The most common argument against determinism has been advanced by such diverse sources as Ayn Rand, C.S. Lewis, and Sogn Mill-Scout.  It may be termed the Determinist Contradiction Argument (DCA): If determinism is true, then the belief in determinism is merely the result of cause and effect in the brain, and thus cannot be known to be true.  Formalized, the argument runs as follows:

1. Determinism - the belief that all events are entirely determined by antecedent causes (definition)
2. Human beliefs are events (premise)
3. If determinism is true, then all human beliefs are entirely determined by antecedant causes (1 and 2)
4. No belief which is entirely determined by antecedant causes could be known to be true (premise)
5. Hence, determinism precludes knowledge (3 and 4)
6. We have knowledge (premise)
7. Hence, determinism cannot be true (5 and 6)

If knowledge is considered as justified belief, what argument could be made in support or refutation of premise (4).  I have yet to hear any argument advanced in favor of (4), it is merely taken to be intuitively true.  Let us then consider a couple examples as intuition pumps to help us reconsider what may be taken as intuitive truth in this matter.

Suppose one glances at the sky and notes that it is blue, that is, one assents to the proposition "The sky is blue."  Did this belief require some freewill choice to be made before the individual could assent to it?  Of course not.  Perceptions are basic beliefs, barring the question of the validity of the senses, we believe our perceptions without deliberation.  Could such beliefs still be held if we were merely deterministic thinking machines which merely process information, such as computers.  Of course.  Robotics research is rife with autonomous devices which take in information about the outside world, process it, and act upon it, presumably without using volition.

The common objection to this example of non-volitive belief is that complex beliefs require deliberation and choice-making.  But how is it clearly the case that such choice-making must be indeterministic?  Consider an AI program designed to perform the task of getting a racing car through a curve as quickly as possible without losing control.  It knows the characteristics of the vehicle enough to determine roughly what velocity the car will slip from the road in  a given situation.  It calculates what the results would be for several different scenarios, entering the turn as various speeds and  angles, turning the wheel at varying intensities throughout the turn, and applying to gas or brakes in various ways.  After all of  the computation is complete, it chooses the alternative which gets it through the turn while optimizing some function of the turn time and the exit speed.  Now, we may say that the program has made a correct choice from among available alternatives, and yet it is evident that volition was not involved.  Most modern neurologists believe that human decision making is similar to this process, except at a higher level of complexity.

If beliefs need not be indeterministically arrived at in order to be either justified or well chosen, then premise (4) is faulty and the argument collapses.  We can cite examples of such beliefs, and expert consensus is that human beliefs are of the same ilk.  The DCA is thus stood upon its head pending further support of this key premise.