I wish to give a brief argument against nominalism. Though I have not to time to verify its formal correctness, I do intend to give a fairly formal argument and not the layers of hints and explanations that I have previously given.
What this post also offers, in addition, is a rebuttal to the common response from nominalists that only the concept is universal and that nothing in nature is. But that presumes that the human is not natural; if the concept is universal, then nature is universal.
If natural laws (habits/patterns/etc.) exist and are real only in and through through their instances, then there is not such thing as a universal or general law. Why? “Law” implies generality or at least habit (natural tendency towards a probable pattern). Yet if a supposed law exists only as particular, then there is no law, universality, or generality. There is no pattern in nature at all. If one insists that there is at least a pattern in the mind, i.e., a concept, then one is mistaken. Why? Because that concept does not refer to anything in particular—not even the particular instance of which it is claimed. How so? Because if the natural pattern or law is not universal, then it can neither be duplicated in nature or in the mind. Hence, claiming that the universal is in the mind and never in the world solves no problems unless one makes the mistake of thinking that the mind is not in nature. That is the “Cartesian shadow.” If one wishes to call the the law or concept an approximate pattern, one could argue in that way as Hume does, but then like Hume then one must give up metaphysics entirely as he did. Consign it to the flames! If one refuses to give up metaphysics, one might use transcendental or abductive methods to argue for metaphysics, but then that proponent openly admits that any use of the method cannot be said to be based on any truth or reality outside of whatever happens to occur to humans—and certainly cannot be justified independently. Any such justification would invoke extra-human criteria that requires some hook into nature that neither concepts nor mere being in the world can provide if one accept the position described.
This is called “nominalism.” It should be obvious why I reject it. Its modern variant is the child of Descartes and raised to maturity by Kant. If the universal is merely a human affair, then Kant might be the end of philosophy. The inwardness of subjectivity that sprung from Kant does not entirely solve this problem as long as it does not reconnect to nature and cease to treat human nature as non-natural. Solving this problem through a reconnection with nature, and not a mystic one, is precisely what American philosophy provides. It is not the only philosophy to do so.
In short, the solution that I accept is to affirm that natural laws, habits, or patterns must be real in some way apart from mere particular existence. This is called “scholastic realism.” Mere “realism” does not affirm this, but instead is often defined in opposition to idealism; I will not enter into that discussion here.
I expect that my opponent might proclaim, again, that patterns emerge out of nature and cannot be understood to be independent from that particular materiality. Then I say, again, you are talking non-sense and confusedly if we accept your position, because you cannot refer to any patterns at all as the terms have not meaning. But if your position is true, then explain why nature is so terribly regular whether humans are there or not? And how can be know these laws? I am not saying, by the way, the the laws are “eternal.” They are temporal and still subject to contingency, which is why the term “cosmic habit” might be appropriate. Different cosmic epochs may have different laws and fundamental cosmic constants, and this view makes the Big Bang and other extreme occurences easier to explain. Finally, this whole view, when expanded, encompasses evolutionary metaphysics. Nature evolves, where biological evolution is a special case of a cosmic phenomenon.