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Causation: A Better Account

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Posted by Harvey on September 22, 2003 16:42:35 UTC

I just posted a reply to a statistical account of causation which according to the approach suggested by Dick, is actually no account at all. It reduces to a denial of relationships of past and future events, or a denial of linear processes (e.g., orderly thinking, etc).

On the other hand, any better account of causation has to take some kind of statistical relationship into effect because of quantum mechanics. In QM, according to Born's postulate, which basically states that a classical probability of an observable (physical event) is the square of the complex amplitude in Hilbert space. This postulate introduces irreducible quantum indeterminism at the quantum level, but Schrodinger's equation for time evolution of the wave function restores this indeterminancy by introducing statistical regularity in the evolution of a classical system. Also, according to Heisenberg's uncertainty principle, there exists a limit of measuring accuracy in nature by which all conjugate observables can be observed. And, then then there is the speculative path integral formulation and also quantum chaos. The path integral formulation simply 'adds' all the potential paths and most paths are eliminated as part of the pertubation where the most probable path is the one that is not eliminated in pertubation. There is a certain indeterminancy of the selected path, but that path is nonetheless the most likely. Quantum chaos is the notion of quantum indeterminancy 'leaks' into classical phenomena by introducing irreducible chance into classical events (i.e., cause cannot be fully deterministic even in classical situations).

Now, in terms of real classical cause and effect, it is quantum chaos that presents the real difficulty since 'cause' is always somewhat indeterministic for classical effects. This is speculative, but I think any causative account must take into consideration this possibility.

A causative account to take into consideration of Heisenberg's UP or Schrodinger's time evolution wave equation are relatively mild problems. The more difficult one is Born's postulate if no hidden variables are present.

So, let's see...

Any genuine causative account must be metaphysical. That is, there must exist cause-effect relations that 'exist', and it is these relations that determine whether A is a cause of B, or B is a cause of A. It is not good enough to claim only a observed-based statistical relationship (e.g., B is more likely to be observed after A since statistically this is how such things work out) since such an acausative account is based on what we happened to observe and this is not causation. On the other hand, a genuine causative account can accept a statistical law account of causation. For example, there is no reason why a cause cannot be statistical and still be a legitimate cause. For example, if I pour sand onto one spot so that a sandpile forms, I could keep adding sand until the pouring sand causes an avalanche. The avalanche could be said to be caused by the pouring of sand (statistical event). Now, someone might argue that one particular grain of sand was the actual cause for the avalanche, but one grain of sand did not singularly cause the avalanche. Rather, it was a collective (statistical) effect of many sand grains having a cummulative effect on the sandpile. Each grain of sand has a probablistic weight to cause the avanlanche, and as more sand is poured, this probablistic effect increases with each new sand grain landing on the sandpile. Once the conditions in the sandpile reach a critical point, the phase transition ensues and the sandpile changes geometry by undergoing an avalanche. The 'cause' is a holistic account that must consider the mathematics of phase change, probablistic weight, path integrals, etc. The point being is that the cause is not a simple equation, but is an elaborate system of variables that can be modelled and approximated by sophisticated math.

Such a causative account does not necessarily mean that it must be completely ridden of indeterministic causes (e.g., random events, or events caused by free will decisions, etc). A random or free will decision can be part of the variables of a cause, and sometimes these variables can be overriding variables. For example, if I choose to draw drop a pencil on the floor, the probability of the pencil following to the floor is probably quite low unless I make the decision to drop that pencil. My decision and subsequent actions are the 'cause', but not the full cause. The full cause is all the complex formula that considers many variables, it is just that the probablistic weight of free will has taken on higher values in this situation, and therefore a pencil dropping becomes a very high probability. The event is still not certain even with a free will decision since I might get a phone call just before I decide to drop the pencil, and this distraction causes me to forget to drop the pencil. The point is that the list of variables for a cause are extremely complex, and yet overridingly simple most of the time since the probablistic weight of some events are so high that we quickly ignore the potential problems that might prevent the effect from occurring and we simply say "Harvey dropped his pencil, that's why the pencil dropped".

Such a causative account can accept Born's postulate, Heisenberg's UP, Schrodinger's time evolution waveform equation, and even the path integral formulation as well as quantum chaos. Since the causative agent can be so diverse as to accept random or indeterministic causes as one of the variables, the only thing that cannot be accounted for is if something is completely uncaused. But, this is situation is a strawman. Even in Born's postulate we actually have a element of 'cause' in the indeterministic event. The cause here is Born's postulate itself. We are told the 'law' of how quantum indeterminate events (represented as a complex amplitude in Hilbert space) can become a classical occurring event - by squaring the complex amplitude. This does not represent a complete breakdown in the causation of an event. Rather, it tells us why a particular observable was constrained in a probablistic manner, and this constraining of a potential to a real value acts as a cause.

Similarly, the path integral formulation or quantum chaos also have indeterminancy for classical action, but this indeterminancy is accounted for as part of the 'law' of the path integral action or part of the 'law' of quantum chaos. No event is happening without complete cause, it is only happening with some aspects being indeterminate.

This slight amount of indeterminancy of an event is a desirable trait of a causative explanation. That is, if any event E was fully reducible to a all its causes C's, then the universe would be deterministic. However, a deterministic universe introduces a paradox. If E is fully determined by C's, then there is no way to distinguish if E is caused by C's, or C's are caused by E. Now, that might look like an odd way of thinking about it, but this in fact is what happens in any deterministic account of causation. If I drop my pencil, then it could be equally said that the pencil was dropped therefore I was born. Neither explanation has a priority in terms of one being the actual cause.

What a small amount of indeterminancy does for a causative account is that it breaks the symmetry of equal claim to cause. The indeterminancy is insignificant enough as to not be an 'uncaused cause', but significant enough as symmetry breaking event. This broken symmetry allows us to establish the causes Cs of an event E, and it does so without sacrificing the whole causal argument.

We can now claim that event E is caused by causes Cs if and only if there exists a non-reflexive relationship between Cs and E where Cs are the parent of E. The Cs are established as parents to E if and only if there exists a series of logico-mathematical laws plus a small but significant symmetry breaking of indeterminancy that can only exist if Cs are the parent of E, and not vice versa. So, in this scenario, E cannot be the parent of Cs since the indeterminant event (e.g., Born's postulate, quantum chaos, path integral approximation, etc) forces the one-way (anti-reflexive) relationship of Cs to E. It does this by establishing a logico-mathematical priority of Cs over E, and not E over Cs. By that, I mean, that whereas one can logically (or mathematically) go from point C to point E, one cannot logically (or mathematically) go from point E to point C. The reason is due to the indeterminant event. That is, you can still get from point C to point E even if there is indeterminancy introduced, but you cannot go from point E to point C if indeterminancy is introduced. There is no logical (or mathematical) way to know what probability weight factor to assign to the indeterminate event if you go from point E to point C. Hence, there are way too many potential Cs (or possible universe) that you can take from point E to get to point C. If those other potential Cs (or possible universes) don't exist, then you have to explain why it is that only a select number of Cs exist if E and Cs are completely symmetrical. This can only occur if Cs are the cause of E, and not vice versa. The causative nexus of the universe is intact and undamaged by a completely deterministic account.

So, what we have here is a much better account of causation that utilizes modern theories of quantum mechanics and even provides a logical explanation on why indeterminism is a feature of our world. Indeterminism exists because it is logically required to preserve causation. Cause is a real metaphysical relation, and any attempt to rid us of this notion is both anti-intuitive and leads to unacceptable paradoxes.

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