The following is from Derek Parfit's, Reasons and Persons, pp. 12, 13):
A man breaks into my house. The man orders me to open the safe in which I hoard my gold. He threatens that, unless he gets the gold in the next five minutes he will start shooting my children, one by one.....there is a risk that, if he gets the gold, he will kill me and my children before he drives away.
I also have a special drug, conveniently at hand. This drug causes one to be, for a brief period, very irrational. Within a few seconds of drinking it, it becomes apparent that I am crazy. Reeling about the room, I say to the man: 'Go ahead. I love my children. So please kill them.' The man tries to get the gold by torturing me. I cry out: 'This is agony. So please go on.'
Given the state that I am in, the man is now powerless...
On any plausible theory about rationality, it would be rational for me, in this case, to cause myself to become for a period very irrational.
On any plausible theory? Perhaps. But I would think that most of us would prefer something a little more substantial than Prof. Parfit's personal assurance on the matter. That's because, for the past several thousand years or so, demonstrating that a notion entails its own negation or opposite has been synonymous with demonstrating that it is false.
Nor is it possible to dismiss the foregoing example on the grounds that it arises from a conflict between two competing "types" of rationality. The practical concerns and the valuative contradictions relative to those concerns make it fairly evident that its target is rationality of the practical variety. Beliefs don't enter in as anything more than a passive backdrop.
On the other hand, for those who might wax nostalgic for the good ole classical view, replace the practical concerns with epistemic ones (e.g., rare manuscripts, etc.) and the practical irrationality with an irrationality characterized by false beliefs or inappropriate epistemic procedures, and the classical rationalist ends up with a little rational irrationality of his own, as the following passage (Gribbon, p. 40) illustrates:
...Planck argued against Boltzmann's statistical interpretation of the second law of thermodynamics long and hard, both publicly and in correspondence with Boltzmann. For him, the second law was an absolute; entropy must always increase, and probabilities didn't enter into it. So it is easy to understand how Planck must have felt near the end of 1900, when, having exhausted all other options he reluctantly tried to incorporate Boltzmann's statistical version of thermodynamics into his calculations of the blackbody spectrum, and found that they worked. The irony of the situation is made more piquant, however, by the fact that because of his unfamiliarity with Boltzmann's equations, Planck applied them inconsistently. He got the right answer for the wrong reason, and it wasn't until Einstein took up the idea that the real significance of Planck's work became clear.
Obviously, our contemporary view of rationality as a strategic attribute or concept leaves a bit to be desired. As it stands, not only is rationality comprised of two domains or types (cognitive and practical) which can conflict with each other (e.g., occasions when false or unjustified beliefs serve to maximize efficiency), but each of the two domains or types is self-defeating. Indeed, with epistemic credentials like this, you can't help but wonder that it hasn't occurred to someone to make a bit more of the distinction between the employment of rationality, whether it be for practical matters, the pursuit of knowledge, or whatever, and the holistic (unconstrainable) attribute or concept of rationality itself. Cheer up. It already has (Roberts, 1996a, 1996b).