By universalism, I mean the idea that there are some fundamental principles that are true of (or apply to) all individuals in some domain (my definition is more general than the wikipedia definition articulated in the article I have linked to). For example, Newton’s laws of physics were thought to be universally valid until relativity theory and quantum theory supplanted them with other physical laws that are now considered to be universal as well.
Another example is the universal declaration of human rights, which outlines certain rights that apply to all human beings. Ever since the discovery of universal physical laws by Galileo and co, scientists and others have assumed that universals capture the most fundamental aspects of the domain in question, its essence, so to speak. Proponents of string theory and other unified theories of physics will go to the extent of saying that certain universal laws constitute the essence of everything that exists. Therefore, universalism at its most extreme postulates that certain universals have a greater claim to being real than anything else, which is also not a new claim, having a pedigree as far back as Plato in the west and (more arguably) the Upanisads in India.

Universalism has clearly been very successful in science, leading to predictions that are remarkable, all the more so when there is no empirical guide available — think of Dirac’s equations leading to the discovery of the positron, where the belief in the universal character of the equations of motion made scientists to look for the missing particle. Similarly, on the ethical front, universalism has lead to the expansion of rights to humans (and one hopes in the near future to animals as well), so that at the international level, it is recognized that all human beings have certain unalienable rights (however lax or hypocritical we might be in enforcing those rights).

So far, so good. But there are two big problems with universalism:
(a) Just because one can model nature remarkably well with universals does not mean that thats what nature is. To reify universals and make them ontologically primary is going too far, and leads to one of my seven deadly sins — reductionism. For example, the fact that the laws of classical mechanics can be derived from the laws of quantum mechanics is often used to justify that we are ultimately made out of atoms. How did that inference ever get accepted? It makes sense only if we accept the following schema:
Laws underlying reality A → Laws underlying reality B
Reality A is more fundamental than Reality B

This is the kind of reductive reasoning that’s made possible by universalism, and there is no reason to accept such reasoning, not one bit. It boils down to that hoary Clintonism, IT DEPENDS ON WHAT THE MEANING OF IS IS.

(b) What happens when something falls outside a universal category? For example, we may agree that humans and other great apes are human-like sentient creatures deserving of legal protection against murder etc. Well, great, but what about all the other creatures on this earth? What about the trees and the mountains and the rocks and the rivers? They are not like us, so what justification do we give in protecting them? That they are important for our survival, making their worth a derivative of ours? When deep ecologists such as Arne Naess, talk about the intrinsic value of the living environment, how do they justify that intrinsic value? What I have read of deep ecology suggests that deep ecologists are appealing to a common human intuition that the woods and the oceans are our womb, and merit protection for that reason. I agree. Underlying that intuition is a logic, and it is not the logic of universals. Like Sri Ramakrishna once replied upon being asked why he wanted to play with God, not merge with her, “I like to eat sugar, not become it”. The sugar tastes just as sweet, and our affinity for the world transcends the narrow ability to abstract common properties (or other universal elements) between ourselves and others.