Universal Theory

We might think of Mathematics as to some extent, the generalisation of singular sentences. Most of these sentences possess a certain logical structure, and whilst these singular cases interest us, we would like to understand the general and universal theory behind them. 

As a basic example, we might be familiar with the solution to an equation $5x - 10 = 0$ as being 2. Our method for finding this happened to be by first adding 10 to both sides and then dividing both sides by 5. Now, why is this justified? Mathematically the answer relates to abstract algebra (in particular Rings). More generally, Mathematics allows us to provide a general solution to an equation of the form $ax + b =0$ as being $-\frac{b}{a}$ assuming $a \not = 0$. Why is this useful and important? Well it means that we have a general method that works in every situation (that our conditions apply under). 

Now note that we can have multiple levels of generalisation, and indeed I think there is a very strong reason to do so. Consider the claim 'it is morally wrong to kill the child named Rob'. Suppose for hypothesis that we think this claim to be true. This is a singular instance of a moral claim. However we wish to have something that is a lot more powerful than that. We're obviously not always going to be talking about Rob, we might be talking about George or Ann who may or may not be children. We would ideally want a moral theory that is more universal. A theory where we could make claims such as 'it is morally wrong to kill children' or 'it is morally wrong to kill anyone named Rob'. The more general the claim there is the sense in which it is more useful. In mathematics we wish to remove as many superfluous factors in a given situation as a possible. It is the same in making general philosophical claims. By aiming for generality we are able to only consider the meaningful and salient features. By making the claim that is morally wrong to kill a person we are able to consider a far larger branch of situations. Further we are able to pinpoint that the relevant factor is personhood instead of that person's name. 

However one can make claims that are even stronger than universal. We can make a claim that is necessarily true. The purpose of necessity is that there is a sense in which a claim must always be true. It's not just due to stars aligning in a certain manner. To say that it is necessarily true than killing a person is morally wrong is to commit to the idea that it is not possible in anyway for killing a person not to be morally wrong. In every world and possible situation, the action is wrong. 

Nevertheless, one might argue that our practical situations are individual instances, and that a universal theory misses out on specific factors. I think that for the purpose of justifying our actions, we need to depend on this universal theory. If I kill a child called Rob, maybe we can agree it is morally wrong. however I think that if we wish to punish me, we need some type of explanation. 

If I choose not to hire a woman because she might become pregnant, presumably I have done something wrong. However we must ask why is this the case? What are the salient features of the situation that make it wrong? Perhaps one responds that it is because she is female, but this doesn't seem particular adequate. Why does her gender matter in this situation? Why does it impede on my right to hire people as I wish? So let's go even more general: perhaps it is because as a female she must pay a disproportionate physical price if she does get pregnant and hence it is unfair to punish her. Or perhaps it is because as a female, she is already discriminated against and as a society we wish to move forwards from this. Regardless of the reason, we have managed to analyse the reasons a bit deeper. We are explaining the issue in terms of discrimination or disproportionate costs. It seems under these claims, it doesn't really matter so much if the person is a woman or not, only if they fall under some these categories.

The power of the universals allow us to move forward from just considering the singular case of not hiring a woman. It allows us to explain what the problematic features are, and why they are problematic. In cases of sexism it provides us an explanation for what we can do if the genders were say reversed. It allows us to be consistent with our theory. By considering how our theory functions under different circumstances we are able to provide stronger justification with what we should do in this circumstance.