I can’t tell if Suki Finn’s Beyond Reason: The Mathematical Equation for Unconditional Love is meant to be taken seriously or not. Irony on the internet is usually indistinguishable from earnestness. The fact that there is an addendum with a mathematical proof may indicate that it’s serious, but maybe it’s a droll bit of farce?^{1}

I read it with interest, in any case. Finn offers an analysis of conditional and unconditional love that is modeled on conditional and unconditional credence. As I’ve discussed in some recent posts, I think that recognizing the difference between conditional and unconditional value is crucial for understanding the relation between values and belief.^{2}

The conditional probability of P given Q, Pr=(P|Q), is often taken to be basic. Nevertheless, when Pr(Q) is not zero, we can calculate it from unconditional probabilities: Pr(P|Q)=Pr(P&Q)/Pr(Q). This, along with some basic math, gets you Bayes’ theorem.

We can treat love or utility as a function that assigns a number to a state of affairs, such that higher numbers mean better. We might write the conditional love of P given Q as Luv(P|Q) and the conditional utility of P given Q as Ut(P|Q).^{3} Unlike the case of probabilities and rational credences, however, it’s not clear that there’s any necessary relation between the conditional utility Ut(P|Q) and the unconditional utilities Ut(P&Q) and Ut(Q). At the very least, it is not usually going to be the case that Ut(P|Q)=Ut(P&Q)/Ut(Q).

So, although the difference between conditional and unconditional value is important, we can’t press too hard on the analogy with conditional and unconditional probability.

- I have a friend on Facebook who uses double brackets [[ like so ]] to mark sarcasm. Finn’s article is not so marked.
- I started to write an explanation here of how conditional probability works, but it looked like it was going to get out of hand. Finn’s explanation is is enough for what I want to say.
- It’s tricky for love, because we often love not just outcomes but objects. So there will be some cases in which Luv(P|Q) is well-defined but Luv(Q|P) is nonsense. For example: I love that I spend time with my wife, by I also love my wife. It makes sense to ask how much I love my wife given that I spend time with her, but it doesn’t make sense to ask how much I love that I spend time with her given that my wife.