Rationality has two definitions that I frequently come across– here's a quick note on some important concepts related to the idea.

Rationality in Economics

In economics, the word 'rational' is used to describe self-consistency– i.e. if you prefer A over B over C, you prefer A over C.  You have a consistent utility function and full knowledge.  Homo economicus is rational and self-interested.

This of course has evolved into 'bounded rationality' in decisions that take into account cognitive limits, costs, and biases.  This concept was coin by Nobel-prize winning economist Herbert Simon, and updated by Gerd Gigerenzer– much of the conversation describes heuristics for decision-making that might be more optimal when accounting for decision costs; the debate rages on whether these concepts are 'biases' and flaws in cognition that we need to correct for, or adaptive and optimal.  (For instance, the cognitive flaw described as the 'mere exposure effect' to prefer and select things that we recognize has been recast by Gigerenzer as the 'recognition heuristic', in which ignorant tennis fans select winners based off recognition better than those that follow the sport).

An ethical corollary to bounded rationality is rule utilitarianism– we should act in ways that conform to principles of behavior.  Even when a local decision is sub-optimal, reinforcing the moral principle is important for both building robust habits in the face of ethical quandaries and minimizing the decision costs.  A common example of this is stopping at red lights– if at every intersection we all got out and presented an argument about who has a greater ethical case for going first, the decision cost outweighs the ethical cost (even with the odd case that someone is rushing to the hospital).  Moral action is evaluated in line with principles of behavior– a kind of virtue ethics, instead of a deontological or consequentialist one.

Rationality in Philosophy

In philosophy, 'rationalism' describes a belief in the supremacy of reason– reasoning and logic are the primary way we come to knowledge.  Kant suggested that there are analytic propositions which are true solely by virtue of semantics, like 'bachelors are unmarried', and early rationalists typically stood in opposition to empiricists, in their belief that principles of logic exist outside of experience and don't necessarily require empirical data to support them.  

It's important to draw some distinctions here in philosophy where (tacitly) empiricism and rationalism stand in contradiction.  An empiricist might say something like 'art is valuable because we perceive it as valuable'– you have to trust your perceptions first before you construct logic and argue from it.  A rationalist might say something like 'there is no articulation from the first principles of reason why art is valuable'– in this construction, reasoning about the value of life, emotion, positivity, etc is elevated above perceptual experience.

The modern intellectual world has drifted towards rationalism– we don't trust our perceptions (after all, we're full of cognitive biases and easily manipulated), and when push comes to shove we are nihilistic (nothing has provable meaning and therefore art certainly doesn't).  We might enjoy art, but we treat that enjoyment with suspicion; intrinsically meaningful pursuits are not in-and-of-themselves meaningful.  

I think it's pretty hard, however, to argue that pure reason or pure logic exists without empirical grounding– rational thought and abstraction follow from empirical experience.  If this is the case, it's completely illogical to apply the empirically derived rules of rationality– the subset of empirical experience that follows simple rules that we use to model the workings of objective reality– to the broader set of subjective  empirical experiences.  If we start by trusting our empirical experience, we should trust all of it.

Anti-rationalists typically reject the application of rational principles to human experience or behavior.  The idea that we can live happily in line with rational ideals, or that rationalism is good for the psyche, is a major point of critique.  

Regardless of the truth of rationalism (i.e. art has no value, in this example), we certainly must operate as if it does.  The more rationally you try to act the more you fight against your nature.  Few have put it more powerfully and succinctly than Dostoevsky in Notes from the Underground:

In short, one may say anything about the history of the world--anything that might enter the most disordered imagination. The only thing one can't say is that it's rational. The very word sticks in one's throat. And, indeed, this is the odd thing that is continually happening: there are continually turning up in life moral and rational persons, sages and lovers of humanity who make it their object to live all their lives as morally and rationally as possible, to be, so to speak, a light to their neighbours simply in order to show them that it is possible to live morally and rationally in this world. And yet we all know that those very people sooner or later have been false to themselves, playing some queer trick, often a most unseemly one. Now I ask you: what can be expected of man since he is a being endowed with strange qualities? Shower upon him every earthly blessing, drown him in a sea of happiness, so that nothing but bubbles of bliss can be seen on the surface; give him economic prosperity, such that he should have nothing else to do but sleep, eat cakes and busy himself with the continuation of his species, and even then out of sheer ingratitude, sheer spite, man would play you some nasty trick. He would even risk his cakes and would deliberately desire the most fatal rubbish, the most uneconomical absurdity, simply to introduce into all this positive good sense his fatal fantastic element. It is just his fantastic dreams, his vulgar folly that he will desire to retain, simply in order to prove to himself--as though that were so necessary-- that men still are men and not the keys of a piano, which the laws of nature threaten to control so completely that soon one will be able to desire nothing but by the calendar. And that is not all: even if man really were nothing but a piano-key, even if this were proved to him by natural science and mathematics, even then he would not become reasonable, but would purposely do something perverse out of simple ingratitude, simply to gain his point. And if he does not find means he will contrive destruction and chaos, will contrive sufferings of all sorts, only to gain his point! He will launch a curse upon the world, and as only man can curse (it is his privilege, the primary distinction between him and other animals), may be by his curse alone he will attain his object--that is, convince himself that he is a man and not a piano-key! If you say that all this, too, can be calculated and tabulated--chaos and darkness and curses, so that the mere possibility of calculating it all beforehand would stop it all, and reason would reassert itself, then man would purposely go mad in order to be rid of reason and gain his point! I believe in it, I answer for it, for the whole work of man really seems to consist in nothing but proving to himself every minute that he is a man and not a piano-key! It may be at the cost of his skin, it may be by cannibalism! And this being so, can one help being tempted to rejoice that it has not yet come off, and that desire still depends on something we don't know?