Norman Geras has written a response to my post about Richard Dawkins. This is my reply to him.
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Britain’s top political commentators last week descended on Richard Dawkins with all the careful analysis of a flock of vultures.

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Most of the concern about the government’s proposed ID card scheme stems not from the cards themselves, but from the enormous pool of centralized information which would underlie them. Plenty of suspicious minds believe that this is actually the real purpose of the plan.

But if Gordon Brown wants access to a vast system of interlinked databases, containing the personal details of millions of people, wouldn’t it be cheaper and easier for him just to join Facebook?

It’s gedankenexperiment time!

Suppose mafioso A pays hitman B to kill politician C. Is B any less a murderer than if he’d committed the crime off his own back? Obviously not: he’s 100% guilty. But does it follow that A is not responsible for the killing? Again, clearly not: it was his actions and his intentions which led to the politician’s death, 100%. But what if A decided to kill C because of informant D, who tipped him off about C’s planned crack-down on organised crime. Then doesn’t D also deserve some blame for C’s death? And if so, does that lessen the guilt of either A or B? Again, and of course, no.

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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. Read More