Saturday, 20 February 2010

Rubbish logic

The city has decided to remove litter bins from the streets and lanes feeding commuters from their flats to my local underground station. The pen pushers and bean counters reckoned it was better that the locals should drop litter on the pavement than that the council should have to empty out litter bins overflowing with household rubbish.

There is a rubbish shed round the back of each house where people are supposed to take out their household rubbish. Rubbish collection rates are included in the monthly rent and rubbish collection is weekly or twice weekly.

It is all well and good when everyone has the time to take their rubbish out and put it in a skip inside the rubbish shed. The system usually works at weekends. On weekdays, though, few people have the time to make a special trip to the rubbish shed, usually requiring going in the opposite direction to one’s destination, when they are in a hurry to catch the underground or get in the car and join the race to the city. Instead of letting rubbish accumulate under the kitchen sink from day to day, people make up last night’s bin contents into a small bundle and take it along with them on the way to the car or the underground to be disposed of in one of the litter bins provided by the city.

The city has caught on to their game. Why should the city be paying to have people’s household rubbish taken away? Better to remove the litter bins altogether. The city can’t lose. Either the people will be forced to take out their rubbish to the rubbish shed, or they will deposit it in front of the entrance to their building or else dump it on the pavement. Of the latter two options, the first will sooner or later make it thoroughly unpleasant for all neighbours, who will take matters into their own hands, perhaps by naming and shaming the offenders, or the offenders will get into the crosshairs of traffic wardens patrolling the streets and be forced to pay fines. One nil to the city.

On an ungenerous interpretation, the city’s reasoning can be summed up like this:

If the city provides litter bins, people will dump their household rubbish in them.
If the city removes the litter bins, dumping will cease. Problem solved.

This is a fallacious argument (denying the antecedent), never mind the arrogance. It is a version of laissez faire economics: stand back and let the situation sort itself out. But since the city cannot defend itself (it is unlikely that it will) in these pages, let us be fair and let us redeem the city by pretending that the reasoning was somewhat like this:

If the city doesn’t provide litter bins, people will either dump their rubbish at the entrance to their building or dump it on the street. If they dump it at the entrance to their building, then their neighbours will intervene. If they dump household rubbish on the street, then the traffic wardens will intervene. If either the neighbours intervene or the traffic wardens do, then people will take household rubbish to the rubbish sheds. Therefore, if the city doesn’t provide litter bins, people will take household rubbish to the rubbish sheds.

This is actually a logically valid argument:
  1. ¬ P ⊃(E ∨S)
  2. E ⊃N
  3. S ⊃T
  4. (N ∨T) ⊃R
  5. ∴ ¬ P ⊃R
  6. * ¬ P / ACP
  7. * E ∨S / 6,1MP
  8. * (E ⊃N) • (S ⊃T) / 2,3Conj.
  9. * N ∨T / 7,8CD
  10. * R / 9,4MP
  11. ¬ P ⊃R / 6-10CP

Quad erat demonstrandum.

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