I have recently read a couple chapters from Thomas Nagel's recent book, Mind and Cosmos. In it, he argues that neo-Darwinian evolutionary theory of the origin of life as we know it must be incomplete or altogether erroneous, because it cannot account for many aspects of our everyday lives, specifically the parts of what's commonly known as mind–body problem. Nagel focuses on the problems with providing a Darwinian account of the origins (and justification of) consciousness, cognition (including knowledge of mathematical truths), and moral values.
I don't want to discuss here the main thesis of the book. I just want to focus on Nagel's definition of moral realism and objective moral truths, in which he follows the tradition of many other moral realists.
According to Nagel, moral realism asserts that moral truths are not merely subjective experiences of individuals contingent on their personal preferences. Moral truths are independently real — and accessible to most individuals through reason. Furthermore, moral truths do not need to be defined or proven in terms of other truths (subjective or objective). After all, we cannot hold that every belief must be defined and verified through an infinite chain of definitions and verifications. That would be impossible and incoherent. Some ground-truths must exist simply because they must exist; according to Nagel's description of moral realism, that applies to moral truths:
[Moral] realism is not a metaphysical theory of the ground of moral and evaluative truth. It is a metaphysical position only in the negative sense that it denies that all basic truth is either natural or mathematical. [...] Value realism does not maintain that value judgments are made true or false by anything else, natural or supernatural.The part in bold is what I am having a problem comprehending. But first, let Nagel continue...
He explains that, of course, our evaluation of certain events as good or bad requires our knowledge of those events. The fact that running over a dog for the fun of it is evil requires knowledge that running over a dog will cause pain, suffering, and death of a living creature for the fun of it. But knowledge that causing pain, suffering, and death to another living creature is bad is self-evident according to Nagel. It does not require knowledge of anything else.
So far so good. But then he elaborates on the bit in bold above. David Gordon, in his review of Cosmos, explains:
But is not moral realism exposed to a decisive objection, famously pressed by John L. Mackie? In suggesting that values are "out there" in the world, rather than human preferences or sentiments, does not the moral realist postulate "ontologically queer" abstract objects, unlike anything else in the universe?
Nagel convincingly shows that this objection rests on a misunderstanding. Moral realism does not hold that there is, in addition to ordinary objects, a special class of metaphysical objects called "values." Rather, its contention is that moral reasons do not require reduction to something else in order to count as legitimate.
"The dispute between realism and subjectivism is not about the contents of the universe. It is a dispute about the order of normative explanation. Realists believe that moral and other evaluative judgments can often be explained by more general or basic evaluative truths, together with the facts that bring them into play.… But they do not believe that the evaluative element in such a judgment can be explained by anything else. That there is a reason to do what will avoid grievous harm to a sentient creature is, in a realist view, one of the kinds of things that can be true in itself, and not because something else is true." (p. 102)
I.e., the statement that causing suffering and pain for fun is evil is not a statement about a law of the universe; nor is it a statement about one's mind (since that would make it subjectivist). It is merely a truth, in and of itself.
(Michael Huemer makes a similar point, but I can't find the quote right now. Perhaps I confabulated it.)
I find this position incoherent. All truths must be either truths about our mind or about the reality outside our mind. Take mathematical truths, for instance. What are they? Several views can exist:
Subjectivist: Mathematical truths are merely descriptions of the internal laws governing our processing of the world outside. Specific laws and notations of mathematics are our ways of making sense of the external world. To say that there are 10 bottles in a pack merely means to say that we have grouped the matter in the pack into 10 objects (per our definition of "ten" and "objects") in our heads. There is nothing more to it.
The reason why Math is useful is because our brain can model the reality pretty well (at least to a certain extent), having been created/evolved for that purpose, and the brains of people are quite similar in this capacity, such that these models can be shared and mutually recognized as either true or false (or, rather, good predictors of reality or bad ones).
As a matter of support for this view, consider that mathematicians and physicists choose different kinds of Mathematics to describe the world. Eucledean mathematics can allow you to build a pyramid, but not circumnavigate the world. And Newton had to invent of a whole new set of mathematical concepts in order to prove his theory of gravitation. Same for Einstein: he had to adopt a radically new set of mathematical models to describe his view of the physical reality.
So, while the physical reality is "external" and objective, our ways of understanding and modelling it are internal and subjective, pure products of our minds.
Realist: The above view is ridiculous. Yes, the specific ways in which we measure and analyze the world and perceive the logic of it are unique to our brains and products of them. But there must be some independent, external aspect of reality that these internal models are representing. That is why Fermat could predict certain property of numbers in his Last Theorem, and people could prove it after a few hundred years, in a book several hundred pages long, itself being a product of seven years' worth of research based on centuries of previous research.
That is why, just from knowledge of geometry and Calculus, I can figure out how tall the level of water (whose rate of flow I know) will be in a pool of known dimensions after a certain number of minutes. I can figure it out theoretically, without knowledge of empirical laws of physics, and then go back and observe my answer being correct in reality (as long as the measurements of the pool's dimension, the flow of water, and the time elapsed were approximately correct). How the heck can I predict something like that about the world outside of my head just through introspection about my own logic? There must be something more to it.
Furthermore, mathematicians sometimes develop theorems that they think are purely abstract. Later it turns out that they can be useful in modelling the world. For instance, extremely abstract Riemannian geometry (developed in the 19th century) was found to be useful in the 20th century as a mathematical basis for Einstein's General Relativity Theory.
This manner of consistency must result from something objective existing "out there", not just a subjective modelling of the world inside our heads, a merely useful way to keep track of all the geese in one's herd. Thus, mathematics must be a part of the physical world.
(Incidentally, perhaps the reason why mathematicians can study this part "internally", without ever getting out and observing the world, is because their brains also operate according to the same laws of logic as the rest of the universe. Thus, lehavdil, "from my flesh, I envision G-d".)
Mystic/Platonist: The realist is right that there is objective reality which mathematicians study. But he is not right that it is a part of the physical world. It is a part of some parallel world of forms, "on which" the matter of this world is built, in a manner of a matryoshka (Russian doll). There, the forms and numbers and other abstract truths exist in their pristine form.
In our, material world, those "ideal objects" are forced onto the matter (or the other way around), such that we can still recognize them through reason and observation of the world, but we have to abstract them in order to mentally study their relationships in the world of forms. This is why we can make precise predictions about the extremely imprecise physical world. Our theories about it must be modified all the time, but not our theories about how to make mathematical sense of it.
This is not because our subjective view of our internal world is so unshakably consistent and reliable (after all, psychological accounts of our internal world evolve constantly). Nor is it because our knowledge of the physical world is so precise (it is constantly corrected as well; in fact, some long-held descriptions of reality, such as Newton's Laws, are eventually proven to be incorrect or imprecise). It is because we can know the world of forms (by inference from the physical world or by internal knowledge through our souls) in a better fashion that we can know the world of the physical matter. There may be a kabbalistic reason for it (such as that the world of forms is one of the Worlds of Truth, while in the physical world, the truth is muddled up by the physical matter).
Whatever the correct view of the ontology of mathematical truths, as I said before, they must be truths about something. They must be a part of the reality: either a subjective part of our brains and minds (similar to tastes), an objective part of the physical reality (like laws of physics), or a part of some parallel non-physical world. To say that something is good, but mean neither that "goodness" is its realistic property nor that its my mind's reaction to it, is not demonstrably wrong or illogical; it's simply incoherent.
To be continued...