A but B or B but A?
Ever since I took formal logic, I’ve been fascinated by the way in which logically irrelevant changes in phrasing totally alter the understood meaning of a phrase. Cato’s Chris Edwards, for example, writes:
Many highways are congested, but at least on the East Coast where I travel, states seem to be continually adding capacity.
I learned in QR-22 that “A but B” is logically equivalent to “A and B” and also that it’s transitive to “A and B” is the same as “B and A.” In terms of Edwards’ observation, someone familiar with induced demand would say something like:
East Coast states have been adding highway capacity, but the roads are more congested than ever.
Edwards’ formulation emphasized the (mistaken) idea that continuing to add capacity will alleviate the problem, whereas my formulation is designed to highlight the fact that the problem has consistently worsened despite past capacity additions. The difference being, of course, that I’m right and Edwards is wrong. Space on East Coast highways is a precious commodity and pricing it at $0.00 at peak-demand time guarantees congestion. Additional capacity will ameliorate the problem only very temporarily as the newly uncrowded highways will encourage people to drive longer distances (re-equalizing the amount of time they’re willing to drive) and spur additional development until things get locked up again. The way to alleviate congestion in crowded areas is through congestion pricing — putting a price on access to the roads at peak times.
41 Responses to “A but B or B but A?”
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October 25th, 2008 at 12:42 pm
Impressively nerdy set of posts today, Matt. Set theory, epistemology, and now formal logic in consecutive posts. Well done.
October 25th, 2008 at 12:55 pm
That post isn’t about congestion Matt. He’s making the point that governments seem to be already spending a large quantity of money on infrastructure, so he doesn’t see the case for more public money spent on it.
Moreover, he advocates at the end of the post to privatize as much of the infrastructure as possible, which would be putting a price on it.
Really sloppy of you.
October 25th, 2008 at 12:57 pm
here in san diego, the best model for freeway traffic is
of a fluid flowing in a channel. No matter how
much you widen the channel, enough fluid will flow
to fill up the width.
October 25th, 2008 at 12:57 pm
The breakdown of truth-conditional semantics in action.
Cognitive linguistics (as a field generally) is equally fascinated by such “logically irrelevant” changes in phrasing (and the construals underlying them).
October 25th, 2008 at 1:17 pm
also that it’s transitive
I think this should be “symmetric.”
October 25th, 2008 at 1:20 pm
Congestion pricing can increase pareto efficiency (i.e. make someone better off without making anyone worse off) but pro-transit progressives take this concept too far. They assume that congestion pricing will eliminate the need for extra capacity when all it does is make the present highway capacity more efficient. For instance, if there were only one bridge out of Manhattan congestion pricing would make people better off (if implemented correctly) but even if pareto optimality exists for this one bridge a second bridge could still increase overall utility. And no Edwards’ A and B comment does not imply your slightly different B and A comment. And while his comment may not be entirely correct if the benefits of more roads are increasing (i.e. because of population or economic growth) then increased capacity might make sense (even with congestion pricing).
October 25th, 2008 at 1:27 pm
Again, this is a rather self-serving argument for a non-driver to make, is it not? A massive (by necessity: the pain is the point), metered tax on people who use different modes of transportation than you– many of whom lack any alternative?
Free Roads + Moderate Congestion > Metered Roads – NoCongestion
I’m with you on reducing road subsidies, reducing parking requirements, improving light-rail infrastructure and creating denser, potentially mixed-use zoning. But I continue to resist the idea of actually taxing mobility.
October 25th, 2008 at 1:33 pm
It sounds like Chris Edwards could benefit from reading Robert Caro’s magisterial biography of Robert Moses. In fairness, I recommend it to everyone; it’s an awesome book.
October 25th, 2008 at 1:34 pm
This is why I believe that Fogelin’s book on informal logic is a more important resource to philosophy majors than formal logic. Rhetoric and logic should be taught together.
October 25th, 2008 at 1:36 pm
You are right about the logical equivalence of “but” and “and”, but your reformulation of Edwards’s sentence adds terms he did not use. He did not say the roads were “more congested than ever“, he only said some roads were still congested. So your version would have to be:
“East Coast states seem to be adding highway capacity, but some highways are still congested.”
That does not obviously imply that expansion is the reason for the congestion; one might more reasonably infer that the expansion has simply not gone far enough. (Consider a parallel example: “The workers seem to be adding more shingles to the roof, but some parts are still uncovered.” The obviously conclusion is simply that they haven’t finished the job yet and ought to continue doing what they’ve been doing.)
This is not a counter-argument to your point about induced demand. I simply point out that restating Edwards’s claim also does not support your argument for congestion pricing. You did not merely reverse the clauses of the sentence, but made one much stronger by increasing its scope from the particular (”some”) to an implied universal, which is not a correct reading of what Edwards said, either directly or by implication.
