We have seen that the strive for linguistic generalization in the finitist paradigm looks very different from the “classical approach”. Work in this direction has been done, but most linguists would consider this work as research on “performance”, which is more about memory etc. than about “language” itself; this is to say: as part of psycho-linguistics or corpus-linguistics rather than of linguistics proper. This is however not necessarily true: we have argued that in fact these approaches belong to linguistics proper, but under the assumption of a very different philosophy (or metatheory) of language.
So I hope to have achieved two things: firstly, to lay out a finitist metatheory of language. This metatheory might not only allow for substantial insights both on the empirical and theoretical side; it might also be a “philosophical backup” to some existing approaches to “language”, which however are rather marginalized in theoretical linguistics. Secondly, I also hope that the formal methods presented here might might be of some help in this approach, and might serve as an inspiration for some linguist more empirically interested than I am.
In particular, PLP seems to be very satisfying both from a mathematical as from a theoretical point of view; we must however take for granted that linguists gather both positive and negative data for their falsificationism. If we do disagree with this theoretical assumption, that is, deny the relevance of negative data, then things get hard, though not impossible: still the approach using classical learning theory might work for us.
Chapter 7
Conclusion and Outlook
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190 CHAPTER 7. CONCLUSION AND OUTLOOK
7.1 Things that have been done
I will not try to summarize my work in this conclusion. Rather, I will first give a list of things I consider important and I think have been sufficiently addressed by this work, and then give a list of things I consider important that should be addressed in further research. In the first list, many of my maybe more “covert”
motivations will figure.
My most urgent concern was maybe the following: the situation in current linguistics is such that strictly speaking, we probably cannot even speak of one field of linguistics. This is not only due to the fact that there are many facets of language, and many different phenomena, such as its social dimension, historical dimension, psychological dimension etc. As a matter of fact, there are many different approaches to the same “core phenomena” of language, which diverge both in their methods as in their goals in a tremendous way. What we completely lack nowadays is an underlying theory which ensures that people can at least talk to each other; we seem to have lost this “common denominator”. One example is the following: scholars from one school of thought say it has been shown that “languages” are not context-free; scholars from another school of thought deny that this statement even has any meaning at all, as we cannot speak of “languages” as formal languages.
The first thing I hope to have achieved is exactly this: providing a common denominator for different approaches to “core linguistics”. My approach was to take a step back away from the subject of linguistics, and look at how we construct it. It turned out that we can construct it in different ways, and each of these ways has a good justification and interesting consequences. So if scholars have totally different views on “language”, one still can have reasonable arguments on “language”, but on the metalinguistic level rather than on the linguistic level. So there is no need for the polemics which (to my impression) has become somewhat overwhelming in the communication between schools. So the first point is: communication between schools should always be possible, though on the level of metalinguistics rather than linguistics.
The second thing I wanted to achieve is: scholars making claims about the formal nature of “language” should be able to formally lay out the premises they make in deriving their consequences. Of course, this is well-known, and it should be well-known to any linguist that a statement as: X proves that natural language are not regularis way too bold: this claim only holds under certain assumptions (note on the contrary that a statement of the form:
X proves that natural language are not strictly localcan be made – finite language property). So it seems rather lack of awareness or simply laziness rather than ignorance which makes people forget to mention these assumptions.
But this might to a large extent due to the fact that there are no theories about these assumptions. I hope to have provided such a theory and raised some awareness to these questions. I have the impression that formal linguists sometimes think that the projection of the language is the uninteresting part of their argument which is quickly done, while the rest of the formal argument has to be done very carefully. On the other side, when it comes to really deciding on a critical case of projection, linguists are often quite lost, as they do not have any hard criteria to guide their decisions. But neither of the two are inevitable: metalinguistics has its own interesting and complex mathematics;
and assumptions we make can be formally included in any argument via the
7.1. THINGS THAT HAVE BEEN DONE 191 notion of methodological universal and universal property modulo (f, P).
The third thing I wanted to achieve is the following: even though there are many different views on language in their own right, this does not open the door to arbitrariness: each assumption and position comes with consequences, commitments and challenges. And this is an important thing: we cannot just conceive of “language” as we like it on different occasions: in order to do proper linguistics, we have to take one position and elaborate it consistently. For example: if we say we skip the whole projection, then we have to make sure our theories verify something like the finite language property or partial language property, and generalizations proceed via finitary falsificationism. Again, I think that formulating consistent positions and working within them consequently might lower the mistrust between different schools of thought. (But as a note:
maybe also not; the Chomskyan paradigm is quite consistent, but still evokes most of the mistrust.)
A fourth thing I wanted to achieve is the following: the theory of linguistic formalisms has reached a very high level of abstraction and sophistication. But it sometimes seems that “real linguistics” is not catching up: linguists see too much of arbitrariness in formalizations and too many foundational problems in the languages we observe to follow into sophisticated formal arguments. Maybe the formalization of linguistic metatheory might help to lift linguistics to a more abstract level, making “real linguistics” more interesting to people with a major interest in formal methods. This of course would require that linguists (roughly) follow the arguments and methods I have laid out. And, of course, it requires that the methods of linguistic metatheory become much more elaborate than what I presented here: after all, I have only tried to lay out possible solutions, and I have not put them to the test against real datasets of languages.
A fifth point is the following: in theoretical linguistics, there is a long and ongoing debate on the ontological nature of its subject: is “language” in the mind, an abstract object, a social convention etc. For example, the entire consistency of the Chomskyan program seems to rely on the assumption that “language” is in the brain (more than in the mind) in a very strong sense, and this assumption is used to “kill” any epistemic concerns (see for example Ludlow, [47]). The main presupposition of this entire work is the priority of epistemological questions over ontological questions: it does not matter in the first place what “language”
is, but rather what we can know about it; in particular, the discussions on what languageis are meaningless if they go beyond what we can know. To make a stronger claim: any assumption on what “language” is which goes beyond what we can know is illegitimate. This view is very old in philosophy – I guess it is the essence of Kant’s Critique of Pure Reason – but does not seem to have found access to linguistics yet. Sure, linguistics is a young discipline, and to promote a research program one needs strong assumptions. But in the light of the current situation, I think there is very good reason to switch to the epistemological position.
So this is my fifth main motivation: promote the priority of epistemology in linguistics. At a certain point I found it startling to find linguists speak of acceptability and its difference to grammaticality, that we only see acceptability but want grammaticality, without the slightest care about the fact that gram-maticality is then no longer an empirical notion, and that consequently it is completely undefined what it means unless they explicitly define it in some way.
Linguists just think they know “language” or grammaticality by the grammars
192 CHAPTER 7. CONCLUSION AND OUTLOOK they write, and I have not found out what makes them be so sure.
One might ask: how can I promote the epistemological point of view, if I presuppose it? As far as I can see, there is no way to falsify the ontological point of view from the epistemical one or vice versa, because for the sake of any argument, we presuppose one of these positions. So the argument for one point of view is rather: taking this point of view, the questions we ask and the answers we get are richer and more meaningful than in the other. And this is the sense in which I wanted to push forward the epistemological point of view: by showing that it opens a whole new world of meaningful, fascinating questions, and that it allows to bridge the gaps between different schools of thought, which at least partly are due to different ontological assumptions and commitments.