Causality
We are not through yet, unfortunately; there are a couple more terms dealing with effects and causes that will figure into what follows and which have to be clarified on the basis of the abstract definitions we have given.
First of all, the causality of a cause is the cause's relation to its effect, or, if you will, it is "what the cause is doing to" the effect to "remove" the contradictoriness of it.
That is, the cause is what resolves the contradiction (the effect); its causality is how it does it. If we take the missing keys, the cause (let us assume) is the relaxation of the hand + the attraction of gravity; the causality is how these two aspects of the situation actually managed to get the keys out of John's hand without his noticing.
Actually, in this example, the cause in the strict sense is more abstract, as whatever it is that is necessary to account for the removal of the keys; and so it would be some aspect of the relaxation and the gravity (whatever this would have in common with any other explanation). You can see that it wouldn't have been necessary for gravity to have been at work, if there had been a strong magnet nearby that could have pulled the keys--meaning that the force in question didn't have to be gravitational to do the job, and its "gravityness" was part of the causer.
But even in the example as it stands, the causality of the cause is not really known (and this unknownness of the causality is actually what made Hume throw out the whole notion of cause). Somehow or other, the cause got the job done; and so even if we don't know how it did it, we can point to the fact that it somehow did it without having direct knowledge of it. That is, we know that there is a causality of the cause, because the effect would be a contradiction unless the cause somehow made it not one; but though we can use a term to refer to this in-itself-unknown relationship, we don't in general know what exactly we are referring to. Once again, we are in the very abstract realm of knowing that we can say certain things without knowing directly what we are talking about.(1)
There is one interesting fact about causality as a relationship, which we can state as a conclusion:
Conclusion 4: The causality of the cause is not a real relation to its effect.
This is because (by Theorem II) the cause is not altered at all by its having an effect; hence, the relationship of cause to effect (the causality) is not a real relation, even though it has a foundation in reality (the fact that the effect depends on (is made different by) the cause).(2)
That is, a "real relationship" or connection is some aspect of an object such that it wouldn't be what it is without the other thing it is connected to--this "dependence" of the one on the other is (looked at from a certain point of view) the reality of the "connection." Thus, the shape of my nose is (among other things) part of my "sonship" to my father, because I got this shape from him, and if he hadn't been my father, my nose wouldn't be this shape. My "sonship" consists of all the aspects of myself which wouldn't be this way if that man weren't my father; and this is a real relation to that man. Note, however, that my father would be what he is without me--except, of course, insofar as he is a causer that is acted on by me as affected object. What I am getting at is that the shape of my nose makes no difference to the shape of his nose. It is the other way round.
Therefore,
Conclusion 5: Being-affected is a real relation.
That is, an effect involves a real relation to its cause, precisely because it wouldn't be what it is (this effect) without the cause. But the cause would be what it is without the effect; and so, even though there is a real basis for thinking of a relationship (because the effect is really related to this cause), still the relation itself is not a reality. If it were, the cause would be the effect of its effect, since it couldn't be what it is without its effect. But this is nonsense; calling it a cause, as I said, makes it no different from what it is.
However, since the "connection" between the cause and effect is a real "connection" when looked at from effect to cause, we need another term to refer to the same relation as causality looked at from this opposite point of view:
Being affected is the relation the effect has to its cause. It is what is "being done to" what is affected by the cause; or it is the effect as "dependent" on the cause--or perhaps more accurately, it is the "dependence" itself of the effect on its cause. This dependence is real, as I said, because the effect would be a contradiction (and so wouldn't exist) if the cause weren't there.
Any relation can, of course, be looked at from two points of view. If it is a relation between A and B, then it can be considered as the relation from A to B or the relation from B to A. As Aristotle said, the road from Athens to Thebes is the same road as the road from Thebes to Athens. So causality and being affected are one and the same thing: the relation between cause and effect; but causality is what the cause is "doing" to the effect, and being affected is what is "being done" to the effect by the cause. The point is that the latter is the only one of these two points of view which itself is "out there," so to speak; the former is just a way of considering the situation(3) .
NextNotes
1. In the case of the cause of our knowledge of the truth of the conclusion of a syllogism, we know that the cause is the known truth of the premises and their known proper logical arrangement. But, as I said, the propositions themselves do not really "produce" the conclusion, because propositions aren't actually active. The real cause, it might be said, is my knowledge of logic (that certain arrangements are valid and others not), plus my knowledge that the rules are followed in this case. So what is the causality here? Probably something like how I know that in this case everything is fine and the logic valid, and so the conclusion is true.
2. Remember, even in cases where there is only something like "logical dependence," rather than cases where something actively alters another thing, the dependence is real when the effect really wouldn't be what it is without the cause.
3. Of course, even the effect itself (and so its "dependence" on the missing cause) is a way of considering the situation, as I have mentioned so often; the point here is that when you consider the situation that way, the cause has to be somewhere in the real situation; but when you consider the fact which is the cause, this doesn't say anything about anything else. So the effect itself is an abstraction, and its being looked on as being affected by its cause is even more of an abstraction; but the causality of the cause on the effect is far more of an abstraction even than that; it's only "there" because any relationship can be looked at both ways. If this is confusing, all I can say is that I'm not surprised that you find it so.