His basic argument was that libertarianism was at least as reasonable from a scientific point of view as other theories of human decision making - determinism, compatibilism, etc. He defined libertarianism

"to be the view that human beings are capable of actions and decisions that are (a) undetermined and (b) nonrandom in a certain yet-to-be-specified sense." (p.189)

Balauguer's "appropriate nonrandomness" is the idea that some neural events which are undetermined by prior physical events do not occur randomly, or without reason. He calls this "neurological libertarianism" or NL, which is the reasonable thesis that "we have free will because of the nature of our brains - in particular, because some neural events are undetermined and appropriately nonrandom."

This idea is not original with Balaguer. He says that "numerous philosophers have defended materialistic (i.e., non-Cartesian) versions of libertarianism – see, e.g., Kane (1985), Nozick (1981), van Inwagen (1983), and Wiggins (1973)"

Balaguer notes that strict logical and physical determinism (he calls it "universal determinism") is not supported by empirical science, since quantum mechanics involves indeterminism.

Ii is better to use the term "predeterminism" to distinguish Balaguer's strict determinism from the "adequate determinism" that we have in the real physical world.

Nevertheless, he introduces an opposing view to his NL that he calls ND - "neurological determinism," which holds that all neural (and mental) events are causally necessitated by prior neural (and other bodily) events. The basic idea is that the world might include indeterministic (e.g., quantum) events, but that these are "for practical purposes" insignificant in the brain.

This is indeed the view of most molecular biologists and neuroscientists. Macroscopic structures as large as neurons contain vast numbers (10²⁰) of molecules, insuring that the statistical laws of physics approach the near certainty of classical physics. This is our "adequate" determinism. Balaguer explains this as a consequence of the "Law of Large Numbers," which it is.

"The most plausible view here – or, at any rate, the most popular – holds that (a) the only undetermined events are quantum events, and (b) all quantum indeterminacies get “canceled out” somehow before we get to the macrolevel." (p.192)

"Macrolevel phenomena consist of huge numbers of elementary particles; thus, even though the particles themselves behave stochastically, huge ensembles of them will be extraordinarily predictable, because the Law of Large Numbers will kick in, and the actual frequencies will coincide extremely closely with the probabilities"...What the appeal to the Law of Large Numbers explains is not how the macrolevel could be deterministic while the quantum level is indeterministic but, rather, how the macrolevel could be predictable while the quantum level is unpredictable. Perhaps it also explains how the macrolevel could be determined for all practical purposes while the quantum level is indeterministic." (p.200)

Balaguer tries to permit indeterminism, but in an "appropriately nonrandom" way. He says he does not take decisions to be abnormal among mental events.

"The problem of understanding how decisions are bound up with neural events is a special case of the more general problem of understanding the relationship between the neural and the mental.

"it might very well turn out that parakeets have free will. If we are free, then the seat of this freedom is not anything particularly noble, or dignified, or human – it is the braininess of our brains. Now, I have no idea how far down the evolutionary scale freedom extends; earthworm actions might be just as undetermined as human actions are, but it is doubtful, at this level, that they are appropriately nonrandom."

Martin Heisenberg has found that a biophysical basis for behavioral freedom exists in fruit flies and bacteria.

In 2004, Balaguer wrote A Coherent, Naturalistic, and Plausible Formulation of Libertarian Free Will (NOÛS 38:3 (2004) 379–406).

Balaguer begins with a variation of the standard argument against free will when he says:

Thus, if our decisions are appropriately non-random, then they couldn’t possibly be undetermined. Therefore, libertarianism is simply incoherent: it is not possible for a decision to be undetermined and appropriately non-random at the same time. (p.379)

He then develops some ideas of Robert Kane into what Balaguer calls "L-freedom" in "torn decisions."

These are decisions that require significant "effort" (C.A.Campbell) or what Kane called "self-forming actions" (SFAs).

Kane's model combines free will and values. Kane claimed his free choice is moral and made in accord with Kant's concept of duty versus one's self-interest or desires. This is the ethical fallacy. Freedom is merely a prerequisite for responsibility.

