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Who are we? Where do we come from? What is it to be a Rule Breaker, and whence do rules derive meaning? These are questions that some of the brightest philosophical minds of the past century, and indeed all of history, have grappled with.

Ludwig Wittgenstein provides a cogent example of the latter problem, which I'll elaborate upon. Suppose a well-meaning but confused Norwegian schoolboy is asked to complete the mathematical series [2, 4, 6, 8 ...] given by the arithmetic rule "+2." He answers correctly until arriving at 1,000, after which he continues [1,004, 1,008, 1,012 ...]. Despite his best intentions, our lad -- let's call him Nelsen -- is unable to properly extrapolate the series beyond previously learned elements.

The question Wittgenstein poses is whether "+2" means what we ordinarily take it to mean. How do we know that the meaning of "+2" corresponds to the concept "plus 2" and not some other bizarre concept?

The example demonstrates that a finite number of past applications cannot determine a unique rule that gives the correct set of infinite future applications, because there are an infinite number of general rules consistent with any finite series of particulars. But the difficulty Wittgenstein hits on is much deeper than the tired philosophical problem of induction, because it suggests that rules have no determinate meaning to begin with. As this haunted individual puts it, "The fact that we cannot write down all the digits of pi is not a human shortcoming" (Philosophical Investigations, §208) -- nor one of the Kansas legislature.

Ain't gonna happen
Saul Kripke exacerbates the puzzle by refuting two candidates for rule meaning: algorithms and dispositions. He observes that algorithms like "count two marbles and put them together with another heap" simply transposes the problem from "+2" to "count."

Predispositionalist accounts, which suggest that the meaning of a rule is given by how one is predisposed to apply that rule, are losers, Saul contends, because they cannot distinguish what Nelsen thinks "+2" means from what "+2" really means. Machines, like people, are fallible, and they sometimes produce the wrong answer. Deep Blue may truncate or circle back through negative numbers that exceed allocated memory, and it's susceptible to power outages and computer viruses, just as a hypothetical Savant Sally might think 7 + 5 = 11, given enough Jagermeister.

Nor will the inclusion of ceteris paribus clauses like "Sally gets us the right answers when she is sober, and does not have a concussion, and is not too tired or talking in her sleep, and is not being affected by potent hallucinogenic substances" suffice, because such clauses presuppose the very norms they are supposed to explain.

Kripke attributes to Wittgenstein a concessionary "skeptical solution" to the paradox of rule determinacy: that there is no virtue by which our rules have determinate meanings. The most we can say about meaning is that Nelsen understands us when he acts like we do.

A Fool's take
But as John Fennell remarks, why should simply multiplying the number of individuals -- transitioning from individual to communal dispositionalism -- supply a superior normative dispositionalist account? Communities are no less prone to stupidity than individuals -- think pogs, clogs, or tulipomania.

I think we should consider rules neither as fixed for all past, present, and future applications, nor as hollow descriptions of social regularities. Instead, we should see that rule making is an ongoing process which continually derives new content from the Rule Breaking particulars of today and tomorrow.

But that's just my view. Let us know what you think. With six players having made it this far in the article, you'd make it a lucky seven. It's easy and painless and 100% free to participate.

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Ilan Moscovitz owns no Wittgenstein memorabilia, and he will deny up and down that he has a shrine to Saul Kripke hidden somewhere in his basement behind a limited edition Hungry Hungry Hippos set. However, he did once purchase a Romanian copy of Frege's Foundations of Arithmetic, which he gave to a friend, since it was even more undecipherable than the English. The Fool's disclosure policy ain't nothin' to trifle with.