The definition given on the Wikipedia page seems adequate:
Free will is the ability to choose between different possible courses of action unimpeded.
Those who deny that we have free will must falsify either the “different possible” or the “unimpeded” parts of the definition. Those who attempt to falsify the “different possible” hold to a deterministic view of Reality. Indeed, they seem to hold to a view of Strong Determinism, not realizing that such a view must violate Occam’s Razor. [I’ll falsify Strong Determinism in a separate essay.]
Some who deny that we have free will point to the fact that our choices are the results of neural processing, which are conditioned, socially and in other ways. They seem to insist that such neural processing is strongly determined, and so, we are not free, in that we must make the choices that we do.
Not only are there stochastic processes interwoven in neural processing, but there is also parallelism, giving rise to race conditions, making determination of what shall be chosen of competing motivations impossible. Moreover, initial choices are often overriden, or reconsidered, with subsequent “second thoughts”.
It also seems to me that denying free will on the basis that our choices are the result of neural processing ignores that this neural processing is itself what makes up our will. Our wills are not some mystical black-boxes into which our motivations are fed; our motivations are part and parcel of our wills.
So, to say that the set of processes that make up our wills determine our choices, and, therefore, our wills are not free seems to be formulating a tautology, in which the definition includes the conclusion. To me, this gives place, as an example of Begging the Question, to dismissal of this approach to denying free will, leaving only the “unimpeded” part of the definition.
In the lack of a fully determined internal mechanism for generating will, the only impedance left to us to consider is external, whether our choices are determined by any external agent. Such an agent must be equivalent to “God”, and, specifically, a god that controls absolutely everything.
Some people actually believe this, and I don’t know of any way to falsify it. However, such an existence is neither demonstrated nor proven, so I am justified in dismissing it.
Some deniers of free will admit that there seems to be an appearance of free will. To make this admission should lead to acceptance of free will, to satisfy an application of Occam’s Razor, that, in the lack of evidence requiring otherwise, what appears to be is what is. [See this short essay.]
Now, to disclaimers and speculations…
I must admit that I am strongly biased in favor of Free Will. Emotionally, I take attempts at falsifying Free Will to be tantamount to proclamations of my slavery. Much rather, I subscribe to the sentiment of William Earnest Hensley, in his poem Invictus.
I am the captain of my soul; I am the master of my fate.
It seems nearly impossible to engage in discussion of this question without interjection of moral judgements. Sometimes, the question of moral responsibility seems to be the lead-in or motivation to reject Free Will in the first place. I find moral responsibility to be an entirely separable question, and one that ought to be resolved separately.
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