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Read about all the problems with reason in our special issue

DO WE know for certain that 2 plus 2 equals 4? Of course we don鈥檛.

Maybe every time everybody in the whole world has ever done that calculation and reasoned it through, they鈥檝e made a mistake. Maybe it isn鈥檛 4, it鈥檚 really 5.

There is a very, very small chance that this has happened. But now I am talking about probabilities: I am using mathematics again, on the basis that it makes sense in the first place. So my reasoning is circular and, as often happens, you have to stand back and ask, well, what is reasonable?

We have to distinguish this question from pure Reason 鈥� with a capital 鈥淩鈥�. Philosopher David Hume notoriously argued, applying the rules of that formal Reason, that induction is impossible: however often we add 2 to 2 and get 4, that does not logically tell us anything about the result next time. And doubt does permeate all our reasoning, or should. But at some point we have to stand back and ask what is reasonable 鈥� with a small 鈥渞鈥�.

When we ask what is reasonable from our direct experiences, we are finding and applying general rules about behaviour which are consistent. In mathematics we demand absolute formal consistency. But often, even when you鈥檙e doing mathematics, you explore something by trying to prove it, get stuck, and say, oh, maybe it鈥檚 not true, and look for a reasonable path for your next round of applying pure Reason.

The mathematician Kurt G枚del went through a process like this as he destroyed any hope that formal Reason could be universal. In 1900 David Hilbert proposed that we should build the whole of mathematics on formal, logical rules. But in 1931 G枚del showed that if you have any set of trustable rules that are computationally checkable (a machine could go through them and see whether you鈥檝e applied them correctly), then statements exist that you have to accept as well, according to the rules, but that you cannot arrive at by means of those rules.

G枚del used the word 鈥渋ntuition鈥� to describe how you get to those statements. For me, that word has connotations which are not quite appropriate: I鈥檇 say we need understanding and insight. G枚del鈥檚 result is one of the things some people correctly use to pick holes in Reason. Another is the very unreasonable behaviour of quantum mechanics where, for example, particles seem to be able to be in two places at once. This doesn鈥檛 match our normal experience, so we say it鈥檚 unreasonable.

鈥淨uantum mechanics is one thing people use to pick holes in Reason鈥�

Personally, I think there is something not quite right about quantum mechanics. And quantum mechanics seems to be to blame for some people who鈥檇 like to be exempt from Reason being able to say: 鈥淪cience is full of these contradictions and unreasonableness 鈥� and so I can more or less say anything.鈥�

You had people saying we shouldn鈥檛 turn on the Large Hadron Collider experiment because a small probability exists that it might create black holes that would annihilate Earth. Sensible scientists say that this is ridiculous, there鈥檚 no chance. On the other hand, there鈥檚 a small chance that accepted theory is wrong, so there is a chance!

That鈥檚 one example of people putting unreasonable standards on being sure. Another is climate change. Most scientists say that the climate is changing and it鈥檚 changing for quite clear reasons 鈥� because we are pumping in all this carbon dioxide, for one. There鈥檚 no puzzle, we can see it happening, and we can see why it鈥檚 happening. But a few don鈥檛 agree. True, sometimes the small minority turns out to be right. But it doesn鈥檛 mean you should do what the small minority say. The majority is a majority for good reasons.

To me, Reason is essential for human discourse and all forms of enquiry, whether legal or scientific or mathematical. It is absolutely central. But we have to be reasonable about it.

Read about all the problems with reason in our special issue