The philosopher Saul Kripke introduced the following paradox. Imagine we a mathematical operation called ‘quadition’. This operation was exactly the same as addition, except after if the sum of the numbers is greater than 57, the result is always 125. If we have only ever added numbers smaller than 57, how do we know that we are following the rules of addition, rather than ‘quadition’? And if we have, what if we redefine quadition to be arbitrarily high (let’s say a million trillion)? More generally, what does it mean to say that some finite set of data is consistent with a rule if it is also consistent with an infinite number of other rules? You could imagine an infinite variety of quus like operations with the same result as any finite set of summations. And if you vary ‘quadition’ further, for example by saying ‘2 quus 2 = 5 if and only if it is November 15th, 2019, at 15:35, otherwise 2 quus 2 = 4', all correct addition can be made consistent with some form of quadition.
Kripke was primarily posing this question as a way of investigating the idea of rule following in language and the nature of meaning. But I think it has a moral application too. One of the most important concepts in moral philosophy is the idea of the Kantian categorical imperative: the idea that we must act in such a way that we could will our action to become a universal law. But what counts as a universal law? Any action can be consistent with a universal law if we allow for a purely formal notion of universality. “Tell the truth, unless you are person X, if so, do as you please” is a universal law in the sense that it can always be applied. OK, we might say, but moral universality cannot refer to a rule applying differently to different people. But what counts as different? It cannot mean, for example, that circumstances are never relevant. Otherwise, as the Woody Allen joke goes, we could never go to a restaurant, because if everybody went to the same restaurant at the same time and the same thing, there would be chaos. What about only accepting those rules which do not apply differently to different people regardless of circumstances? But we have problems here too. It would seem very strange to exclude all things conceivable as personal differences. Otherwise moral rules like ‘give what you can’, ‘help others if you are able to’ would not be acceptable as moral rules. OK, so what about universal laws which other people would be willing to subscribe to? That seems more reasonable. But the question then becomes, what is actually added by describing our behaviours in terms of universal laws? Any behaviour is consistent with a universal law, and what really counts in deciding whether it is acceptable or not is something different.