Brave New Logic

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 20^th 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.

 

Though this avant-garde logic is intriguing, surprisingly coherent, and has applications in both the foundations of mathematics, and in computer science, the problem is that it seems to lack a natural model. Some people have suggested, not entirely persuasively, that it might be used to handle wave/particle duality in quantum physics, or to provide a means of resolving self-referential conundrums, such as the liar paradox.

I’d suggest that the best model for this peculiar new logic is New Labour: paraconsistent to the core, it both is, and isn’t a Labour government.

For an example of paraconsistency in policy-making, take the recently announced plans for the labelling of homeopathic medicines, which may read “Contents: 100% water. This product can be used in the treatment of lung-cancer”. Which of course it can, despite all the evidence saying that it can’t.

A paraconsistent approach also provides neat resolutions to the major questions of the New Labour era. For instance: Did British foreign policy cause the 7/7 bombings? Well no, obviously it didn’t. And yes it did.

Because it is specifically designed to withstand it, this whirl of contradictions needn’t entail the collapse of the whole party machine, or even indicate any problem whatsoever. The system is simply functioning as it was intended to. New Labour is inconsistency-tolerant.