Paradoxes make good mind sweet, in my view. As a tough approximation, statements might be deemed a paradox once they provoke the response “That may’t be proper however I additionally don’t see how it may be mistaken.” W. V. Quine as soon as described how paradoxes might be put into three completely different classes: veridical, falsidical, and antinomy.
A paradox is veridical when it appears unattainable or contradictory however seems to be true when correctly understood. Statistics is stuffed with these sorts of paradoxes. One instance is Simpson’s Paradox, which, as Steven Landsburg has defined, can result in the seemingly paradoxical scenario the place you possibly can see “median earnings shoot up in each demographic sector whereas the general median stays practically unchanged.” Russ Roberts has additionally skillfully unpacked this paradox as effectively.
The second class is a falsidical paradox. This can be a when the paradox is dissolved by understanding why it’s really false. A traditional instance is Zeno’s argument for why Achilles can by no means catch as much as a tortoise in a race. We instinctively perceive the argument have to be mistaken—certainly, we all know it’s mistaken as a result of we see the supposedly unattainable end result happen in actuality on a regular basis. However for hundreds of years no one might clarify what the error was, till mathematicians proved an infinite sequence can sum as much as a finite complete.
The third kind of paradox is antinomy, which is the class of “wait, are logic and actuality damaged?” These are paradoxes that stay unsolved. To resolve a paradox is to maneuver it out of antinomy and into the veridical or falsidical areas.
Recently, I’ve been pondering Condorcet’s paradox on this framework. Very briefly, this describes when majority rule produces a rock-paper-scissors type of outcome. Individually, I’d favor waffles over French toast, and French toast over pancakes. These preferences can be transitive—since I like waffles greater than French toast and I like French toast greater than pancakes, I additionally like waffles greater than pancakes. However voting doesn’t essentially produce transitive outcomes. Amongst these three choices, people can rank them in a special order, and voting by majority rule can produce outcomes the place waffles beat French toast, French toast beats pancakes, and pancakes beat waffles.
This end result appears paradoxical. When the bulk prefers waffles, the bulk prefers pancakes. However when the bulk prefers pancakes, the bulk prefers French toast. Nonetheless, when the bulk prefers French toast, the bulk prefers waffles. How can we use democracy to discern and perform the desire of the bulk, when what the bulk desires is concurrently not what the bulk desires? We appear caught in a contradiction.
One solution to resolve the seeming contradiction by recognizing there’s a fallacy of equivocation. The fallacy of equivocation is when the identical phrase is used all through an argument however refers to various things at completely different factors within the argument. On this case, we’re utilizing the identical phrase—“the bulk”—to seek advice from partially overlapping however completely different collections of people. Let’s say there are 300 voters in complete. The “majority” that picks waffles will not be the identical “majority” that picks French toast, and so forth. What we even have are three distinct “majorities”—with apologies to any financial economists studying this, we will name them M1, M2, and M3. M1 consists of the primary and second hundred voters, M2 is made up of the second and third hundred voters, and M3 is the primary and third hundred. Now we will reformat our beforehand paradoxical statements as “M1 prefers waffles, M2 prefers French toast, and M3 prefers pancakes.”
This method may appear to resolve the logical contradiction, however there are nonetheless sensible issues on the desk. Democracy, we are sometimes advised, is justified as a result of it makes the federal government accountable to the bulk. However M1, M2, and M3 can all with equal legitimacy declare to be “the bulk,” and so they all need incompatible outcomes. How will we resolve this downside, in a means that preserves democratic legitimacy?
The reply to this, in my view, is to acknowledge that the very query is falsidical. To talk of “the desire of the bulk” or “what we as a society have determined” is to commit a class error. It makes the error of making use of ideas like choices, needs, will, and so forth, to a class the place they merely don’t apply. It treats “the bulk” is although it had been a factor that has an energetic and unbiased existence, as if “majorities” or “societies” are the sorts of issues which might be able to having needs or making decisions. However the assertion “M1 prefers waffles” is meaningless.
It’s because a majority will not be a factor that exists. Or, to phrase the purpose extra exactly, the bulk doesn’t exist as a factor. A majority is solely a relative type of measurement, not an entity with an actual existence that’s able to having preferences or making decisions. “The bulk” is actual and exists in the identical means and in the identical sense that velocity exists. That’s, issues have velocity, however there’s nothing that’s velocity. Equally, a sure variety of folks or issues in numerous schemas might be outlined as “the bulk,” however there’s nothing that’s “the bulk.” To make use of phrases like “the desire of the bulk” or “as a society, we now have determined such and such” is as essentially incoherent as saying “for this experiment, I’m going to wish three kilos of velocity.”
And that’s how I see Condorcet’s Paradox. As an alternative of questioning how it may be the case that what the bulk desires can also be not what the bulk desires or questioning how a democracy can respect “the desire of the bulk” when there are a number of, equal majorities with incompatible “wills,” we’d do higher to acknowledge that the entire premise is ill-formed. Hayek as soon as mentioned, “We will not develop wiser earlier than we study that a lot that we now have accomplished was very silly.” Endlessly looking underneath the rainbow for “the desire of the bulk” is a silly activity—as a result of there by no means was such a factor to begin with.
