Monthly Archives: October 2006

In classical formal logic, every statement is either true or false: those which are false are precisely those which are not true. In the early 20th century however, constructivist mathematicians wanted to see how far they could get without this “law of the excluded middle” and began to develop new intuitionistic logics in which some statements are true, others false, and the rest neither true nor false. Though at first glance this may seem more mystical than mathematical, many years later, intuitionism remains the focus of a reasonable amount of serious scientific and philosophical interest.

Far less well-known is its eccentric younger cousin: paraconsistent logic. In most versions of this, the middle is again excluded, so each statement must be either true or false, but now some are allowed be both true and false. In all other systems this type of contradiction would spell immediate meltdown, but paraconsistent logic is built to cope with it: it is inconsistency-tolerant. Read More

When I’m feeling cheap, which has happened a lot lately, I shop at Asda. (I know, I know, but they’re all bad in their own ways.) The most pleasant way there, not that there is a great deal of choice in routes, is down Clive Lane, which is marked on maps, though it’s really a back alley between Clive Street and the railway, and its few doors open to pocket gardens and garages. Maybe it justifies having a name because a handful of these appear to be commercial, not that they stretch to anything as dignified as name signs. A few weeks ago, I was walking down there and the way was blocked with vehicles. This doesn’t usually happen as it’s not neighbourly to bar egress to someone’s house. As I approached I realised that the main culprit was an ancient, almost antique car, which four people started to push out of the way. Once I got through, I found I’d strayed onto a film set centred round a lock up which could give a bad name to dilapidation. The car was heaved into a side street (not for my benefit; they’d clearly done with it), people stood behind cameras and lights, and others sat in folding chairs. The nearest one said something – he had an American accent and I recognised him. The last time I’d seen him was on a YouTube video where he sang Springtime for Hitler. I thought about mentioning this, but I realised that it was probably a lot more recent for me than for him. So I said nothing, looked about a bit and went on.
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In today’s Britain, the ability to think logically appears to be under serious threat. This is most apparent when browsing sections of the blogoball* and when listening to our politicians.

Here’s a non-specific example of a particularly common error. Let’s say that A is a defined characteristic or experience and that X is a particular act. We do a study and discover that every single person who commits act X has first conformed to characteristic A. Can we conclude that characteristic A causes act X?
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Thomas Paine once wrote:

Every age and generation must be free to act for itself, in all cases as the ages and generations which preceded it. The vanity and presumption of governing beyond the grave is the most ridiculous and insolent of all tyrannies. Man has no property in man; neither has any generation a property in the generations which are to follow.

This precept is of course routinely flouted by governments, generally in the interests of short-term gain. In particular, the current UK administration has a track record of allowing the national interest to be decided by private commercial interests in such a way as to place future generations at risk. Now, the results of the government appointed review of options for long term storage of high level nuclear waste look set to add bribery to connivance in the list of their misdemeanours.

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