Our sample size of intelligent species is pretty small. We don't have any good reason to think that they would prefer "rational" entities or would even have a notion of "rational." One could easily construct other hypotheticals, like an alien species that was intensely religious and considers signs of rationality to be bad (there are humans who do just fine in careers like engineering and claim to have such viewpoints, so the idea of a species reaching high tech levels and having such hang-ups isn't implausible.)
True, but would you agree that it is more likely that rational entities attain spaceflight capabilities? Also, rationality is likely to share some universals, whereas religion seems far less likely to.
Allow me to propose a thought experiment. Suppose you, and you alone, were to make first contact with an alien species. Since your survival and the survival of the entire human race may depend on the extraterrestrials recognizing you as a member of a rational species, how would you convey your knowledge of mathematics, logic, and the scientific method to them using only your personal knowledge and whatever tools you might reasonably have on your person on an average day?
When I thought of this question, the two methods that immediately came to mind were the Pythagorean Theorem and prime number sequences. For instance, I could draw a rough right triangle and label one side with three dots, the other with four, and the hypotenuse with five. However, I realized that these are fairly primitive maths. After all, the ancient Greeks knew of them, and yet had no concept of the scientific method. Would these likely be sufficient, and if not what would be? Could you make a rough sketch of the first few atoms on the periodic table or other such universal phenomena so that it would be generally recognizable? Could you convey a proof of rationality in a manner that even aliens who cannot hear human vocalizations, or see in a completely different part of the EM spectrum? Is it even in principle possible to express rationality without a common linguistic grounding?
In other words, what is the most rational thought you could convey without the benefit of common language, culture, psychology, or biology, and how would you do it?
Bonus point: Could you convey Bayes' theorem to said ET?