Once those two basic concepts are understood, two crucial axioms to understand:
- If some property is not compatible with some other property (in the argument itself uses the example of property a being incompatible with b), then it is compatible with the negation of that property (so a would be compatible with not-b). This is true simply because property a has to be logically possible (logically impossible properties are not properties at all), and either b or not-b must be true. If you think about it, if a were incompatible with both b and not-b, a would be logically impossible. Now, one could always say that property a is impossible and that would mean it could be incompatible with both b and not-b, but that doesn’t work in response to this argument, as will be seen later.
- If it is possible that a property is situationally necessary (i.e. if that property is compatible with situational necessity), that property is situationally necessary. This is a consequence of the S5 axiom of modal logic, which is used in the standard modal ontological argument. This video is I think a good defense of the S5 system of modal logic, if you feel it needs defending: youtube.com/watch?v=azHzZ2ADJkA
Once these concepts are down, there are basically three other steps to the argument that are needed- the rest of the argument logically follows:
- The property of situational necessity is incompatible with the property of injustice.
If you remember back when I talked about the first axiom, I mentioned saying the first property is impossible as a potential escape route, but that it won’t work here. The reason it won’t work here is because if the property of situational necessity was impossible, that fact would itself be situationally necessary, which is obviously self-defeating. Also, there are necessary truths of mathematics and logic that are situationally necessary.
Now let’s get back to the premise. Essentially, the premise says that for every unjust situation, there is a logically possible world in which it is “replaced” by a just one. So for instance, if an innocent man is unjustly found guilty in a court of law, there is a logically possible situation in which the same man is never accused. It seems that we only call things unjust in contrast to a coherent just situation.
If you still have doubts about this, here are two additional angles from which you can see this:
a) The axiom that “ought implies can”. It doesn’t seem that anyone can be said to have an obligation to do something if they are not able to do so.
b) The definition of injustice, used back when we talked about the “foundational concepts”. Injustice is defined as something that can be said to be lacking a due good by some coherent evaluative standard. Now, if the due good cannot logically possibly exist in that situation, wouldn’t that mean the standard itself is incoherent? If I were to say that “situation X is unjust because it doesn’t contain square circles”, that would not seem to be a coherent evaluative standard.
If you accept everything seen above, the conclusion can be reached that
the property of justice is situationally necessary. This conclusion can be reached in the following way:
P1: The property of situational necessity is incompatible with the property of injustice.
P2: If some property a is incompatible with property b, it is compatible with its negation, not-b.
C1: The property of situational necessity is incompatible with the property of injustice.
P3: If a property is compatible with situational necessity, the property is situationally necessary (by the S5 axiom).
C2: The property of justice is situationally necessary.
Now, let’s resume to go over the last two steps to the argument.
- Since the property of justice is situationally necessary, either there is no sense to the concept of injustice, or there exists an infallible justice-making power.
This may sound like a false dichotomy, but think through the logic here: we have already concluded that justice is situationally necessary- that everything is just. That would mean that either nothing can logically possibly be considered unjust, or that unjust situations are transformed. Whatever transforms unjust situations must itself be a being whose existence can’t be said to be an unjust situation (otherwise such a situation would itself need to be transformed, and we have an infinite regress). If you remember back to the definition of injustice from before, this means that this being cannot be said to lack any goods by any coherent evaluative standard. In other words, there would have to exist a being that than which none greater can be conceived.
- There is a sense to the concept of injustice.
As the final step of the argument, we have one of the most indisputable premises one could come up with. Every time you say that a certain situation sucks, you are saying that that situation lacks a due good by a standard of evaluation. The only other step left in order to get to this premise is that one of those standards by which we say something is unjust is a coherent one. To deny this, not only do you have to deny that these standards are objective, you have to say there is something incoherent about them. You have to hold all of these standards hostage until you admit this premise.
By the second and third steps, the conclusion follows:
There exists an infallible justice-making power.
As was explained before, this justice-making power must be that than which none greater can be conceived.
