We cannot live by logic alone and here is why: logic can only connect axioms to conclusions so that either: if the axioms are true that the conclusion is also true, or, if the conclusion is false then at least one of the axioms is false. To get anywhere, we still have to judge whether we accept the axioms and/or the conclusion. We have a further problem when logic is used with natural language (as opposed to numbers or meaningless symbols) because we have to judge whether a word or phrase has kept the same mean through various logical manipulations.

In order to use logic in making decisions we have to judge how good various outcomes are. Logic may or may not help to give us the possible outcomes and their corollaries but it cannot help us decide on the criteria to use in ranking those outcomes.

So logic is a great tool. It is a tool that everyone should be taught how to use. Logic protects us from all sorts of folly. But it should never be someone’s only tool. Many people long for a system where logic and cost-benefit and game theory and utility and… as many formal methods as we can create are there to use. This means that they will not have to make those fuzzy judgments that can turn out to be wrong or second best. But it is not just logic that includes hidden judgments, it is all those formal methods.

I am reminded of this longing for impossible certainty by coming across a couple of recent things. One is the result of Boas Keysar outlined (here). He showed that people made more ‘rational’ decisions when they used a foreign language rather than their mother tongue. I presume that words and phrases in their mother tongue had more emotional baggage attached to them. They did not ‘do the math’ in effect but took the intuitive path to a decision rather that of utility theory. Even when the hypothetical situation is relatively simple, most people are unlikely (especially if they are hurried or have no actual stake in the outcome) to actually figure out the best answer according to utility theory.

I am what you would call a non-gambler. For me to gamble the bet has to be fun and the stack has to be low and very affordable. In other words, I am willing to pay a small amount for fun – for a ride, an ice cream treat, a game, a show or an entertaining bet. It has nothing to do with any prospect of profit. Give me a chance with very good odds to make a lot from a sizable stake, and I will probably turn it down. I am very risk-averse and happy to be so. When I hear of someone being taken in by a sure thing that turned out to be a scam, I think that is what you get for thinking that a gamble is going to be fair and that you can get something for nothing. Con men pick on the greedy and superstitious. I may have missed some opportunities but I will have avoided some traps. I have used my emotions and intuition. My emotions and intuitions are there to protect me.

Another example is the ‘problem’ of the prisoner’s dilemma. Here is Wikipedia’s description:

Two men are arrested, but the police do not have enough information for a conviction. The police separate the two men, and offer both the same deal: if one testifies against his partner (defects/betrays), and the other remains silent (cooperates with/assists his partner), the betrayer goes free and the one that remains silent gets a one-year sentence. If both remain silent, both are sentenced to only one month in jail on a minor charge. If each ‘rats out’ the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept secret from his partner. What should they do? If it is assumed that each player is only concerned with lessening his own time in jail, the game becomes a non-zero sum game where the two players may either assist or betray the other. The sole concern of the prisoners seems to be increasing his own reward. The interesting symmetry of this problem is that the optimal decision for each is to betray the other, even though they would be better off if they both cooperated.

A situation like this is only a problem if you take game theory seriously. To do what is in your own interest is to defect. To do what is in both of your interests is to cooperate. What is the choice? You cooperate. I am reasonable and intelligent and so is my partner and the best outcome follows us cooperating so that is what we will both do – no dilemma. There is no need to speak to one other. But what if my partner uses the game theory method and defects. This is not that likely because I am very risk-averse and would be unlikely to do a ‘heist’ with someone that was too selfish, too stupid or too suspicious to see their way out of the dilemma. Of course if I thought that I had been silly and got myself into a mess with someone I did not trust, I would defect – again no dilemma. The intuitive and emotional method is what I would use and I am satisfied with that. I would make a judgment using the tools that evolution and personal experience has given me.

I am not putting down formal tools but I’m just saying they have limits.