John Stuart Mill famously posited that pushing principles to their extreme can reveal their true worth, declaring, “unless the reasons are good for an extreme case, they are not good for any case” (On Liberty). This assertion, however, is not straightforward, as extremes often produce contradictory or non-generalizable outcomes.
Consider the hypothetical act of stealthily pilfering $25 from Elon Musk to provide a meal for a struggling family. One might argue that the utility gained by the family far outweighs the minor loss incurred by Musk, who likely doesn’t sweat the small stuff. Yet, when we step back from such extreme scenarios, it becomes apparent (as I contend alongside many economists) that the idea of “aggregate utility” is fundamentally flawed, as it is impossible to quantify or compare individual utility experiences scientifically. As Anthony de Jasay aptly pointed out, it often boils down to “my say-so against your say-so.” (For further context, see my review of Lionel Robbins’s 1935 work, An Essay on the Nature and Significance of Economics.) While some principles, such as the impossibility of interpersonal utility comparisons, may seem absolute, they are more accurately described as “relatively absolute absolutes” (to borrow from James Buchanan) that can falter under extreme conditions.
Take the famous paradox of the Cretan who claims, “all Cretans are liars.” This statement is inherently contradictory: if it’s true, it must be false; if it’s false, it might be true. However, as de Jasay reminds us through his pragmatic lens, when we assert that all Cretans lie, we are speaking metaphorically, implying that most do. This nuance supports his argument for the feasibility of privately producing “public goods” in an anarchic setting by discounting extreme cases. If all potential beneficiaries of a public good are convinced that none among them will free-ride (i.e., refrain from contributing), paradoxically, they all will. In reality, potential free riders will hedge their bets, believing that some will contribute while others will not, and choose to subscribe in hopes that their contributions could be pivotal for the public goods they desire. (For more on this, refer to de Jasay’s Social Contract, Free Ride, which I also reviewed in Regulation.)
It seems that extremes often baffle our understanding, at least within the confines of our limited cognition. The concept of mathematical infinity serves as a prime example of an extreme that poses significant challenges. Yet, “tending toward infinity” remains a valuable notion, particularly for calculating the present value of perpetuities (like perpetual bonds or consols), which hinge on dividing the recurrent coupon by the discount rate.
While theorizing about a nearly omnipotent deity may seem to offer solutions to every dilemma, contemplating an infinitely powerful God leads to the “omnipotence paradox”: Can God create a rock so heavy that He cannot lift it? Aquinas clarified that divine omnipotence pertains only to “possible things,” or those that do not invoke contradiction—Summa Theologica, Part 1, Question 25, Article 3. Thus, even God cannot transcend logical contradictions. Unsurprisingly, human governments are not omnipotent; however, they can inflict considerable harm when they drift toward that illusion.
The challenge lies in identifying the extremes and discerning which extreme cases cannot effectively test a theory. In certain situations, such identification is feasible—such as when examining a variable that shifts from 0% to 100%, like the percentage of Cretans who lie or the number of voluntary contributors to a public good.
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“Woman walking toward infinity”