Balaguer's model and Kane's model are "restrictive," a term coined by John Martin Fischer to describe Peter van Inwagen's claim that only a tiny fraction of our decisions and actions could be free actions. For van Inwagen, it is those which have closely balanced alternatives (the ancient problem of the liberty of indifference. For Kane, it is those rare and difficult decisions that are deeply moral. They are those moments in which are character is formed. Later decisions made consistent with our character and values can then be traced back to these "self-forming actions." This provides us with what Kane calls ultimate responsibility or UR.

Although Balaguer argues, unlike Kane, that we may make many torn decisions a day, they are still restricted to cases where reasons for the alternatives are closely balanced. The ancients called freedom in such cases liberum arbitrium indifferentiae. To prove that only humans had such a freedom, they denied it to animals in the classic example of Buridan's Ass.

Balaguer says,

A torn decision is a decision in which the person in question (a) has reasons for two or more options and feels torn as to which set of reasons is strongest, i.e., has no conscious belief as to which option is best, given her reasons; and (b) decides without resolving this conflict —i.e., the person has the experience of "just choosing". (p.382)

He defines L-freedom, in the case of these torn decisions, in terms of "appropriate non-randomness" and authorship and control as follows:

L-freedom is defined as the ability to make decisions that are simultaneously (a) undetermined and (b) appropriately non-random. Much needs to be said about what appropriate non-randomness amounts to, but for now, let me just say that the central requirement that a decision needs to satisfy in order to count as appropriately non-random is that of having been authored and controlled by the person in question; i.e., it has to have been her decision, and she has to have controlled which option was chosen. (p.382)

Balaguer knows that he is open to the criticism that he makes indeterminacy the direct cause of actions. He quotes Daniel Dennett that

"It would be insane to hope that after ... deliberation had terminated with an assessment of the best available course of action, indeterminism would then intervene to flip a coin before action (1978, p.51)"

In a forthcoming book from MIT press, Free Will as an Open Scientific Question, Balaguer adds to this definition that "the indeterminacy generates or procures the nonrandomness." This is not the common view (in Dennett for example, which says indeterminacy in the moment of choice (especially following the careful balancing of reasons) would reduce agential control.

Balaguer expands the definition of appropriate non-randomness in terms of indeterminacy. He differs from most compatibilists and determinists who think that the laws of nature and the fixed past require our choice to be determined. He entertains the idea of quantum events in the brain just prior to choice, but if they are the direct cause of the choice, then it is not L-freedom.

when I say that if a torn decision is undetermined, then it is appropriately non-random, what I mean is that if it’s undetermined at the moment of choice, then it’s appropriately non-random. Thus, if I say that a decision was determined, that does not mean it was determined prior to the agent’s birth, or any such thing; if an undetermined quantum event occurs in my head two seconds prior to a decision, and if this event (together with physical laws and other circumstances) causally determines my decision, then on my usage, the decision counts as determined. (p.383)

if our torn decisions are undetermined at the moment of choice, then we author and control them. And I would like to point out here that this conclusion is introspectively satisfying. To appreciate this, suppose that a race of super-intelligent neuro-cognitive scientists studied your brain and told you that, in fact, your own torn decisions are undetermined at the moment of choice, so that when you make these decisions, nothing external to you makes you choose as you do. Would you conclude from this that you do not author or control these decisions? It seems to me that it would be downright bizarre to draw that conclusion. Indeed, if I found out that when I make my torn decisions, nothing external to me causally influences how I choose, I would conclude from this (together with what I already know about these decisions, namely, that they’re conscious, purposeful, intentional, and so on) that I do author and control these decisions. And this suggests to me that the intuitive notions of authorship and control do apply here, and hence, that if my torn decisions are undetermined at the moment of choice, then I author and control them. (p.393)

Balaguer realizes that he is trying to balance some indeterminacy with the control needed for us to be the authors and originators of our actions, that they are "up to us" (Aristotole's ἐφ' ἡμῖν).

He describes the standard two-horn dilemma argument against free will as randomness vs appropriate non-randomness.

