Symbolic Logic for Transit Advocates: A Short but Essential Course

Part of our job as informed citizens and voters is to sift through the political claims that we hear and arrive at our own sense of what’s true.  I’ve been listening to such claims in the transit business, and sometimes making them, for almost 30 years now.  It occurs to me that one of the most important tools for evaluating these claims is something you probably learned in high school math and forgot.  (Yes, some of you remembered, but I’m really talking to the ones who forgot.  To those of you who just don’t like math, don’t worry if you don’t follow this next bit; just skim ahead to the example.  This IS really important.)

Here it is.
Consider a statement of the form “If A is true, then B is true,” [A –> B]
IF that statement is true, then:
  • The Converse, [B –> A] is not necessarily true.
  • The Inverse [NOT A –> NOT B] is not necessarily true.
  • The Contrapositive [NOT B –> NOT A] IS true.

You already know this. Consider the statement “John is very tall.” Your first job is to see the “if-then” formulation of the statement, in this case “If this person is John, then this person is very tall.”
So in this case:

  • The Converse (“If this person is not John, then this person is not tall”) is obviously not true in this case.
  • The Inverse (“If this person is tall, then this person is John”) is also obviously not true.
  • The Contrapositive (“If this person is not tall, then this person is not John”) IS true.  In fact, it’s logically equivalent to the first statement.

Duh. And yet, a huge percentage of our political rhetoric is designed to make you get this wrong. Political rhetoric is often just trying to create a vague feeling of intimacy between ideas A and B, and discourage you from asking what the logical relationship of the two ideas really is.
Consider this slogan from the Seattle Monorail Project (1996-2005)

 Monorails never get stuck in traffic.
Logically this is:
IF (monorail) THEN NOT (stuck in traffic), i.e.
If I’m on a monorail, then I’m not stuck in traffic.
 That’s certainly true, but the people uttering this slogan don’t just want you to believe what they’ve said. They really want you to believe the CONVERSE of what they’ve said:
IF NOT (stuck in traffic) THEN (monorail), i.e.
 If I’m not stuck in traffic, then I’m on a monorail.
 …because if that were true, we’d all be monorail advocates. But it’s not true. The converse does not follow from the first statement. It might be true, it might not, but it’s a different idea.
(Note, in passing, that I’m not talking at all about the notion of cause and effect, which is a more advanced and philosphically vexed topic.  For now, just remember the statistician’s mantra: “Correlation is not causation!”  In other words, saying “If A then B” is not the same as saying “A causes B.”)
All this came to mind in when I looked at the concept that redevelopment requires streetcars:
 IF (redevelopment) THEN (streetcar), i.e.
 If you’ve had redevelopment, there must have been a streetcar.
Cap’n Transit noted that streetcar advocates don’t often come out and say this. Their claim is often closer to the converse:
 IF (streetcar) THEN (redevelopment), i.e.
If there’s a streetcar, then redevelopment happens around it.
 … which happens to be true, right now, at least in Portland and Seattle.  But once you look at it this way, it obviously fails to close the deal for streetcars.  Many of the commenters on my earlier streetcar post assumed that because I was questioning the need for streetcars, I was therefore questioning the value of redevelopment.  That’s utterly false.  I’m simply raising a question about the logical relationship between (streetcar) and (redevelopment).
Now that everyone’s mad at me, let me retreat to the less emotional example (though it was very emotional five years ago in Seattle):
Monorails never get stuck in traffic.
What’s really happening here, as in a great deal of political rhetoric, is that superficially sensible statements are being used to create a vague but emotive feeling of association between ideas A and B, such that your feelings about A will transfer to B without you thinking about the relationship between the two ideas.  The temperature of association is important; this kind of hoodwinking is likely to work better when at least one of the items is something that you feel strongly about (“stuck in traffic” in this case).  The hope is that the surge of feeling that you have whenever the sensitive subject is mentioned will flow through the speaker’s statement and thus attach itself to the other idea that the speaker is presenting in a way that bypasses your mind.  Too often, it works.

