I was watching The Unbearable Lightness of Being when a scene suddenly made me realize a possible problem with regularity theory of physical laws and the ought implies can principle.

Regularity theory’s view of physical impossibility

Regularity theory implies that what it means to say that something is physically impossible is just to say that it will never happen (in this world). N. Swartz writes this in his book about about the theory:

“Indeed, the Regularity Theory – in withholding physical possibility from rivers of Coca-Cola – asserts only what Molnar himself hypothesized: namely, that there never are any such rivers.”¹

Here the example offered was a river of Cola-Cola. Supposing that there never is such a river and that regularity theory is true, then it follows that rivers of Cola-Cola are physically impossible.

The ought implies can principle

Ought implies can is an ethical principle that seems to fit many people’s intuitions. Suppose someone killed another person. We are initially disposed to think lowly of that person. But if it comes to our attention that the person doing the killing could not have reasonably avoided doing it, then we don’t think lowly of the killer. One example of this would be if someone jumped outside your car when you were driving at normals speed.

I’m further supposing that this “can” expresses physical possibility. It does not seem like logical possibility or epistemic possibility. Thus, ought implies physically possibility. Contra-position: Physical impossibility implies not-ought.

Deontic logic and formalizing

We have to be careful with “ought” and “not”. There is a difference between “He ought not to fuck other women.” and “It is not the case that he ought to fuck other women.”. Formalizing them requires deontic logic. I’m using “O” to mean “It is obligatory that “ or equivalently “It ought to be the case that “, “P” to mean “It is permissible that “, and “F” to mean “It is forbidden that “. “A” is taken to mean whatever action it is we are talking about. I follow standard notation in deontic logic according to SEP².

“He ought not to fuck other women.” is thus simplistically formalized as “O¬A” which is equivalent with “FA” which means “It is forbidden that he fucks other women.”. “It is not the case that he ought to fuck other women.” is thus simplistically formalized as “¬OA”. For simplicity I will refer to this latter use of “ought” as “not-ought” and the former use as “ought not”. Keep this distinction in mind.

I write “simplistically formalized” because that I omitted the agent in the formalizing.

The problem

Now that we’ve understood the concepts in use, let’s look at an example slightly inspired by the aforementioned film. Suppose that Tereza and Tomas are married, and that Tomas cheats on her every time we has the chance. In other words: It is never the case that when (a description that uniquely identifies Tomas) has chance to cheat on (a description that uniquely identifies Tereza), then (description of Tomas) cheats on (description of Tereza). This together with a regularity theory of physical laws implies that it is physically impossible for Tomas not to cheat on her. [¬◊_PhyA] using “◊_phy” to mean physical possibility. Suppose further that he knows that she will find out when he cheats on her, and that this hurts her, but he still continues to do it. The question now is: Is it immoral of him to cheat on her? I think we’d have to say yes. But if he physically cannot not-cheat on her, then it is not the case that he ought not to cheat on her. [¬◊_PhyA→¬O¬A] Thus, it is not the case that he ought not to cheat on her. [¬O¬A] Further: if it is not the case that he ought not to cheat on her, then he is not acting immorally by cheating on her.[¬O¬A→¬Ia] using “Ix” to mean “x is immoral” and “a” for the action. Thus, he is not acting immorally by cheating on her. [¬Ia] In other words: The action of cheating on her is not immoral. This conflicts with our judgment from before. [Ia] So someone who accepts regularity theory and the ought implies can principle would have to find someway out of this situation and regain consistency among his beliefs.