philosopher G.E. Moore's open question argument highlights the circularity in attempting to define 'good' with another 'good' without offering informative content, further demonstrating the complexity of measuring moral properties. Similarly, the diverse nature of values such as love or friendship cannot be encapsulated within a numerical value as they are too distinct to be evaluated using a mathematical framework. As Leibniz suggests, rational and non-rational creatures may overwhelmingly exist without commensurate comparison in terms of their intrinsic good. The relationship between numbers and real-world applications often involves dealing with approximations rather than exact values.