11 Responses to Symbolic Logic for Transit Advocates: A Short but Essential Course

  1. EngineerScotty July 29, 2009 at 3:09 pm #

    Man…. I substitute “contrapositive” when I meant “converse”, and I get an entire thread dedicated to the subject. As a computer scientist who should know better, I suppose I deserve it. 🙂
    That said, non-modal Boolean logic, while often studied as part of rhetoric, is (unfortunately) not of much use in public policy debates. You seldom find iron-clad premises on which to base an argument or conclusion; circular reasoning (with elaborate cycles of inference) is commonplace, confusion of correlation, causation, and coincidence abound–and to top it off, in many subjects the only data you have available is anecdotal; and seldom controlled for the parameter you want to test.
    The study of rhetoric and logic is important in developing a finely-tuned bullshit detector. But demonstrating anything in the positive (as opposed to falsifying blatant crap) frequently requires expensive and time-consuming empirical research–and even if such research is done with sound methodology, it still will get attacked by those who dislike the result. (The debate around climate change is an obvious example). Obviously, we can’t set up experiments on the effect of streetcars vs busses on development; the best we can do is try and draw useful inferences from the data that’s out there.

  2. Michael July 29, 2009 at 3:32 pm #

    “Monorails never get stuck in traffic.” would lead no one to conclude “If I’m not stuck in traffic, then I’m on a monorail.” What it might lead people to conclude is “If I want to avoid getting stuck in traffic, I want a monorail.” Which is a matter of judgment, but certainly not illogical.
    Nobody ever claims that streetcars are the only way to get development. What they do claim is that they are a good way to bring about development. No false logic there.
    I’m sorry, I just don’t see much substance here. People are often bad at statistical reasoning, but they’re okay with basic logic — though not in formal language. If you want B, and A reliably brings about B better than not A, then you should do A. The answers aren’t pretty — you have to go and compare how good A and its alternatives are at producing B. Exercises in formal logic won’t help.

  3. Michael D. Setty July 29, 2009 at 4:13 pm #

    You’ve obviously opened a hornet’s nest with your recent line of discussion. Here’s another tack.
    As most of us know, the usual rule of thumb for walking distance to local buses is a maximum of 1/4 mile. For rail transit such as light rail and heavy rail this number is about 0.5 mile, or perhaps up to a kilometer.
    I’m curious if you have any information on typical walking distances to bus rapid transit, and frequent bus service in general? Your recent work for Canberra has an allusion to this (750 meters) but not a lot of detail. I’m curious about this, because I haven’t been able to find any information about BRT/frequent bus service walking distances in the U.S.

  4. Michael D. Setty July 29, 2009 at 4:17 pm #

    I’d add some of the worst offenders in crafting dubious associations between ideas are the Gadgetbahners (for example, those hanging out at
    Their funniest, most dubious formulation is “Rail is 19th Century technology.”
    Of course, such logic falls apart when it is pointed out that “the wheel is 5th millenium BC technology,” ” concrete is Roman technology.” and so forth.

  5. Jarrett at July 29, 2009 at 5:29 pm #

    Yes, it’s obviously silly to believe, in the present tense, that “If I’m not stuck in traffic, then I’m on a monorail.” But why is it more logical to state the same thing as a relationship between desires, “If I don’t want to be stuck in traffic, I want a monorail?”
    If your goal is really to not be stuck in traffic, then you should investigate all the possible options for not being stuck in traffic, and pick the best one. And it’s well established that to not be stuck in traffic, you just need a form of transit that doesn’t mix with traffic, period. Monorails are just one of many such types of transit.
    And if, as it turned out in Seattle, monorails aren’t that good at actually getting built on budget and with acceptable community impacts, then it isn’t logical to want a monorail. As it played out in Seattle, the decision to want a monorail actually resulted in people being stuck in traffic for a decade longer than necessary.
    This is not an argument about monorails, of course. But I am pointing out that when we transfer our desire for A onto proposed project B, we often blow it, and end up supporting something that doesn’t serve our desire at all.
    And I do contend that watching the underlying logic can help us be smarter about those things.

