I never accepted the arguments put forth in favor of a lack of human freedom based on foreknowledge, and over time I've learned to express those objections effectively, with a considerable debt to philosopher Norman Swartz.
So why write on a topic that most find as dry as moon dust?
I've written quite a bit on the topic, but it's spread all over the Internet. One post I produced for the CFI discussion forum summarized my argument in fairly tidy (formal) form.
The argument tries to address the contention that Libertarian Free Will is incoherent, along with the suggestion that free will is lost since we cannot change what we have done. The definition that leads off the post illustrates the bankruptcy of those arguments. "J" represents one making a choice and X represents an option. The symbol "~" means "not," so option "~X" represents any option or option that is not X.
LFW: J at time t is able to select X xor ~X, where the selection correlates to J’s intentions.
“Select” will be taken to automatically correlate with J’s intentions in the examples below.
Note: It may be argued that more is required to create a thorough distinction between LFW and CFW. I’ll consider that issue negotiable depending on the objections, but meanwhile I would argue that the ability to select X xor ~X is sufficient to distinguish the two while the correlation with intention suffices to equal CFW notions of control.
Remember that “xor” means one or the other but not both.
If J at time t is able to select X but not ~X, then J’s behavior is identical with causally determined behavior.
Behavior identical with causally determined behavior is causally determined behavior (principle of identity).
If J at time t is able to select X but not ~X, then J’s behavior is causally determined.
If J at time t is able to select X xor ~X, then LFW is possibly true in the example.
If J at time t is able to select X xor ~X is possibly true in the example, then causal determinism is not assumed in the example.
If J at time t is able to select X xor ~X is not possibly true in the example, then causal determinism is assumed in the example.
If J at time t is able to select X xor ~X, then X and ~X are accessible options at t.
If J at time t is able to select X xor ~X and J selects X, then ~X is an accessible option at t.
If J at time t is able to select X xor ~X and P selects ~X, then X is an accessible option at t.
If J at time t is able to select X xor ~X and P selects X xor ~X at t, then X and ~X are accessible options at t.
If one has understood the above statements, it should be clear that selecting one option over another does not inherently result in the inaccessibility nor impossibility of the option not selected.
Possible worlds representation
p(J selects X at t) and p(J selects ~X at t)
that is, worlds X and ~X could possibly exist, though the instantiation (actuality) of either is contingent on the selection of p at t. Causal determinism is not assumed, LFW is assumed for the sake of argument.
If J selects X at t then a(J selects X at t) is also p(J selects X at t)
(possibility is a necessary precondition of actuality, nothing impossible is actual; everything actual is also possible)
If J selects ~X at t then a(J selects ~X at t) is also p(J selects X at t).
In other words, if (possible world X) is actual then (possible world X) is both possible and actual.
It should go without saying that if possible world ~X is possible at t (necessary to avoid assuming causal determinism), then the possible world ~X remains possible at t even if possible world X is actual. The modal fallacy tends to lead to a misunderstanding of this point, as “possible” is misunderstood as “might in fact be the actual world” instead of merely understood as the definition of “possible” (could be actual). People mistakenly conclude that if X is actual then ~X is not possible.
Following the above, if J at time t selects X where J at time t is able to select X xor ~X, J has fulfilled all the reasonable expectations of a LFW choice. Nothing inherent in the selection process itself subtracts from LFW unless we count the prior assumption of causal determinism. Which would be cheating.
Criticism is welcome, and a visit to Norman Swartz's philosophy notes should help clear up questions about necessary, possible and actual worlds.