Domain and Range in Logic using PD

 Mathematical functions have domains and ranges. The domain is the set of numbers which produce valid equations. E.g. f(x) = 1/x is not valid for x=0. Likewise logical proofs have domains, and the validity is restricted to the domain. 

 In the prisoner's dilemma, provided both players are rational, it is always best to cooperate. No form of defect/cooperate is possible, so the only options are defect/defect and cooperate/cooperate. So, you morons,, pick cooperate/cooperate.

 This proof is not valid for anyone who doesn't meet some minimum standard for rationality. For example, game theorists are not sufficiently rational. You can't trust them to know they ought to cooperate. 

 

 When using theoretical principles, the first important thing is to remember they have domains of validity. If you get into a car, check the gas in the tank. If you get into a theory, check the domain.
 The second important thing is using the domains in reverse. Outside the domain, the theory is flawed, and the flaw in the theory is an exploitable vulnerability. While being outside the prisoner's dilemma domain isn't proof you should always defect, it is a hint that there is some profitable defection. Further, there are times you should always defect, and in those moments, knowing the domain directs your attention to exactly the topic of defection.

 It is also possible to use the domain as a measurement instrument. If you're not sure if the theory is valid, try it, and if it's falsified, you have determined that you're outside the domain. Physicists pull a trick like this all the time. Pick up theories not for their useful conclusions, but for useful domains, for the purpose of using the theory as a domain-measuring instrument. If you have a kind of stove you can't see with your eyes, you buy a frying pan not for the purposes of cooking, but for attempting to cook, to see if a thing is a stove or not. 
 Likewise you can attempt cooperate/cooperate to test the rationality of a person. Indeed mortals are supposed to naturally do this; you permit an opportunity for a small treachery, to see if they're trustworthy.
 

 

 P.S. A [high-trust] soyciety is when you permit large treacheries without testing first. A [low-trust] soyciety is when you never attempt to be trustworthy. Turns out both never-defect and never-cooperate are bad strategies.