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Science demonstrates that all interactions of matter--including all events in the human brain--are sufficiently caused by previous events. If we know enough about the laws that govern these interactions and the current state of the universe, we would be able to exactly predict any future event. Does this mean that the doctrine of "free agency" or "free will" is false, since all human choices are predetermined by the laws of physics?
Everything we think and feel is probably correlated with some physical changes in the brain. And, really, this shouldn't surprise the LDS, since they do not believe that "mind"/"spirit" and "body" are two totally separate and utterly un-similar things (See Cartesian fallacy):
Thus, in LDS theology there is no spirit/matter dichotomy. Spirit is matter, though less easily detected by mortal eyes. If a spiritual experience or a "thought" from our spirit/mind is to have an effect upon a mortal being, it's not surprising to find detectable physical changes in the gross "non-spiritual" matter which we can study. You won't detect the actor (the 'spirit matter'), necessarily, but you might expect to see the effect of the action (on the 'body matter').
Classical physics (the physics of Newton) is deterministic—by "deterministic" we mean that if you know the starting conditions in enough detail, then everything just happens "inevitably," and the outcome is predetermined in advance.
We might notice that this could create big problems for free will—if God (or someone else) can know the starting conditions of the universe (including us and our brains), then He can predict exactly how things are going to work out. Many thinkers and philosophers accepted this conclusion of classical physics.
However, we now know that classical physics is not the whole story about the physical world, due to the early 20th century revolution in quantum physics.
A great deal of nonsense has been written about quantum physics, and we do not wish to here overstate the case. As one author wrote:
In quantum mechanics, at any rate, it is no longer quite so clear that everything is deterministic. Events happen which seem to have 'no cause' at all. Other causes come after the events they caused. It is weird stuff, but suffice it to say that there seems to be enough evidence from the physical world that we can study to say that pure determinism probably isn't the whole story. Or, at least, we are not compelled to accept that things must be deterministic.
This is an active area of debate in philosophy; some LDS and non-LDS resources on the topic are available below.
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