The book's main conceptual claim is summarized, to a pretty good extent, by the paragraphs mentioned at the top page of this website, which I repeat here.

The last paragraph of Chapter 1:
"It is generally agreed that it is not possible outside physics and its closely related fields to deduce definite predictions and expect them to be borne out experimentally. I am going to argue that it is indeed possible. The book's slogan is: language faculty science as an exact science is possible; yes, it is. Some may say that I am a dreamer. But I am not the only one. I hope upon reading the rest of the book some of the readers will join us."

The last paragraph of Chapter 8: Summary and concluding Remarks):
"What I envisage is a time when we will be able to deduce hard predictions (predicted schematic asymmetries) in various languages, will be able to evaluate by experiments the validity of our universal and language-particular hypotheses, and will be able to formulate hypotheses of a successively more general nature, without losing rigorous testability. When something like that has become the norm of the research program, an experiment dealing with one language can be understood clearly in terms of the universal hypotheses (along with language-particular hypotheses) in question so that the implications of the result of an experiment dealing with a particular language can be transparent with respect to other languages. Researchers "working with" different languages will at that point share (many of) the same puzzles and issues pertaining to universal properties of the language faculty. They will know precisely what necessary care and checks they need to do in order to design effective experiments for testing the validity of the same universal hypotheses. That will enable us to proceed in a way much more robust than what has been presented in the preceding chapters, still on the basis of confirmed predicted schematic asymmetries. The field will at that point be widely regarded as an exact science, and everyone will take that for granted. And I also suspect that, at that point, other fields of research that deal with the brain and the mind pay close attention to the research results and methodology in language faculty science as an exact science because they find it useful to try to learn from the categorical nature of the experimental results in language faculty science and its methodology that has guided its research efforts.²¹³"

FN 213: This reminds us of Chomsky's (1975: 5) remark that "it is not unreasonable to suppose that the study of … the ability to speak and understand a human language … may serve as a suggestive model for inquiry into other domains of human competence and action that are not quite so amenable to direct investigation."

The last two paragraphs of Appendix: the accompanying website:"It may not be an easy matter to obtain an experimental result that constitutes a confirmed predicted schematic asymmetry even in a single-researcher-informant experiment. But it is, ultimately, the replication of a confirmed predicted schematic asymmetry in a multiple-non-researcher-informant experiment that makes us confident about the validity of our hypotheses that have given rise to the predicted schematic asymmetry. It is also such replication that would prompt us to pay serious attention to the empirical and "factual" claims put forth by others dealing with a language about which we do not have native intuitions. One may in fact suggest that it is the replication of a confirmed predicted schematic asymmetry in multiple-non-researcher-informant experiments that would make us hopeful that language faculty science as an exact science may indeed be possible.
As stressed above, the replication of particular judgments by informants on a set of particular Examples is not our concern. We are concerned ultimately with the replication of our experimental results at a more abstract and general level. We are interested in finding out universal properties of the language faculty. We have chosen to work with a dependency interpretation as a probe for that purpose; see Chapter 3 for a conceptual basis for our choice. What type of dependency interpretation can be a good probe for the purpose may differ among languages, and even among speakers of the "same language." In our experiments dealing with individual speakers of a particular language, we check predicted schematic asymmetries given rise to by universal hypotheses, language-particular hypotheses and bridging hypotheses. It is the universal hypotheses among them that would help us see what universal properties underlie individual informants' judgments on Examples of "different constructions," with "different dependency interpretation," in "different languages." Before we begin to be able to address replicability of our experimental result at such an abstract and general level, however, a great deal of work has to be carried out dealing with particular languages, starting with the establishment and the accumulation of confirmed predicted schematic asymmetries, first in a and ultimately in multiple-non-researcher-informant experiment."