  6. Jarrett at July 29, 2009 at 5:38 pm #

    Scotty. I agree completely that logic is better at tearing down arguments than at building them. But I do think that there are stronger and weaker logical paths to get us from a desire for outcome A to a project B that will actually deliver that outcome. Scientifically, we do that by observing a correlation between similar projects and similar outcomes in other places, while understanding that similarity will always be a matter of degree and open to debate.
    But I would also argue that if (unlike climate change) we are talking about something like real estate value, which is fundamentally an aggregation of what a lot of people think, it’s logical to ask “is this value based on a lot of people thinking something that’s just untrue (e.g. streetcars are a mobility improvement)?” Because if so, there’s a danger that at some point in the future, the truth may become apparent to more people.
    Personally, I don’t think for the moment that the value of land in the Pearl District is going to crash as people discover that the streetcar isn’t especially fast or reliable. The Pearl District’s real virtues are in all the things you can do just by walking.
    But knowing what I know as a transit professional, would I spend more for a condo on a streetcar line than for an identical condo in an identical neighborhood on a bus line? No, I personally wouldn’t do that. I’d judge the latter as the better long-term investment, because it’s more likely to be underpriced right now due to the prevalence of disapproval about buses, and the likelihood that the bus experience will continue to improve.

  7. Jarrett at July 29, 2009 at 5:44 pm #

    The citations aren’t ready to hand, but I suspect you’ll find something about this if you research the LA Metro Rapid, which raised the quality of limited-stop service over local-stop service on the same line. There’s probably data on the degree to which the rapid stops drew customers from further.
    I think you could also construct a fully-informed-rational-actor model to assess how far you should be willing to walk to a Rapid stop in order to optimise your overall trip time. It would certainly show that you should be willing to walk further to a rapid stop than to a local stop.
    And of course there’s a lot in the literature about rail rapid stops drawing from as far as 1 km (obviously this is a hazy edge, as different people have different threshholds). From the rail data, you’d just need to decide how much of that attraction is about rail as opposed to the mobility rail provides. My inclination is always to assume the latter, but that’s partly an extrapolation from how I make decisions as a fully informed rational actor who likes walking, and shouldn’t be the last word.

  8. Michael July 29, 2009 at 6:09 pm #

    I think your point here isn’t really about logic so much as it is about doing careful evaluation of options. Technology A leads to outcome B but isn’t very good at it, whereas technology A’ ….
    There’s a lot hiding in a statement like “If I want to avoid getting stuck in traffic, I want a monorail.” As I said, it’s a matter of judgment whether monorail is the right way to avoid getting stuck in traffic, and such a statement is the end result of a process involving reason and emotion — it is not the logic itself. So whether it’s logical depends on how well that process was carried out.
    I think the main problems lie not in the kind of reasoning people engage in, but in how accurately they weigh the costs and benefits and how well they predict practice from theory.

  9. Ed July 30, 2009 at 1:51 am #

    How much of the development around streetcar lines in Portland and Seattle was the product of subsidies? Have we seen development follow the introduction or re-introduction of streetcars in areas that didn’t subsidize this redevelopment? Does land next to buses or brt lines attract the same level of subsidies? If not why not?
    Do federal or state programs increase funding if there are rail lines involved? Or is the decision to redevelop purely a local one and the locals end up pushing the transit oriented development along the rail lines to pump up ridership numbers along the rail lines?
    Lastly are any of these newer street car lines going through areas outside the CBD? Are streetcar lines a pretext the downtown interests use to get government subsidies for the CBD?

  10. Jarrett at July 30, 2009 at 2:09 am #

    Good questions, Ed, which I’ll leave to the streetcar experts on the thread. At least in Portland’s case, the capital funding flowed the other way: an assessment on property owners along the route provided a large chunk of the money to build the Portland Streetcar. However, tracing the ongoing flows of subsidy and government preference that affect rail vs bus outcomes can be the work of a lifetime …
    Funny thing, this wasn’t a post about streetcars originally … but somehow we keep coming back there …

  11. Jennifer July 30, 2009 at 8:26 am #

    Hm, this whole discussion reminds me of this cartoon.