Groucho Marxism

The is–ought problem, first articulated by the 18th century Scottish philosopher David Hume, concerns the question of whether we can make claims about what ought to be that are based solely on statements about what is. Hume himself thought not, arguing that at an ethical or judgemental conclusion cannot be inferred from purely descriptive factual statements. The same view was put forward by the 20th century English philosopher G.E. Moore using what he dubbed the ‘open question argument’. Moore’s argument may be summarized as follows: if X is objectively good, then the question “is it true that X is objectively good?” is meaningless; but the question “is X good?” is never meaningless, as it is an open question; therefore X cannot be objectively good.

It is remarkable that such a shaky argument can hold any sway in philosophical circles. Each step in the chain of reasoning has obvious holes. First and foremost, if a statement Y is objectively true, it doesn’t follow that the question “is Y objectively true?” is meaningless. This objection is particularly relevant in situations when we don’t know whether Y is objectively true or not. Second, it is not hard to come up with statements X that are objectively true but where the question “is X good?” is meaningless. And third, even you ignore the first two problems, the argument as a whole is circular as it assumes that the question “is X good?” is open, which, according to Moore’s logic, is only true if X is not objectively good – the very thing we were meant to be demonstrating!

So much for the open question argument. What about arguments in favour of the opposite position, i.e. the claim that you can get an is from an ought? The idea that moral properties are reducible to natural properties that can be studied through empirical or scientific means is known as ‘ethical naturalism’. This school of thought rejects the so-called fact–value distinction and argues that inquiry into the natural world can increase our moral knowledge in just the same way it increases our scientific knowledge. Proponents of ethical naturalism argue that humanity needs to invest in a science of morality which grounds morality and ethics in rational, empirical or scientific consideration of the natural world.

A science of morality begins with two basic premises: (1) some people have lives which are objectively better than the lives of other people; and (2) these differences can be traced back to the material conditions in which people find themselves. I don’t think many people would disagree with premise (1). Idealists would object to premise (2) and argue instead that differences in well-being are traceable to ideas rather than material conditions. In a previous blog post I argued that materialist worldview is superior to the idealist worldview because the former enables us to fully explain the world around us whereas the latter does not. Materialism is the philosophical backbone of the scientific method, which has been extraordinarily successful in enabling us humans to understand how the universe works.

In order for us to say that one outcome is objectively better than another outcome, we need to define a function v() with the property that v(x) > v(y) if and only if outcome x is objectively better than outcome y. The function v() might be referred to as a value function as it assigns values to different outcomes. Thus, the study of morality is closely linked to the study of value. How might we go about defining such a function? One way is to consider the likelihood of an outcome occurring. As a general rule, rare outcomes are considered to be more valuable than common outcomes. We can state this mathematically as v(x) > v(y) if and only p(x) < p(y), where p() is a function which assigns probabilistic to outcomes.

Another way of saying this is that there is a decreasing function i() with the properly that v(x) = i[p(x)] for each outcome x. What other properties should the function i() have? If x and y are independent outcomes – that is, the occurrence of x does not affect the probability of occurrence of y, and vice-versa – then the probability if both outcomes occurring, z, is given by: p(z) = p(x)p(y). For such outcomes it makes sense to say that the value of both outcomes occurring is equal to sum of the values of each outcome occurring; that is, v(z) = v(x)+v(y), which implies that i[p(z)] = i[p(x)p(y)] = i[p(x)]+i[p(y)]. One decreasing function which satisfies this criterion is -log(). Thus, we can set v(x) = i[p(x)] = -log[p(x)] for any outcome x.

Suppose now we have a random variable X which can take different outcomes x. We can analogously define the value of this random variable using the equation v(X) = ∑p(x)i[p(x)] = -∑ p(x)log[p(x)]. Those with a background in mathematics or physics might recognize this as the formula for entropy. The idea that value is equivalent to entropy is appropriately referred to as the ‘entropy theory of value’. But what does this theory actually tell us?! Let’s consider a simple example: wealth distribution. Suppose there are two people with relative wealth levels p and q, where p+q = 1. If X is a random variable which takes the value x with probably p and the value y with probability q, then v(X) = -plog(p)-qlog(q). Using the fact that p+q = 1, we have v(X) = -plog(p)-(1-p)log(1-p).

It can be shown that this value is maximized when p = ½ and minimized when p = 0 or 1. In other words, the highest value is obtained when wealth is equally distributed between the two people and the lowest value when wealth is most unequally distributed. This result can easily be generalized to a population of any size and provides an objective justification for the intuitive idea that we should aim to minimize inequality. So perhaps you can get an ought from an is after all.