A reconstruction of the logic of Lefebvre's paper (1995) reveals several non sequiturs. In particular, and most important: (a) the problem of free will is argued to enter in an arbitrary form, and (b) the anthropic principle should (and could) not be combined with any non-necessary statement of the kind discussed in the target paper.
1. I have the bad feeling that it's a complete misunderstanding on my side (it should be), but I can't help finding Lefebvre's paper (1995) an impermeable mixture of issues in philosophy of mind, philosophy of science, logic, and psychology, doped with casual moral and metaphysical remarks.
2. Having said this in advance, I also add that I know from experience how frustrating it is to read aggressive yet ignorant reviews of one's own work. So, I try to put aside my aesthetical reservations caused by the far too many different things combined in the paper, indeed ranging from free will to the problem of golden section to that of the Universe. With these qualifications in mind, this is how I reconstruct the main line of the argument:
(i) Lefebvre postulates a thesis he calls the "principle of freedom" which states that "We have free will and under certain circumstances also freedom of choice";
(ii) he develops a model in mathematical psychology to generate formulas that operationalize "free will" and "free choice";
(iii) by applying this model (one based on probability distributions), Lefebvre obtains numerical results which coincide with statistics of certain empirical binary choice tests, and with what could be obtained by using certain ad hoc methods such as the golden section rule;
[(iv) from this state of the affairs he tacitly concludes that, since his model of free choice yields empirically confirmed results, the principle of freedom must be true;]
(v) then, Lefebvre combines his principle of freedom with a sentence that states the anthropic principle, which is a metacosmological concept about Man and the Universe, something exposed in the title and briefly explained in the introduction, but not even appearing in the paper itself;
(vi) finally, from the combined sentence (i.e. anthropic principle plus principle of freedom) the author draws the inference that this Universe is constrained by the condition that free choice (and maybe free will) must be possible.
(Note that I took the liberty to add (iv) which appears nowhere in the paper but without which (v) and (vi), which do appear, would be impossible.)
3. I must admit that I find this argumentation very difficult to understand. Minor details, such as the problem whether there is a golden section phenomenon at all (a problem correctly discussed by Lefebvre), or the problem of whether the anthropic principle should be viewed as a scientific or as a metaphysical statement (a heavy issue that cries for analysis but is not even mentioned by the author) are of little importance at this point, not to speak of the author's treatment of morality, which I entirely refrain from discussing here.
4. What matters for me is the above structure of the argumentation. There are three different topics that I would like to comment on in this context. In parenthesis, I indicate the respective steps in the above reconstruction.
5. Mathematical psychology is a field of its own, with a strong tradition. You may like or dislike it. In either case it is very doubtful that it can be used in the context of free will at all -- or at least that it can be used in the form as applied by Lefebvre here. For example, it is well known since Descartes, Ada Augusta, or Schopenhauer (to pick a few names randomly) that the problem of free will is impossible to separate from that of mental determinism, an eminent problem for philosophy, physics, and philosophy of science. Without paying attention to mental determinism, and to the characterization of mental events in general, the problem of freedom as understood both by intuition and tradition can probably not be addressed.
6. Take, for instance, the fact that a human or a machine can without any kind of "will" (lest free will) easily perform those "free choices" Lefebvre speaks about (cf. equation 2.3.). This is so because, in Lefebvre's overwhelmingly performance-based model of freedom, the state of having the gift of "freedom of choice" is characterized by nothing else but a certain behavior in a certain situation of probabilistic decision-making. It is clear, however, that a suitable deterministic gadget, using rusty cogwheels or whatever else, can be designed so as to perform identically. Of course, alternatively, the choices "forced" upon a decision-maker by the "world influences" of Lefebvre can be made by somebody who does have a free will and does exercise his freedom of choice, only he chooses to use it in a way as foreseen by Lefebvre for somebody deprived of freedom. (In other words, I can behave like a vending machine if I want to.)
7. That is, maybe probabilistic choice might grasp certain aspects of human will but not human will as such. That is of utmost importance if we want to proceed backwards, as does Lefebvre, using choice results to ground free will.
8. The inference "if from the principle of freedom we get results that coincide with observable facts then the principle of freedom is true" is false, and it is false in a most elementary fashion: there can be zillions of other ways, with or without using principles of freedom, for obtaining the same results (in Lefebvre's case, for obtaining the golden section or other magic numbers).
9. That is, if a model works fine, this alone proves nothing. There are so many bad models that give out the right results for the wrong reason.
10. A standard story is Planck's discovery of quantum mechanics. What he initially solved was the problem of finding an expression for black body radiation. Yet that in itself would have been completely uninteresting mental gymnastics: all right, he's got a trick to compute the right results, so what? Quantum mechanics was born at the moment Planck gave a reason why his expression should apply if a testable hypothesis (i.e., that there are quanta) is true. By analogy, in order to accept the principle of freedom, one needs reasons provided by testable consequences and by phenomena that don't go without the principle. Maybe there are some, but the paper did not discuss these.
11. As to this point, consider the following inference (for the excessively pedantic, let us assume that I am a human, so that part is o.k.):
"The Universe must be compatible with human existence." "I am professor of the university."
Conclusion: "The Universe must be compatible with the condition that I am a professor of the university."
However, the Universe does not mind me at all (or so I often feel), hence the conclusion is wrong. Yet this is exactly the sort of "result" obtained by Lefebvre when jumping into the conclusion that this is a Universe particularly supportive of free will. By the same token, he could have said it's a Universe supportive of mathematical psychology. More than the principle of free will, it was the mathematics of choice behavior that was proved by Lefebvre's results, so why not plug it into the same form?
12. Of course, logically speaking, the error lies in assuming that the sentence "I am professor of the university" is a necessary truth. I happen to be a professor but that could be otherwise. The same goes for the principle of free will (if for a moment we consider the principle of freedom to be a true statement). To take the principle of freedom as a necessary truth is ungrounded on account of the evidence presented.
13. Necessity is the key problem here. Modal logicians would say that only what's true in all "possible worlds" is necessarily true, and only what's necessarily true (or necessarily false) can be used in non-modal inferences -- that is, without using "qualifications". In this sense, even the anthropic principle itself fails to qualify for Lefebvre's treatment. What the anthropic principle states is exactly a non-necessary nature (in the logical sense) of our particular world. It is the nongenericity of our world that makes it so easy for many people to get from the anthropic principle to God or to the belief that we are lucky guys who won this Universe in a lottery.
14. There are degrees of necessity. Most utterances rank very low on this scale. Even if the principle of freedom was accepted, or replaced by quantum mechanics, or by something else we are ready to accept, it would not pass as a necessary truth. It would still be conditional, maybe mildly so, but still. One could not conclude, for instance, that "This Universe must support the science of quantum mechanics", for other developments in physics are equally thinkable.
15. And, finally, what if we could conclude all the above? What would be gained by a cosmological imperative? If this is a friendly Universe that supports life (as stated in the anthropic principle), it does so together with life's products: quantum mechanics, freedom of choice, poetry, Lefebvre's paper, and this commentary -- or at least together with the possibility of all these. Is this possibility not enough?
Lefebvre, V.A. (1995). The Anthropic Principle in Psychology and Human Choice. PSYCOLOQUY 6(29) human-choice.1.lefebvre.