Slippery slopes to vagueness

The basic form of the slippery slope argument is that you concede that some policy x (lowercase) is prima facie acceptable, but that it sets a precedent for progressively stronger versions of that policy.  Ultimately, the strongest version of the policy, call it X (uppercase), at the extreme, will seem acceptable.  But X is clearly not.  The reasoning then goes that to stem the tide of precedent to X, we must not take that first step to accept x.  For a slippery slope argument to be acceptable, the slope must be genuinely slippery.  That is, there must be a relevant relation between x and X (namely, that x is not just a  preconditon for X, but that it must make X more acceptable), there must be no places where other considerations prevent the intermediary moves, and so on.  In cases where those desiderata fail, the slope isn’t slippery.  It’s more a bumpy staircase.

Some slippery slope arguments take the form of sorites (or vagueness) lines of reasoning.  And sorite reasoning is good only when there is a restricted range of considerations.  When there are other variables, vagueness arguments stink.

Here’s Ron Ross, over at the American Spectator, on President Obama’s recent proposal to raise the minimum wage.

When I taught economics, when possible I liked to use the “Socratic method,” which is essentially teaching by asking questions. The Socratic method helps the student deduce the answer by using what he already knows.

Most people, especially college freshmen and sophomores, feel that minimum wage laws are beneficial. When discussing the topic I would ask, “If a minimum wage of $8 is better than one of $5, why skimp? Why not make the minimum wage $10, or $20, or $30?” Passing minimum wage laws is relatively easy. If eliminating poverty is that easy, why not go all the way? Why be so miserly? It’s not your money you’re spending. Go big or go home!

He takes it that this is a full-on reductio of minimum wage proposals.  Ross’s argument is classic sorite version of slippery slope.  Here’s how I’d reformulate it:

P1. (Fact of case evaluation): $5 an hour isn’t enough.

P2. (Principle of tolerance): If a wage isn’t enough, then if we add 1 cent an hour to the wage, the new wage still isn’t enough.

Once we accept P2, the pile quickly accumulates.  Iterate modus ponens 500 times, 5,000 times on the inputs and products of P1 and P2, and you end up with Ross’s conclusion. (On the assumption that P1 and P2 are true, all those MP iterations will be sound.)  Go big or go home.

As I take it, Ross’s conclusion is that we should, to prevent the pile, reject P1.  But I think liberals, to prevent the pile, reject P2.  That’s what the concept of living wage is supposed to be — that there is an economically determinable line one passes where the one cent an hour makes a difference between having enough to pay all the bills (and perhaps save a small amount) and not.   And that’s why they want to raise the minimum wage.  Running a vagueness argument misses the point.  Not surprised that Ross ran it on his college undergrads.  They must not have taken a good logic class yet.


5 thoughts on “Slippery slopes to vagueness”

  1. Ross’ argument is about the broader economy, which is not directly overly affected by whether people make a bit less than a living wage or not; none of his premises should have the word “enough” in them. He points out that liberals already reject P2 below:

    P1: The higher* people’s wages, the better.

    P2: (Principle of tolerance): If a minimum wage isn’t macroeconomically harmful (by deterring employment), then if we add 1 cent an hour to the wage, the new wage still isn’t harmful.

    He’s saying, in effect: you liberals implicitly and correctly rejected sorite’s paradox when you limited the minimum wage to an amount, but no more than that amount. The same concerns that led you to restrict it also apply to lower levels of minimum wage, and even apply at the level to which you set it.

    The problem with his argument is that he measures the goodness of a policy by unemployment alone, rather than by both unemployment and the wages earned. A living wage is a plausible Schelling point as it minimizes the number who can’t survive indefinitely on their wages, at the expense of increasing unemployment above its minimum.

    Here a (the?) chairman of the economics department at Harvard makes a similar point:

    “There is one question I would like to see some reporter ask Alan Krueger, the president’s chief economist: How did they decide that $9 per hour is the right level? Why not $10 or $12 or $15 or $20? Presumably, the president’s economic team must believe that the adverse employment effects become sufficiently large at some point that further increases are undesirable. But what calculations led them to decide that $9 strikes the right balance?”

    There, Manikiw similarly points out that liberals did not assume the truth of P2 as I have it above, and uses that to show that even liberal ideology assumes the truth of minimum wage’s adverse effects. Unlike Ross, he does not say that those effects demand falling down an entirely separate slippery slope to abolishing the minimum wage. Instead, he correctly frames the issue as demanding the balancing of relevant valued outcomes, and he does not partisanly ignore inconvenient issues (either increased unemployment for the poor (as conservatives say) or lower wages for the poor (as liberals say)).

    *Adjusted for inflation, measured in ppp, other caveats. I don’t think any are central to the point.

  2. Hey Longname,

    Maybe I’m not reading very carefully here–if so, apologies–but it seems that Mankiw is making the very same mistake Ross is. Having looked at his post, it’s unclear to me whether he means that as a refutation of the idea of raising the minumum wage, or a genuine question about what sorts of calculations mean that is the right number. I’m guessing the former.

  3. Well, I think reconstructing the slippery slope as a form of ad hominem argumentation — that is, to uncover a hidden premise in your opponent is fine. In this case, as {longname} observes, the argument shows that liberals, too, hold that there’s an upper limit to wages. One that’s determined by economic sustainability. But, look, nobody in any of these debates is denying that. What’s at issue isn’t whether everyone should be millionaires, but whether people deserve to be paid enough to live on. That is, the issue is whether there is a definable point below the sustainability point that’s a living wage. For sure, liberals who hold that there is such a have the burden of proof, and it’s appropriate *for Manikiw* to insist that they live up to it. But if you read all the the Ross piece, even twice, there’s no hint of that there. So, erm, there’s that.

  4. So there is the factual question about living wages. I think if Mankiw is asking about that, then indeed, fair question. It seems to me, however, he’s just heap-paradoxing. The case has been made, by Obama at least, the current minimum wage is too low. He then argued that a couple more dollars would help. That 10 more dollars would help even more doesn’t matter so much, as no one has proposed that. The fact that no one is around to answer for that question doesn’t entail that the current system is any more fair.

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