We are not here to argue the meaning of a word, not even if that word is “rationality”. The point of attaching sequences of letters to particular concepts is to let two people communicate—to help transport thoughts from one mind to another. You cannot change reality, or prove the thought, by manipulating which meanings go with which words.
I don’t think it’s very helpful to oppose a logical definition for a certain language that would allow you to do this. As it is, you currently have no logical definition. You have this:
Epistemic rationality: believing, and updating on evidence, so as to systematically improve the correspondence between your map and the territory. The art of obtaining beliefs that correspond to reality as closely as possible. This correspondence is commonly termed “truth” or “accuracy”, and we’re happy to call it that.
Instrumental rationality: achieving your values. Not necessarily “your values” in the sense of being selfish values or unshared values: “your values” means anything you care about. The art of choosing actions that steer the future toward outcomes ranked higher in your preferences. On LW we sometimes refer to this as “winning”.
That is not a language with a formalized type system. If you oppose a formalized type system, even if it were for the advancement of your purely practical goal, why? Wikipedia says:
A type system associates a type with each computed value. By examining the flow of these values, a type system attempts to ensure or prove that no type errors can occur. The particular type system in question determines exactly what constitutes a type error, but in general the aim is to prevent operations expecting a certain kind of value from being used with values for which that operation does not make sense (logic errors); memory errors will also be prevented.
What in a type system is undesirable to you? The “snake oil that cures lung cancer”—I’m pretty sure you’ve heard about that one—is a value whose type is irrational. If you may use natural language to declare that value as irrational, why do you oppose using a type system for doing the same thing?
The foundations of rationality, as LW knows it, are not defined with logical rigour. Are you adamant this is not a problem?
http://lesswrong.com/lw/31/what_do_we_mean_by_rationality/ says:
I don’t think it’s very helpful to oppose a logical definition for a certain language that would allow you to do this. As it is, you currently have no logical definition. You have this:
That is not a language with a formalized type system. If you oppose a formalized type system, even if it were for the advancement of your purely practical goal, why? Wikipedia says:
What in a type system is undesirable to you? The “snake oil that cures lung cancer”—I’m pretty sure you’ve heard about that one—is a value whose type is irrational. If you may use natural language to declare that value as irrational, why do you oppose using a type system for doing the same thing?