October 25th, 2008 at 1:41 pm
Back when I worked in a local government planning office, the transportation planners used to have a rule-of-thumb: Increase highway capacity by 10%, and traffic increases by 15%. And they meant this in a causal sense–more capacity caused more traffic.
October 25th, 2008 at 1:52 pm
Don’t be stupid.
It is easy to conceive of the east coast where you add so much capacity that the roads are no longer crowded.
If you wipe out Central Park and pave it with 40 cross town 6 lane highways then the roads would not be crowded until they got to 5th of CPW.
If you make each avenue stack 3 or 5 or 30 bridges on top of each other then it wouldn’t be hard to imagine being able to go from 57th Street to Wall Street at 50 MPH.
The flaw with this logic is that you would probably destroy any reason for being south of 96th street if you increased the miles of roads by a factor of 30. It would also be far too expensive to even consider adding 20 additional lanes above 5th Ave.
Seriously, I agree that it isn’t practical to build our way out of road congestion. I think the best answer is a combination of congestion pricing and expanded bus capacity.
October 25th, 2008 at 2:11 pm
A third way of looking at it is to say that “but” is not “logically irrelevant” the way introductory formal logic courses taught in philosophy departments tell you it is.
October 25th, 2008 at 2:23 pm
I think this is partly a case where formal logic is failing to capture the meaning of these words as conventionally used. If I say “McCain is a Republican, and Sarah Palin is a Republican”, it is a banal truth. But if I say “McCain is a Republican, but Sarah Palin is a Republican”, it is either: a) a non sequitur, or b) something given additional meaning by context or emphasis (as in: “McCain is a Republican, but Sarah Palin is a Republican“). In common usage, “A and B” means (A is true) and (B is true), whereas “A but B” means (A is true) and (B is true) and (the truth of B modifies the significance of the truth of A).
October 25th, 2008 at 2:48 pm
a) There is lots of traffic, so let’s reduce it by adding highway capacity.
equals
b) College kids are gettting too drunk at keg parties – So let’s add more kegs to the parties so they won’t crowd
the limited kegs and binge drink.
October 25th, 2008 at 2:50 pm
Matt,
I’m not against the idea of congestion pricing, but I wish you would stop saying that access to space on the highways is “[priced] at $0.00 at peak-demand time.” There may be zero monetary cost imposed, but the costs in time, hassle, and gasoline usage are significant. Practically speaking, these non-monetary costs already serve as a significant deterrent to peak highway usage. They affect the choices made by consumers of the highways.
This observation doesn’t prove that the additional deterrent of congestion pricing wouldn’t help solve the problem. It might help, and it deserves consideration, but pretending that driving on congested roads currently has zero cost just because none of the costs are currently imposed in the form of congestion-sensitive access fees distorts the psychology and economics of the real-world situation. I don’t see how such distortion is helpful.
October 25th, 2008 at 2:55 pm
The only thing I learned from formal logic is that “P hook Q” means “P hook Q” and nothing else. It bears no reference on the nature of flowers in May, the true meaning of life, the cause of my tummy ache, or the state of East Coast transportation.
Aristotelean logic, however, at least purports to have such reference. But then one also would have to study Aristotelean grammar and rhetoric – neither of which I recommend.
October 25th, 2008 at 3:09 pm
Additional capacity will ameliorate the problem only very temporarily as the newly uncrowded highways will encourage people to drive longer distances (re-equalizing the amount of time they’re willing to drive) and spur additional development until things get locked up again.
The same claim could be made about adding transit capacity to relieve congestion on standing-room-only bus and rail services. For some strange reason, Matthew never seems to make this argument.
Whatever induced demand effect there may be, there is obviously a point at which the added capacity will outstrip the increase in demand, at which point congestion will go down.
I’m with you on reducing road subsidies
Given that highway subsidies are only around $5 per thousand passenger-miles (as opposed to around $400 per thousand passenger-miles for transit), reducing highway subsidies probably wouldn’t do much to change usage. It’s not terribly viable politically, either.
October 25th, 2008 at 3:17 pm
a) There is lots of traffic, so let’s reduce it by adding highway capacity.
equals
b) College kids are gettting too drunk at keg parties – So let’s add more kegs to the parties so they won’t crowd
the limited kegs and binge drink.
Since the problem here is congestion and not “traffic,” not terribly relevant.
If the partygoers are having to wait in line for 10 minutes to get a drink because of the limited number of kegs, adding more kegs will probably reduce the wait time.
October 25th, 2008 at 4:58 pm
I am going to have to agree with Jeff. His post doesn’t seem to say what Yglesias thinks it says. Yglesias is probably right about congestion pricing though and Edwards is probably wrong about privatizing road infrastructure. In a fantasy world private competition would satisfy our transportation needs, but in the real world that takes government.
October 25th, 2008 at 5:09 pm
@ Martin Bento:
Your “conventional definition” of “but” seems true:
“A but B” means (A is true) and (B is true) and (the truth of B modifies the significance of the truth of A).
