Two more cents.
An, sometimes unappreciated, argument against determinism is based on our direct introspective experience of freedom as related to acknowledging multiple potential courses of action (ie ability to do otherwise).
Like the Cartesian cogito, which is certain indubitable knowledge, based on our direct experience of thinking and what this entails; it has been argued, many times, that our direct experience of freedom, is of the same type of certain and indubitable knowledge, which cannot be separated from our experience of ourselves. Some other types (or times) of introspection, lacking such clear and distinct qualities as our sense of freedom, notwithstanding.
Existential/phenomenological arguments for freedom, as for example, in J.P. Sartre's nothingness and freedom in Being and Nothingness are along similar lines, in that our phenomenological inquiries reveal our freedom to us in the constant process of always (re-)creating ourselves through the nothingness that reflects a lack of fixed essence, an openness to options, and an absence of strict determinism, besides the facticity of the moment.
Furthermore, it is argued that in order to know that we have an ability to do something, it is not required to actually do it. In other words, an ability is like a property that it can be known, in principle, like other properties, independently of any realized action, associated to that ability.
For example, having jogged some kilometers in the past week, I know I have the ability to perform a jog now, I do not need to actually jog to know I have the ability. Or, in other words, the fact that I decided not to jog now, did not eliminate my ability to jog (possibly tomorrow).
This argument addresses the counterargument that an ability to do otherwise cannot ever be known since only one thing is eventually realized. It is pointed out that not only is there nothing in principle problematic in knowing to have an ability to do otherwise, regardless of what option is finally realized, but it is also the basic way our direct experience of freedom is made manifest.
Arguments along these lines are given, for example, in
a) LIBERTARIANISM AND AGENTIVE EXPERIENCE by Justin Capes:
Experiences of many kinds play a role in justifying our beliefs, and
agentive experience is no exception. Just as we often treat sensory
experience (perhaps in conjunction with other background beliefs and
experiences) as providing pro tanto justification for beliefs about
our physical environment, so too we often take agentive experience
(again, perhaps in conjunction with other background beliefs and
experiences) to provide pro tanto justification for beliefs about our
own agency. Take, for example, my (presumably justified) belief that
I’m currently typing this sentence. What justifies that belief? I’d be
amazed if my experience as of typing the sentence didn’t figure in an
answer to that question. Or consider our (presumably justified) belief
that we often behave intentionally. What justifies that belief? Surely
our experience as of doing things intentionally has a role to play
here, too. At the very least, it provides, or plays a role in
providing, some defeasible support for the claim that much of what we
do is done intentionally. The agentive experiences just mentioned
aren’t infallible, of course; even very basic experiences, including
basic experiences of our own agency, can be non-veridical. But an
experience needn’t be infallible to play a role in justifying the
relevant beliefs, provided, of course, that we lack good reason to
believe that the experience is non-veridical.
b) Can We Know That We Have Free Will by Introspection? by Keith Lehrer:
[I] shall attempt to prove that certain introspective data provide
adequate evidence for believing that man has free will. The
introspective datum that I shall argue supplies adequate evidence for
the belief that we have free will is the fact that we deliberate about
future actions. When we deliberate about whether or not we shall
perform some future action, we must be convinced that the action in
question is in our power, that is, we must be convinced that it is up
to us whether or not we shall perform the action. In order to
deliberate about whether or not we shall perform some future action we
must be convinced that we can choose to perform the action and also
that we can choose not to perform it, for we cannot seriously
deliberate about whether or not we shall perform an action unless we
believe that we can choose whether or not we shall perform it.
c) PERSONHOOD AND FREEWILL, Ockham’s Razor and a Revival of the Introspective Argument by Sharon Kaye:
I endeavour here to restore confidence in self-knowledge, and hence in
personhood, by reviving the introspective argument. In so doing, I
turn back to one of its earliest and most committed defenders, William
of Ockham. The determinist relies on Ockham's razor to justify the
elimination of free will, but I will argue that this constitutes an
abuse of the 'razor' and that the determinists have misrepresented the
introspective argument as an argument from feeling.
PS: See a different argument on same post and one more different argument on same post as well