Sound and Fury

When I went for an interview at Oxford for my undergrad degree one of the things we had to do was a kind of logic test. It had things like “All men wear hats, some men wear ties” and you were asked what it was possible to conclude from that. Presumably they were looking for something like “Some men wear ties and hats”. One of the questions was “Most men wear ties, most men wear hats”. I said that it wasn’t possible to conclude anything from this. But it was then explained to me that if hat-wearers and tie-wearers are both in a majority, then there must be some who are both: the proper conclusion is that “Some men wear ties and hats”.

“All men” is standing in for the universal quantifier (x) and “Some men” stands for the existential quantifier (Ex). But “Most men” is awkward to put in similar terms without resorting to some sort of logic enriched with predicates relating to numerical proportions. But that sort of “statistical logic” is too complex. The fact that some predicate applies not to all but to a majority of some domain is an easily understood fact that does not need a whole logic of proportions behind it. Let’s make “Most of” a new kind of quantifier: (Mx). What properties does (Mx) have?

This is the property my interviewer at Oxford was exploiting. If most x’s are P’s and most x’s are Q’s, then some x’s must be both.

These two properties simply say that if all men wear hats then most men wear hats and if most men wear hats then some men wear hats.

Do we really need a third quantifier here? Is there some way to express “most of” in terms of universal and existential quantifiers? I’m not sure there is. Here’s a first stab. When you say “(Mx)Px” what you are really saying is:

But that’s no good, because that expression still contains an “Mx”. We are kind of going beyond standard predicate logic, but only a little bit. Perhaps Mx shouldn’t be a quantifier, but a property of predicates? But I don’t think that is a particularly satisfying suggestion. A property of predicates would be a third-order entity, and that seems extravagant given the modest goal of formalising the easily understood concept of a majority.

Soon I’ll post again and discuss the “dual” of (Mx): “Only a few men wear hats” “Hat-wearers are in a minority”.

A note on the symbolism: I wanted to use and but I couldn’t think of a way to “invert” the letter “M” in a similar fashion. It shares the vertical symmetry of “A” but when reflected around a horizontal axis as is, you get a “W”, which is no good if the idea is to come up with a new symbol. So I reverted to old-style quantifiers. Suggestions regarding how to “symbolise” majority are most welcome.

It’s about time I weighed in on the ongoing “MP expenses scandal”. First, the outrage seems a little disproportionate to the amount of money involved. If you want to be outraged by massive wastes of the taxpayers’ money, be outraged at the bank bailouts, the trident replacement, the ID card scheme, the “super-database” or something in that vein. (If you consider all of the above reasonable and proportionate expenditure, I’m there’s something else shockingly expensive you’d want to add to the list…) Or how about being outraged by the demented profligacy of the European Parliament decamping to Strasbourg for four days a month simply because the French won’t give it up. We* pay for the upkeep of a building in Strasbourg which is empty most of the year. We also pay to have the 600-odd members of parliament shipped down to Strasbourg from Brussels along with various aides advisers and so on. We also put them up in hotels for the few nights they are there. That is madness. The current expenses fallout is small fry, all things consdered.

But what does bug me is the insistence by the MPs that they were acting within the rules. This is a morally bankrupt way to justify actions that are clearly wrong. Regardless of whether it really is the case that the expense claims under scrutiny were acceptable given the current wording and structure of the rules, the claims should not have been made. Whether or not the claims conform to the word of the law, they are emphatically at odds with its spirit. People who cannot make this elementary distinction should not be in government. The illegality or otherwise of the MPs actions is not what is at stake, it is their moral authority that has been undermined and that is more worrying.

On a related note, here is another reason I don’t want David Cameron to be Prime Minister. A quote from the leader of the opposition in today’s Guardian:

We have to acknowledge just how bad this is. The public are really angry and we have to start by saying “Look, this system that we have, that we used, that we operated, that we took part in – it was wrong and we’re sorry about that.”

It’s not the system that is at fault here, Mr. C. It’s the people abusing it. Of course, the system is faulty if it is open to such flagrant abuse and it does need reform, but that is not why people are angry. People are angry because their elected officials, those people who are supposed to be representing their interests are exploiting the system to line their own pockets (or furnish their own homes…) What Cameron is trying to do is deflect anger away from himself and his party and turn peoples’ outrage on the current expenses system. But people aren’t angry with a system that allows abuse. No system is perfect. Why this affair has provoked so much anger is because it shows politicians engaging in what is effectively benefit fraud. These people are not fit to be in charge and that is true of the Conservatives as well as Labour (and possibly all the other parties too, I haven’t read anything about Lib Dem or SNP or whatever…). How are we to accept new laws, new databases, new intrusions of our privacy as being for “the greater good” or “in our best interests” when the people who come up with these schemes are dishonest and fraudulent. Lord Naseby apparently suggested that the public’s confidence in parliament has been so damaged that it should be dissolved and new elections held. But that wouldn’t solve the problem, I don’t think. I’m not sure what could, since it seems the skills needed to get elected are not the same skills as the ones that make someone a good representative, a good decision maker or a good leader.

That said, I’m sure many of the expenses claims have been portrayed in a way so as to make them seem maximally suspicious and with little or no right to reply. At least some of the supposed “dodgy” claims are probably legit. What is worrying is the sheer number of dubious expenses claims that seem to be flying around. Some of them surely have to be dodgy, I suppose…

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* By “we” I mean taxpayers in EU states. Though as a student I probably contribute so little tax money that my outrage is unwarranted, as it’s not really my money they’re wasting…