Free will is one of those issues where you have to think deep and hard about your definitions. Many philosophers will subscribe to one definition, but not another, so sometimes the whole debate on whether we have “free will” revolves around semantics that you can’t do justice to in a single post, so I won’t try. However, it is fairly clear that Latter-day Saint theology not only makes space for (at least some version of) free will (except we refer to it as “agency” in our vernacular), but puts it at the cornerstone of our teleology.
Scientifically, the most famous experiment that addresses the concept of free will is the so-called Libet experiment. While there’s some dispute, my understanding is that there is a soft consensus that, when you ask someone to make a random decision such as moving a finger, scientists can detect a buildup of brain signals that predicts whether they will “choose” to move the finger moments before they are consciously aware of deciding to move it, suggesting that what we think we are choosing is actually the result of non-conscious brain mechanics.
Assuming that the technical aspects of the experiment are sound, there are still a lot of steps before we get to a “it’s all brain mechanics” conclusion (for example, the experiment begs the question of whether free will can operate subconsciously). Predicting responses from brain patterns is an exciting area of cutting edge research, but unless we get to the point where we can conclusively predict behaviors and thoughts based on our knowledge of synaptic arrangements and mechanics (which I highly doubt we ever will), neuroscience won’t ever be able to prove that free will is a myth, so like a lot of other issues discussed in this series it kind of comes down to your a priori suppositions.
Whether or not one believes in free will as an intellectual matter, it seems that virtually all of us base our actions and feelings on the assumptions of free will. Occasionally I’ll bump my head on a cabinet door corner and will feel the completely illogical urge to slam it in anger as if to hurt it (and as a young child I did just that). It’s illogical because it makes no sense to get angry at an inanimate object that is only following the laws of physics. Similarly, if we take it as a given that there is no free will, and our actions are defined purely by the setup and mechanics of our synapses, in my view it makes just as much sense to get angry at people as it does to get angry at the door (there’s a perspective known as compatibilism that holds that you can have free will and have everything determined, but that’s one of those deeper semantics issues alluded to above; for the purposes of this post I’m assuming that they aren’t compatible).
Although we might feel the urge to be angry at the individual who killed our family, in a world where, say, the difference between killing and helping comes down to a carbon molecule being just close enough spatially to form a bond and connect a synapse that leads to the decision to kill instead of help the family (yes, decisions have many more biochemical reactions, but in principle the number of molecules involved doesn’t change the principle), it makes just as much sense to get angry at the boulder that fell on our family because of a similar mechanical process. I’ve read attempted justifications for, say, moral outrage in a mechanical, meat robot world, but they always come off as post-hoc attempts to justify not biting the bullet and dealing with the implications of not believing in free will, as opposed to a systematic argument built up from first principles.
In the same sense that non-believers sometimes accuse believers of resting on comfortable fictions, I believe that most non-believers are willing to operate under logical outgrowths of beliefs that they see as fictional (whether they are aware of doing so or not), with the primary example here being free will. At the end of the day it is hard to completely divest ourselves of non-naturalistic, or, dare I say, spiritual, beliefs.