In his critique of popular conceptions of justice, Mill uses a simile that contrasts the complexities of justice to the certainty of mathematics:
We are continually informed that utility is an uncertain standard, which every different person interprets differently, and that there is no safety but in the immutable, ineffaceable, and unmistakable dictates of justice, which carry their evidence in themselves and are independent of the fluctuations of opinion. One would suppose from this that on questions of justice there could be no controversy; that, if we take that for our rule, its application to any given case could leave us in as little doubt as a mathematical demonstration.
Here, Mill critiques popular belief in an “immutable, ineffaceable, and unmistakable” set of rules that apparently define justice in favor of his own utilitarian model that balances public harm against public utility. The application of justice by, for example, the law would be uncontroversial if it were as certain “as a mathematical demonstration.” Through this simile, he compares the certainty of mathematics, in which the solution to a problem or equation can be declared right or wrong with a high degree of accuracy, to justice, which is far more subjective. While an easy consensus might be reached in mathematics, he highlights the fact that people often disagree about what is “just” or fair, suggesting that justice cannot be easily reduced to a set of rules.
