Here I just want to add a brief addendum to my previous post. One fascinating line of arguments in favour of moral realism compares morality to mathematics. The argument, in simplistic terms, runs roughly as follows:

Critics of moral realism assert that moral facts are too strange and insubstantial to have the same weight as objective facts. Moreover, they are derived by reason and rational deduction rather than empirical experiment, unlike physical facts. However, these objections apply all the same to mathematics, and nobody has any real problems saying that mathematical statements have truth values and convey valid propositions. Nobody doubts the existence of mathematical facts. Therefore, we are being unfair and holding morality to a higher standard of proof than we should. If we accept maths as being true, or at least don’t reject it due to the lack of empirical testing, neither should we reject morality for those reasons.

This is a very subtle argument, and I largely believe it correct. My solution is idiosyncratic however, we shouldn’t believe that maths is “true” either. For this point not to be dumb, I need to make a crucial distinction, between mathematics as system and mathematics as model.

Fundamentally, mathematics is a system defined by a series of basic axioms such as the Zermelo-Fraenkel axioms. Most of these seem fairly unarguable, such as the axiom of extensionality, informally: if there is a set A and a set B, and every element in that set is an element if and only if it is also an element of the other set, then the two sets A and B are the same, so A = B. It is worth noting that this axiom was not necessarily derived by any empirical observation, but rather rational deduction.

All mathematical truths can be derived from these axioms. Therefore, from within the system, all mathematical propositions can be assigned a truth value. But from the outside, where the tuth of the axioms are unknown, they cannot.

The ultimate use of mathematics is not system building for its own sake (though that is fun) but as a model for the physical world. It is possible to build, in the system of mathematics, a system which is in some sense like the real system, and use that model to derive predictons about the real physical system which turn out to be correct. As a simple example, we know mathematically that 1+1 = 2, and we can use this system to model a physical system consisting of objects. For instance, we model a single object as the mathematical object, 1, then from this we are able to derive the (correct) prediction that if we are to put the two together, modelled as the mathematical operation of “addition” then, mathematically we get “2”, which we translate back from our model to predict that we will observe two objects.

Of course writing this out explicitly seems stupid, because we have become so used to thinking of mathematics for simple cases as reality, and not a (incredibly successful) model of reality. But a model it is. A model is not true or false, it merely reflects reality to a greater or lesser extent. Of course, mathematics can be used to model our reality extremely succesfully, this being the “unreasonable effectiveness of mathematics”, but ultimately it is just a model. It is therefore not correct to speak or think of mathematics being true or false, but rather as a good model or not a good model. So, in the strictest sense, we can say that mathematical facts are not true or false from outside their own system. However, if that system is able to model ours incredibly well, then we can broaden the meaning somehow to bestow upon them the appelation of “True”

.This is all well and good, but what about morality? I would argue that, in agreement with the argument at the start, that mathematics and morality are in the same class of objects - rational, deductive systems which can be used to model our reality. The question is, then, is morality a good model of the system. Or, at least, good enough to be considered “true” in the broad sense? My argument is that it is not.

First, I would argue that the system is poorly specified. There are no clear set of axioms which can be universally agreed upon, which can generate the general boundaries of “morality”. Nor is it clear what domain morality is meant to be modelling. It is certainly not physical systems. Not really even the behaviour of individual agents - people can act immorally without any problem at all. Moreoever, the model tries to have a prescriptive force. It does not just say this is what the system does, but instead: this is what the system should do. It’s not at all clear how a normative model should even work.

I’m making two separate arguments here. The argument that just because morality is a rational and not an empirical exercise, so we should not just dismiss its truth out of hand I think is correct. However, in and of itself this is not an argument for moral realism. It simply shifts the ground towards the question of whether morality is a good model, and in this case I think it is clearly inadequate, though obviously this question is debatable.