Ummm...those words define linear causes. Using the language of logic, "for everything that happens there are conditions such that, given them, nothing else could happen" is written "X -> Y", or "if X then Y". That's the definition of a linear cause.
It's the definition of a cause, which could include some kind of non-linear cause. Indeterminism is rejecting causes in favor of ??? (hence the term "indeterminism")
Wikipedia disagrees: (http://en.wikipedia.org/wiki/Indeterminism#Types_of_cause)
Necessary causes:
If x is a necessary cause of y; then the presence of y necessarily implies that x preceded it. The presence of x, however, does not imply that y will occur.
Sufficient causes:
If x is a sufficient cause of y, then the presence of x necessarily implies the presence of y. However, another cause z may alternatively cause y. Thus the presence of y does not imply the presence of x.
Another way is to consider not yet a single cause, isolated, but a complex course of cause. So we have linearity or non-linearity in the courses of causes: deterministic in the first case, indeterministic in the second one.
Are you telling me that if I believe that in order to turn on my car, I have to both turn the key and there has to be gas in the car, this is an example of non-linear causality and therefore indeterminism?! Because that's perfectly consistent with what my understanding of determinism has been up to this point.
No. A non-linear cause means that the cause doesn't fit the logical definition of "If X then Y". In logic, X can be any number of specific conditions -- for example, "My car is fully functional, it has gas, and I put the key in the lock and turn it." That's still just 'X'. If X, then my car will start.
Symbolic logic is traditionally structured in a straight line from left to right. That's linear, and therefore deterministic. It's also temporal in nature -- left is the past, right is the future. Nonlinear logic necessarily includes some elements that also move from right to left, which makes it extratemporal and thus nondeterministic. For example:
If I say "If I go to the store or l go to the library, then I will not go to the theater", written (AvB)-->~C (If A or B then not C), that's linear logic.
If I say "If I go to the store or I go to the library, then I will not have done either of those things", written ->~ (AvB)-|
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or (If A or B then neither A or B), that's a paradox under the terms of determinism, and yet it's completely viable under the terms of nonlinear logic. More importantly, not only is it viable, but allowing for non-linear logic allows rational analysis of puzzles that completely fail under deterministic logic. For example, you can't write a deterministic logical equation to solve the following puzzle:
But as you can see, Nonlinear logic does so nicely by using the outputs of one logical operator as the inputs of another logical operator -- something that deterministic logic cannot do. Trying to write out that little set of logic gates above ends up in an infinitely long circle of deterministic logic because of the self-referential nature of the operators.
In other words, in order to have a nondeterministic cause, you cannot be operating inside of the ordinary everyday world of one-directional time. Determinism is great for assuring you that your car will start when you turn the key -- but not so much when you're trying to determine the dual nature of light, measure the quantum behavior of quarks, or establishing patterns by which to determine ultimately chaotic behavior like the weather.
Also, that's another example for Kael of how indeterminism gets
results.