Any event that’s undetermined is uncaused and, hence, accidental. That is, it just happens; i.e., happens randomly. Thus, if our decisions are undetermined, then they are random, and so they couldn’t possibly be "appropriately non-random". Or to put the point the other way around, if our decisions are appropriately non-random, then they are authored and controlled by us; that is, we determine what we choose and what we don’t choose, presumably for rational reasons. Thus, if our decisions are appropriately non-random, then they couldn’t possibly be undetermined. Therefore, libertarianism is simply incoherent: it is not possible for a decision to be undetermined and appropriately non-random at the same time. (p.379)

I would like to say a few words about cases in which the agent’s reasons pick out a unique best option and perhaps even causally determine the agent’s decision. I think that decisions like this can be free in the ordinary sense of the term, and I think that libertarians ought to allow that they can be L-free. (p.401)

it may be that these decisions are determined for all practical purposes; e.g., it may be that the neural events...are composed of large numbers of indeterministic quantum events that "cancel each other out."

In two-stage models of free will, quantum events may allow random alternative possibilities in the first "free" stage. But in the second "will" stage, Balaguer is right that the conscious will is adequately "determined for all practical purposes".

What would Balaguer's race of super-intelligent neuro-cognitive scientists conclude about choices we make for good and sufficient reasons consistent with our character and values, with our habits, and with our current desires? As he said earlier,

"when you make these decisions, nothing external to you makes you choose as you do. Would you conclude from this that you do not author or control these decisions?...It seems to me that it would be downright bizarre to draw that conclusion."

His 2009 book Free Will as an Open Scientific Problem is an expanded and revised version of the three articles - SJP as chapter 2, Noûs as chapter 3, and Synthese as chapter 4.

Balaguer has a new explanation for his “appropriate non-randomness.” On page 10 of his new introductions he adds a new clause b),

"Libertarianism is the view that human beings are L-free, where a person is L-free if and only if she makes at least some decisions that are such that (a) they are both undetermined and appropriately nonrandom, and (b) the indeterminacy is relevant to the appropriate nonrandomness in the sense that it generates the nonrandomness, or procures it, or enhances it, or increases it, or something along these lines."

In chapter 3, titled "Libertarianism Reduces to a Kind of Indeterminacy," Balaguer expands his Noûs idea of an appropriately nonrandom decision, defining it as one that is authored and controlled by the agent.

Balaguer notes that from many alternative possibilities an agent might narrow down the choices for prior determining reasons, but might leave some of the possibilities “tied-for-best.” It is choosing among these “tied-for-best” options that is “wholly undetermined at the moment of choice.” A specific example is choosing to have dessert after dinner for a prior reason, but leaving the particular dessert undetermined.

He then (p.92) confronts two objections. 1) the "luck" or “chance” objection. and 2) if a decision is undetermined, then it isn't determined by the agent's reasons or character, which seems like less control and authorship.

Contrary to most commentators (van Inwagen, Fischer, Mele, Clarke, G. Strawson, et al.), Balaguer maintains that even if the agent's decision were to be randomly distributed (if the world could be rewound and the same circumstances were replayed - following van Inwagen's thought experiment - and the results were random), this simply shows that it is the agent who makes the choices (p.92-94). If there were a pattern in the decisions, it would imply a hidden cause. For Balaguer, randomness is evidence that no prior cause was involved! So we must be the cause.

He then denies the familiar idea that "the looser the connection between the agent’s reasons on the one hand and her decision on the other, the less authorship and control she has over the decision" (p.95).

The basic idea seems to be that the agent had good reasons for winnowing down her alternatives to the "tied-for-best" options, so whichever of these she chooses, it can be considered a conscious, intentional and purposeful choice.

Balaguer then (p.96) offers two theses why "Wholly Undetermined Torn Decisions" (he calls this TDW-Indeterminism) procure, increase, and enhance authorship and control.

Thesis 1) Such decisions, he says “provide as much authority and control over them as we could possibly have.”

Thesis 2) If the decision were in any way causally determined , he says we would "have less authorship and/or control."

