Note: I apologize for leaving the equations in this post as text, but I haven’t been able to figure out how to pretty print them and turn them into images on my mac. If you know how to do this please leave a message.
I have described, among other things, how identity over time and consciousness are really descriptions or abstractions based on what is “really there”. An important criterion of being real is the ability to have a casual effect on the world. Earlier I have defended the idea that certain abstractions are real (see here), but in a very informal way. Now I will present exactly how a description or abstraction can be a cause, and thus give us reason to consider it real.
A “real” description is necessarily dependant on some aspects of “physical” reality. (Ultimately, possibly it is dependant on other descriptions, which are themselves dependant on the “physical” reality.) Thus we will formalize our description with a predicate, D, that acts on some subset of the world, ws (as usual we will call the set that represents the world w). If D(ws) then the description applies to that subset, and obviously then ~D(ws) means that the description does not apply. We also need an “object selector”, which is simply a function that acts on the set representing the world and returns a subset that represents the system that we are examining. We will designate this function S. Using these we define the predicate WD, which acts on the set representing the world. WD(w) is true if and only if D(S(w)) is. Finally, we define a function Dep(WD, w) that returns the minimal subset of w that D depends on given that WD(w), that is if the description actually applies to the set w (the world). (Note: what a description depends on was defined in this paper as being that which allows us to apply the description, and thus as a consequence: ~WD(w – Dep(WD, w)) if WD(w).) Note that Dep(WD, w) can never be the empty set when the description applies (WD(w)), if it could possibly be the empty set then that would be equivalent to saying that the description depends on nothing, which is the same as saying that the description is baseless, and hence meaningless. (Additionally if Dep(WD, w) is empty then it follows that ~WD(w), which contradicts our assumption that the description applies).
Now consider the definition of causation (from here and here)
In this case the predicate Z holds true if and only if the event we are searching for the cause of has occurred. Once we have determined what the fundamental causes of an event are we can determine if the description is a cause as follows: the description is a cause if and only if WD(x) is true when x is some member of C(n, Z). This in turn implies that Dep(WD, w) is a subset of some member of C(n, Z). Of course if Dep(WD, w) is a subset of some member of C(n, Z) it follows that ~Z(T(n, w – (Dep(WD, w) + x))), and thus that there exists some y such that ~Z(T(n, w – y)) and ~WD(w – y). This is to say that removing the description from the world, possibly along with some other factors in the case of a compound cause, results in the event, Z, not occurring. It also follows from this analysis that WD can be considered the cause of something if and only if there are possible worlds where WD(w) holds and likewise there are possible worlds where ~WD(w). (In plain terms: so long as the description applies in some cases and not in others.)
Now that the math is out of the way let me these statements back into English. My original definition of causation, in plain words, was that something is a cause of an event when taking that something away would have caused the event not to happen. So then a description is a cause of an event when it is the case that if the description hadn’t applied the event wouldn’t have happened. Of course how a description can “not apply” can also be reduced into simpler terms, resulting in the criterion that a description can be said to be the cause of an event when a removal of elements from the world sufficient to prevent the description from being applied would result in the event not occurring.
That still might seem a little dense, so let me illustrate with an example. Let us consider the phenomenal description of the mind. We can then ask the question: if our arm rises is it possible that our conscious will is a cause of this event? First we must figure out how to “remove” the conscious will. Ultimately our conscious thoughts depend on physical activity, so in order to “remove” phenomenal description we must “remove” the activity that it depends on. However if this activity was removed there is no reason to believe that the arm raising neurons would fire, thus justifying the idea that our conscious will is a cause of the event. If you don’t believe me consider this: if your arm was able to rise with the activity that your conscious will depends on missing then it must be the case that it was really some unconscious desire to raise your arm that did the work. Although we might consider this situation possible, how likely is it that every time you consciously will something there is an unconscious thought motivating the same action? So at least in the vast majority of cases a person’s conscious will must be a cause of their actions.
And from this argument it follows that descriptions of the mind, as described in this paper, are not epiphenomenal; they are a real cause of events (proving or disproving this statement was the motivation behind my entire investigation of causation, so it gives me some satisfaction to be able to conclude this). Some other surprising results can be derived as well, which I postpone revealing until later (simply to keep you reading my blog).