Basic layout of traditional positions in philosophy regarding the relation of free will (FW) and moral responsibility (MR) to determinism. Compatibilism is the view that FW and MR are compatible with a deterministic universe. Incompatibilism is the view that they are not. Incompatibilists come in a variety of flavors: Hard determinists think that determinism is true and we are not free; Libertarians believe that determinism is false and we are free in virtue of indeterminism. Hard incompatibilists believe that FW and MR are impossible, for they are not compatible with either determinism or indeterminism. There are a variety of compatibilist positions that provide different accounts of how FW and MR are not threatened by determinism. There are also accounts (not discussed here) that separate the conditions for FW and MR, and thus allow that MR is possible in a deterministic universe even if FW is not. These are sometimes referred to as versions of compatibilism, and sometimes called semi-compatibilism.

Neural mechanism of a decision about direction of motion. (A) Choice-reaction time (RT) version of the direction discrimination task. The subject views a patch of dynamic random dots and decides the net direction of motion. The decision is indicated by an eye movement to a peripheral target. The subject controls the viewing duration by terminating each trial with an eye movement whenever ready. The gray patch shows the location of the response field (RF) of an LIP neuron. (B) Effect of stimulus difficulty on choice accuracy and decision time. Solid curves are fits of a diffusion model, which accounts simultaneously for choice and decision time. (C) Response of LIP neurons during decision formation. Average firing rate from 54 LIP neurons is shown for three levels of difficulty. Responses are grouped by motion strength and direction of choice, as indicated. Left graph, The responses are aligned to onset of random-dot motion and truncated at the median RT. These responses accompany decision formation. Shaded insert shows average responses from direction selective neurons in area MT to motion in the preferred and anti-preferred directions (solid and dashed traces, respectively). After a transient, MT responds at a nearly constant rate. The LIP firing rates approximate the integral of a difference in firing rate between MT neurons with opposite direction preferences. Right graph, The responses are aligned to the eye movement. For Tin choices (solid curves), all trials reach a stereotyped firing rate before saccade initiation. We think this level represents a threshold or bound, which is sensed by other brain regions to terminate the decision. (D) Responses grouped by RT. Only Tin choices are shown. Arrow shows the stereotyped firing rate occurs ∼70 ms before saccade initiation. Adapted with permission from Gold and Shadlen () insert from on line-data base used in Britten et al. (), www.neuralsignal.org data base nsa2004.1.

Models of bounded evidence accumulation. (A) Random walk or drift diffusion. Noisy momentary evidence for/against hypotheses h1 and h2 is accumulated (irregular trace) until it reaches an upper or lower termination bound, leading to a choice in favor of h1 or h2. In the motion task, h1 and h2 are opposite directions (e.g., right and left). The momentary evidence is the difference in firing rates between pools of direction selective neurons that prefer right and left. At each moment, this difference is a noisy draw from a Gaussian distribution with mean proportional to motion strength. The mean difference is the expected drift rate of the diffusion process. (B) Competing accumulators. The same mechanism is realized by two accumulators that race. If the evidence for h1 and h2 are opposite, then the race is mathematically identical to symmetric drift–diffusion. The race is a better approximation to the physiology, since there are neurons in LIP that accumulate evidence for each of the choices. This mechanism extends to account for choices and RT when there are more than two alternatives. Reprinted with permission from Gold and Shadlen ().