The problem with arguing against reason is that it is a psychologically untenable position. We all proceed through life trusting our senses. From a neuro-psychological perspective, there is good reason to be humble about our perceptions. There are certain biases that render our senses unreliable. In that regard, each person constructs a subjective reality. There are even biological limitations on what particular senses evolution has bestowed on each species and what range of sensory data can be perceived.
When we say that reality is constructed, however, this does not mean that there is no objective reality. The question is whether we can know it. If a tree falls in a forest and nobody is around to experience the event, the tree has still fallen. Denying objective reality may be fun to contemplate but anyone who claims to trust such a fantasy is being disingenuous. Our biases may work against objectivity, but it does not follow that there is no objective reality independent of our experience. Our experience of reality is indeed constructed, but not in a vacuum. Scientists can be biased, but there are professional controls to keep bias in check. Biased science is arguably not science at all, but a perversion of science. It fails to live up to the standard of objectivity that defines science.
I once found myself in the bizarre position of arguing with a Postmodernist that science is not a religion. The argument was that science has set itself up as the only legitimate way of knowing the world. I argued that we are all scientists and the world is a science lab. We hypothesize and experiment on a daily basis. The scientist just documents the results with professional rigor. The nature of phenomena determines which mode of inquiry is most suitable to describe them. The hierarchy of inquiry with science at the apex is a phantom.
In another trip down the rabbit-hole, I found myself arguing with another Postmodernist that the Enlightenment was not a form of colonialism. We hear this a lot in the discussions about tolerance toward Islam. The fact that the Enlightenment occurred in Europe and that Islam is particularly resistant to its influence does not mean that it was not a desirable and necessary response to theocracy. Islamic apostates are imploring the defenders of the Enlightenment not to coddle Islam with cultural relativism.
Going deeper still down the rabbit-hole, I was compelled to defend the social sciences against charges of general misapplication of the research paradigms of the natural sciences. Apparently, this is evidence of the phantom hierarchy of inquiry and of the aspirations of the social sciences to data-crunch their way to the top. My defense was that there is nothing wrong with using statistical models to lend authority to one's observations, as long as the researcher is open about the limitations of the study and the conclusions follow from the data.
What this postmodernist failed to recognize is that arguments in the physical and social sciences are constructed according to the same rules of logic that apply in the humanities, and that data is never an adequate substitute for a well-constructed argument. The generalization about the social sciences, for example, would have more authority if supported by a meta-analysis that made a case-by-case judgment on the appropriateness of measures in a representative sample of research studies.
My favorite postmodernist argument is that science is a religion, an argument also invoked by theists. To avoid straw-man arguments, it is important to remember that religion doesn't mean the same thing to all people. The case that science is a religion, however, can tell us a lot about what we all understand to be the essential nature of religion. If you want know what people really think of religion but dare not say, ask them to elaborate when they say that atheism is a religion. Do they mean that it is doctrinaire? Authoritarian? Mindless?
Postmodernism, like religion, settles for explanations that reject reason. The difference is that theist's reality is largely constructed of superstition. Our experience of reality is, in fact, constructed from sensory data filtered through biases. Subjective reality is, at best, an indirect representation of an independent objective reality. Reason is a noble aspiration by which we endeavor to overcome our biases, to whatever extent that we can, in order to to steal glimpses of objective reality.
Glimpses of objective reality, when pieced together, have told us that the earth is round and orbits the sun, that germs cause infection, that mental illness is biochemical, that all life on earth is genetically related and that we are all composed of elements found in the farthest reaches of the known universe. These are objective facts that have displaced the supernatural explanations that proceeded them. It would be unreasonable to dispense with our accumulated knowledge and revert to superstition.