These two theses, Balaguer claims, entail that TDW-Indeterminism is freedom-enhancing, i.e., procuring or increasing authorship and/or control.

Since any less indeterminism (e.g., prior reasons) would reduce control, more indeterminism must increase it. He makes this synonymous with generating freedom. (QED?)

One interesting new item is that Balaguer says (p.123) that readers might have assumed from arguments in the book thus far that L-free decisions must be wholly undetermined and appropriately non-random (he calls them "type-1" decisions).

But, he says (p.123), "I never said that." He only claimed that if decisions are undetermined and appropriately non-random, then they are L-free.

So the Balaguer novelty is his argument that even actions that are causally determined by reasons ("type-2" in the article, "type-5" in the book) can be regarded as "L-free" (libertarian-free). The argument is that because agents are capable of "type-1" (undetermined and appropriately non-random) decisions, even decisions that are "determined" by reasons can be regarded as L-free.

(It's not obvious how the prior reasons that previously reduced authorship and control are now brought out as L-freedom.

Balaguer notes that he differs from Robert Kane, who says that if our reasons and motives even partially cause our decisions, then they are not free, unless the reasons in question were caused by prior undetermined L-free choices. On the contrary, Balaguer says that if an agent is L-free, and makes many undetermined L-free decisions every day, then her decisions that are caused by her reasons can also be called L-free.

He also differs from Kane, whose original idea of "torn decisions" is central to Balaguer's work, in that torn decisions need not be weighty and difficult moral decisions as Kane would have it. Indeed, we may make many torn decisions in the course of everyday actions, according to Balaguer.

In his Noûs article, Balaguer made the common mistake among philosophers of claiming that R. E. Hobart's classic 1934 article asserted that determinism was required for free will. Like many others including Philippa Foot, Balaguer misquoted Hobart's title - "Free Will as Involving Determinism."

He also misunderstands Hobart, when he says (p.6), "most compatibilists endorsed determinism. Some of these philosophers (Hobart for sure and arguably Hobbes and Hume as well) also held that freedom requires determinism."

Hobart's correct title is "Free Will as Involving Determination," which he defines only as the idea that reasons, character, values, etc. are determining factors in our free decisions. Neither he nor Phillipa Foot argue for determinism in the sense of predeterminism. Both think that chance is real

Balaguer (or his fact-checking editors) corrected Hobart's title in the book's bibliography. And in new material in the book, Balaguer argued, as had Hobart and Foot, against predeterminism, which is of course the real problem that is solved by some indeterminism in the world.

Hobbes and Hume did think they had reconciled free will with determinism, The hard problem is to reconcile free will with indeterminism. Balaguer attempts to do this with his claim that indeterminacy in the torn decision enhances "appropriate non-randomness."

In his Noûs article, Balaguer had distinguished only type 1 and type 2 decisions. Type 1 are "a) undetermined at the moment of choice and b) appropriately non-random." Type 2 are "determined by the agent's reasons for choosing." In his book (p.122-3), Balaguer distinguishes several more types of decision, including "Buridan's-ass decisions" that are wholly undetermined, "Maybe decisions" that are spontaneous and "not teleologically rational," and decisions in which the agent is "leaning toward one or more options."

With ideas that are hardly new (cf. Peter van Inwagen's Consequence Argument and Ted Honderich calling determinism a "black thing"), Balaguer says "The idea that determinism might be true can seem disturbing and depressing to us, and the reason, I think, is that it can seem to follow from determinism that we are something like puppets. If it was already determined before any of us were born that our lives would take the exact course that they in fact take, then it can seem that we don't have free will in any interesting or worthwhile sense."

In Balaguer's final chapter, "No Good Arguments for or against Determinism," he argues that there is no good evidence from empirical science in favor of determinism (quantum mechanics clearly denies it). He also notes that logical arguments alone cannot establish an empirical truth and therefore indeterminism is an open question. And since he argued in chapter 3 that the right kind of indeterminism would generate L-freedom, he concludes that free will is indeed the "open scientific question" of his title.