But this is a case where the truth of B does notmodify the truth of A. Formal logic may “(fail) to capture the meaning of the word as conventionally used,” but mindfulness of this helps in spotting those cases where the “conventional usage” of the word provides the illusion of connection (or whatever) when there isn’t one.
October 25th, 2008 at 5:31 pm
(facepalm)
Too bad you didn’t learn what the word “transitive” means. Please don’t post any further on mathematical topics. You look stupid.
October 25th, 2008 at 5:54 pm
E. Floyd. Not quite. Evaluating the statement under the definition I gave and testing against other facts, shows it is misleading. As you say, the common implication of “but” is not true, but one determines lthis by looking at the common implication of “but”, not the formal logic definition. In terms of formal logic, there is not problem, just a statement of two independent truths. The misleading quality can be demonstrated without bringing the formal definition into the discussion, but not without the conventional definition in.
October 25th, 2008 at 8:43 pm
The same claim could be made about adding transit capacity to relieve congestion on standing-room-only bus and rail services. For some strange reason, Matthew never seems to make this argument.
That’s because increasing transit use is a good thing. Also, how many standing-room-only bus and rail services do you know of? Transit use for the most part is below capacity (the exceptions being large cities during rush hours), so an increase in ridership is not going to cause significant strains on the system.
Given that highway subsidies are only around $5 per thousand passenger-miles (as opposed to around $400 per thousand passenger-miles for transit), reducing highway subsidies probably wouldn’t do much to change usage.
An increase in transit ridership will reduce the per thousand passenger-miles cost of transit, because an increased number of passengers will increase the number of passenger-miles. A far greater number of people use highways, which is why the cost of the subsidies appears to be much smaller, while in reality, highway spending far outstrips transit spending.
—
Personally, I would like to see reinvestment of money that would be going to capacity expansion projects into projects to repair the existing infrastructure. What good is another two lanes if the existing four are falling apart?
October 25th, 2008 at 9:22 pm
Luthe,
That’s because increasing transit use is a good thing.
No, it’s because of Matthew’s personal preference for more transit use. Just because you personally prefer something doesn’t mean it is “a good thing.”
Also, how many standing-room-only bus and rail services do you know of?
Huh? Many bus and rail routes are very congested (”standing room only”) during peak travel periods and uncongested at other times. Just like roads. If expanding road capacity isn’t a solution to road congestion, why is expanding transit capacity a solution to transit congestion?
An increase in transit ridership will reduce the per thousand passenger-miles cost of transit, because an increased number of passengers will increase the number of passenger-miles.
That doesn’t follow at all. If an X% increase in passenger-miles would require an X% increase in capacity, the cost per passenger-mile won’t go down at all. To reduce the per passenger-mile cost you have to increase efficiency. And you’d have to achieve a truly staggering increase in transit efficiency to allow transit subsidies to be reduced to a level comparable to highway subsidies. How do you propose to do that?
October 26th, 2008 at 6:31 am
Or commutative.
October 26th, 2008 at 6:49 am
Tolls kill. Digging in your cupholder for a quarter is no way to get run over by an 18 wheeler.
October 26th, 2008 at 10:19 am
I actually like the toll roads in my area near NYC. I find a drastic difference in how much time I spend in traffic when compared to the areas around DC. The key test of this for me would be the Balt-Wash. Slap a $5 toll on it and see what happens. I am always stuck there, delays last days, and it gets painful with no facilities actually on the thing (always two miles down the exits).
October 26th, 2008 at 11:14 am
Matt, you should stop making flip comments and investigate the real evidence for induced demand. I realize it’s an article of faith among the NPR set, but the actual evidence is much weaker than you think. There’s really very little (I would say no) real support for the strong version of induced demand, that new roads cause so much demand that they lead to no net improvement in transporation speeds.
October 26th, 2008 at 7:04 pm
Early comment says “…here in san diego, the best model for freeway traffic is of a fluid flowing in a channel….” I’m in the Bay Area and would argue the model should be marbles – not fluid – in a funnel: at some rate of addition of marbles, the flow will choke up. Freeways are also choked by the inability to move traffic off a highway into city streets and parking places. I’m for congestion pricing as policy, but personally, I’ve arranged my life so I don’t commute anymore.
October 26th, 2008 at 10:03 pm
I was 8 once.
October 27th, 2008 at 1:22 am
Congestion pricing is already in effect in Boston and Chicago, I-90 in both places is subject to a heavy toll. I know in Boston, the toll is so high that I avoid the turnpike and take alternate routes, so it does indeed reduce congestion on the Turnpike. The tunnels and bridges betwen NYC and NJ also have heavy tolls, which undoubtedly reduces the amount of traffic.
It’s a proven principle, there’s no doubt about it. The only questions are those of logistics and figuring out how much to charge.
I think it’s funny how people who are otherwise gung-ho capitalists, fail to see how the capitalist solution solves this problem. They revert to their “socialist” beliefs that the roads should be open to all. Quite odd, indeed.
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