I did some thinking about this last night. It seems that “causality” is a human-level explanatory term to refer to one of three concepts:
- Deduction from a model. For example, assuming perfect Newtonian mechanics, if we know that a rock is falling toward a planet, we know exactly what will happen if we plug in different values for time t. If we know the initial velocity, mass, and so forth, we can derive exactly how the system will change through time: neglecting friction, the rock will accelerate on its way down. To put things in terms of human usefulness, we say gravity “caused” the rock to accelerate. But really, in this case we started with a pure mathematical model and simply deduced the conclusions for given times; all the results were already contained in the initial conditions. We have noted nothing more or less than that in the equation
F=ma
F (the force acting on the object; in this case gravity) being positive “caused” a (acceleration) to be positive. Well yes, increasing F increases a; that’s one of the things being implied by the equation - the directly proportional relationship of F and a. The premises of our system already contained that fact, and we are just recognizing it in a different way for our human purposes and comprehension. So in this case, we can make a logically certain statement of the form “Event A is always followed/accompanied by event B (assuming the model)” but that is only phrased in these more human terms of causality for our ease of comprehension. To say that something caused something else is no more than merely choosing a way to carve up the concept space of that system so that the significance of certain aspects is more readily apparent to humans.
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Strong enough correlation, often backed by a “story” given in terms of 1 (whether or not the model in 1 is so idealized), to form a data-fitting tentative hypothesis of the form “Event B will always be observable following observation of event A.”
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Chains of the above.
I believe science uses 1 when using mathematical models or other idealized systems of axioms, 2 when making empirical theories to fit observed data, and 3 when the mechanisms in the gaps are not well-understood or are when it’s simply not necessary to go into the details at that time.