Advantages of Using Logic

ADVANTAGES OF USING LOGIC

One of the main reasons to have a clear framework for accessing truth is to be able to agree about things. This seems very radical in a world in which people seem to revel in disagreeing with other people as much as possible. And it even happens in sport, when fans get angry with a decision that a referee has made, although the referee is supposed to be simply applying the agreed rules.

I remember watching the Oxford–Cambridge boat race one year when the boats clashed dangerously, and Cambridge was penalised. As a Cambridge person I was outraged because it looked to me that Oxford had obviously veered into them deliberately, so it looked like Oxford’s fault. I thought the referee was in a conspiracy with Oxford and was being biased. However, instead of railing against this assumed conspiracy I looked up some expert commentary to try and understand what had happened. I learnt that during the race up the river Thames, an imaginary line is drawn along the middle of the river, and each boat has priority on their side of the river. This means one boat can leave a lot of space, perhaps when taking a bend, and “lure” the other boat across the line. Then the boat with priority can deliberately veer into the boat that crossed the line, knowing they won’t get the penalty. Is it morally right? Who’s fault is that, really? We’ll unravel questions of blame and responsibility in Chapter 5.

This idea of a clear framework for reaching consensus is also a bit like how medical diagnosis works. The medical profession tries to make a clear checklist so that a diagnosis is unambiguous, and so that diagnoses are made consistently by different people across the profession.

The idea of logic is to have clear rules so that conclusions can be drawn unambiguously and consistently by different people. This is wonderful in theory, and perhaps here “in theory” means in the abstract world of mathematics. Mathematics has a remarkable ability to make progress. Philosopher Michael Dummett writes in The Philosophy of Mathematics:

Mathematics makes a steady advance, while philosophy continues to flounder in unending bafflement at the problems it confronted at the outset.

Why are mathematicians able to reach agreements about what is true? And why do those things remain true thousands of years later, where other subjects appear to be continually refining and updating their theories? I believe the answer lies in the robustness of logic. That is its great advantage.

There are also some disadvantages of the logical world. One is that you can’t win arguments just by yelling loudly. Of course, this is only a disadvantage if you like winning arguments by yelling loudly, which I actually don’t. But unfortunately plenty of people do, so they don’t like the logical world. And they don’t like the fact that in the logical world they can’t get the better of a small, soft-spoken, uncool person like me. Because in the logical world strength doesn’t come from big muscles, large amounts of money, or sporting prowess. It comes from sheer logical intellect.

Another disadvantage of the logical world is that you don’t really have your feet on the ground any more, because we’re no longer in the concrete world. It can sometimes feel like you’re floating around in mid-nowhere, but I find that this is quite a pleasant sensation once you get used to it. The key, as with putting the first human in space, is to be able to come back again. In this book we are not just going to float around in the abstract world for fun. We are going to come back to earth and use powerful logical techniques to disentangle real, relevant, urgent arguments about the state of society. We are going to show that accessing the logical abstract world enables us to get further in the real world, just as flying through the sky enables us to travel further and faster in real life. In essence, this is the whole point of mathematics.