''You are getting pedantic. It's just shorthand for ''it is the brain alone that is responsible for generating behaviour'' What your examples suggest is will as the generator or agent of behaviour, which is not supported by evidence.
You just need to know how to search and what to search for. That may be difficult if you aren't familiar with the subject matter, as appears to be the case;
The Agent Brain
''Many neural structures have been associated to specific attributes of agency experience or to specific steps of the process that leads to sense agency. The collection of neural structures that are thought to mediate agency-related processes is rather wide and includes: the dorsolateral prefrontal cortex (dlPFC), the cingulate cortex (CC), the supplementary and pre-supplementary motor areas (SMA and pre-SMA), the posterior parietal cortex (PPC) and its inferior regions and the cerebellum (Gehring et al., 1990; Lee et al., 1999; Blakemore et al., 2001; Chaminade and Decety, 2002; Cunnington et al., 2002; Farrer and Frith, 2002; Blakemore and Sirigu, 2003; Farrer et al., 2003; Lau et al., 2004, 2006; Synofzik et al., 2008a; Balconi and Crivelli, 2009, 2010a,b; Balconi and Scioli, 2012; Balconi et al., 2017). The plurality of those structures and their distribution over the whole brain (see Figure Figure1)1) likely mirrors the complexity of the phenomenon and the different methodological and experimental approaches devised to study its facets (for a review see also David, 2010). Again, they are due to the contribution of multiple mechanisms in the coupling of behavior with mental states and sensory effects. Those mechanisms—and the structures that subserve them—can be traced back to overarching functions: monitoring of sensorimotor congruence and multimodal integration, intentionalization (i.e., elaboration and implementation of intentions), action monitoring and ownership/agency attribution.
Stimulating The Agent Brain: Non-invasive Brain Stimulation Evidences
''Neuroimaging and electrophysiological methods can be both enlisted among the correlational techniques (Walsh and Cowey, 2000), which allow for qualifying and quantifying ongoing neural activity during implicit or explicit tasks to compare it with co-occurrent subjective experience, cognitive performances, or behavior. By superimposing and integrating those series of data, it is possible to draw conclusions on anatomical-functional correlates of investigated functions and processes by means of association. Conversely, non-invasive stimulation methods can be enlisted among interference or causal techniques, which grant the advantage of drawing conclusion on neural causation and on the effective role of neural structures in supporting or modulating a specific function or process (Woods et al., 2016). Indeed, NIBS can be used to perturb the ongoing activity of a target structure during implicit or explicit tasks and then observe the consequences of such perturbation on behavior and/or neural activity (e.g., by means of EEG). It is worth noting that conclusions that can be drawn thanks to NIBS studies also show fewer potential biases than those deriving from clinical lesion studies (Walsh and Cowey, 2000). Relevant for the present discussion, NIBS techniques then present notably greater cognitive resolution—defined as the ability to tell something new about brain processes and to answer a wide range of questions on cognitive functioning and its physiological correlates (Walsh and Pascual-Leone, 2003)—with respect to other investigation tools.''
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You shouldn't try to simplify it by extending what are references to specific states within a system to the whole universe. If the universe is deterministic, all references to freedom are an illusion.
We are talking about the condition of a specific attribute or feature of brain cognition, will, what does will do? What is the role of will. Well, it doesn't make decisions, it doesn't acquire and process information, it does think or initiate actions. The brain does all that Conscious will merely serves as a conscious prompt to act, a sense of urgency, a felt need to take action...will does not decide to do this, it is just a part of conscious response as represented by the brain in response to a given situation.
So, the Agent Brain...brain agency if you like. One and the same thing. ''
