August 27, 2012

The Tow Truck Puzzle

Filed under: Philosophy — camcintosh @ 1:35 pm

Imagine a tow truck towing a tow truck. Now imagine the tow truck being towed is itself towing a tow truck. Keep adding to the series until we have enough to form a circle of tow trucks, all connected to each other (for any two trucks in the series, I am imagining the cable from a prior truck lifting the front of a posterior one). The question: are any tow trucks being towed?

To get at the question, let’s stipulate that two necessary conditions for towing are:

(i) There has to be at least one active member (doing the towing) and one passive member (being towed) in the series
(ii) Any passive member has to move uniformly relative to any active member

I. Yes, there is towing
Given the nature of the situation, transitivity seems to rule this option out. For example, let’s say there is just one active member towing, and the rest are passive. If we have a series that connects to form a circle, condition (ii) entails that the whole series is moving uniformly, or each member in the series is moving uniformly relative to the others. But if the series is moving uniformly, we could say with equal force that the active member is either being towed by the truck in front of it or pushed by the truck behind it. This is true no matter how many active or passive members are in the series, so long as (i) and (ii) hold.

II. No, there is no towing
I take this to be a violation of the clear ostensible fact that there is at least some towing going on.

Furthermore, nothing seems logically, metaphysically, or nomologically impossible about the situation, which is the case with most instances of circular causation.



  1. You posted this on your old blog. I don’t remember if I commented, but I’ll go ahead and comment here.

    Are all the tow trucks front wheel drive? If this is the case, then none of them would move according to your scenario. If not, are all of them rear wheel drive? If they are, then any truck being towed would be lifted by it’s rear wheels. This, however, does not fit your scenario.

    Let’s assume for the sake of argument that the tow truck driver’s weren’t professionals and that although all of their trucks are rear wheel drive, they lifted the front wheels of the posterior truck (so as to satisfy your scenario). This would remove steering from the equation and this is a physics problem. The drive (rear) wheels on the active member of this group would constantly be propelling the truck in a straight line (not a circle). The towing of it’s own front end through the series of other trucks will become irrelevant and a kink will be introduced. This could be overcome by all of the trucks but one being active, but I’m not sure of the affects that this would have or the effects that it would produce.

    Ultimately, I think this is a scenario worthy of Mythbusters as the setup is certainly plausible in the sense that you can physically connect tow trucks in this manner, but I don’t think that you could achieve a situation in which the “series was moving uniformly.”

    Comment by Christian Penrod — August 27, 2012 @ 2:00 pm | Reply

  2. Three points:

    Condition (ii) is not a necessary condition for towing. Consider any ordinary instance of towing. When the vehicle being towed is hanging from the vehicle towing it and the vehicle doing the towing begins to accelerate (thus exerting force on the vehicle being towed) then there is towing occurring but no uniform motion (the towing vehicle is moving faster than the vehicle being towed).

    Condition (i) is not necessary either if you accept that in your described scenario (a scenario in which all vehicles are moving uniformly relative to one another) the ‘no tow’ answer is not available (due to the ostensible fact that towing is occurring). Here’s why:

    Consider any ordinary instance of towing. Imagine the two vehicles (the one towing and the one being towed) are travelling down a straight and level highway (no slope up or down). Furthermore, at time t the operator of the tow truck removes his foot from the gas pedal, thus initiating deceleration. At some point during the process of deceleration both vehicles will be moving uniformly relative to one another (they will reach the same speed), this is a physical fact.
    For example, say the tow truck operator removed his foot from the gas pedal when the vehicle was travelling at 65mph. When the tow truck reached 60mph (about 10 seconds later) let’s say that the vehicles were moving uniformly relative to one another (both travelling at the same speed in the same direction). At this point no force is being exerted on the vehicle being towed by the truck doing the towing AND no force is being exerted on the tow truck by the truck being towed. Since, as you write, towing must be going on (it’s an ostensible FACT!) then condition (i) is violated. Why? Because there is no active member exerting force and yet towing is occurring.

    Finally, assume your scenario and the veracity of your necessary conditions for towing, it is not clear that towing is really going on. You call the fact of towing both ‘clear’ and ‘ostensible’ but it seems more likely that there is a mere appearance of towing. If the scenario described were to obtain then it seems more sensible to say no towing is going on (though there is an appearance of towing) then to say (as you do) that towing MUST being going on AND the physics we would expect to obtain if towing were going on in the scenario DO NOT obtain.

    Comment by NorthCarolina — August 27, 2012 @ 2:30 pm | Reply

  3. Interesting comments, but many of the points made are irrelevant. The thought experiment can be tweaked to accommodate concerns about back wheel drive, steering, cables, etc: replace tow trucks with train cars, where you have at least one engine and at least one cattle car, connected not by a cable, but a strong swivel bar of some sort. This simple modification, I think, takes care of Christian’s points, and several of NC’s.

    If I understand NC’s proposal, a “coasting scenario” provides a counterexampel to (i): if we have one tow truck towing another, the latter moving uniformly relative the former, it’s possible that they can both coast along with neither assuming a passive or active role, yet there is still towing. Response: There is no towing in a coasting scenario, despite appearances. There is only coasting. Therefore, this is not a counterexample to (i) as a condition for towing.

    Therefore it seems most plausible to say, going along with NC’s last suggestion, that despite appearances to the contrary, there is no towing going on. This would just be an interesting case of appearances being deceptive, or defeasible intuitions or appearances.

    Comment by camcintosh — August 27, 2012 @ 3:34 pm | Reply

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