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.
7.2. THINGS THAT SHOULD BE DONE 193 of intensional languages I have presented might be unsatisfying in many regards – the foremost being: it seems hard to do linguistics with it. This is a general problem of the intensional position: whereas in the classical and finitist approach, the philosophical position quite clearly determines the ontology, in the intensional approach the ontology (what is “language”?) is rather mysterious, and there are many possible answers. So it is another big challenge to work out this position to the point where I can say: whoever has this philosophical position wrt. “language” has to accept our mathematical conclusions. I hope to address this in further research.
There is a fifth problem I have not addressed at all, which concerns my work in particular, but also most of formal linguistics in general. I have not found it mentioned explicitly except for one place, and there only in connection with a formal argument (see Mohri [51]). I will call it the problem of fragmentation.
A concrete instance is the one brought up by Mohri. Everyone reading this should be familiar with the proof of non-regularity of English; we construct a sublanguage{peoplen seen:n∈N}of English, intersect English with people∗ see∗, and there we are. There is however a flaw in this argument: how do we know that if peoplen seemis English, then necessarilyn=m? That is a point we have not made yet, which however is strictly necessary for the argument!
And just think about (1) People see, see, see
– syntactically, that should be as fine as (2) People talk, talk, talk.
We will not argue about whether the argument for the particular non-regularity of English can be saved in some way or rather not. For us, the interesting point is rather: making statements of the form: “English is not a regular language” are not only made dependent on a certain projection; they also depend on the fact that we only look a certainfragment of English. This means: statements of this kind are not only dependent on a pre-theory, but also depend on the assumption that further data we have not yet considered will not spoil the argument. Note that neither monotonicity nor upward normality are of any use in preventing us from this problem: we either cannot help the projection of a pattern being blocked, or we cannot help it being “covered” by a “larger” pattern.
To put it simply: claims of the above type are always based on fragments.
In our ontology, we never know whether we have observed all relevant data for a certain pattern. So what can we do to make them complete? There does not seem to be a solution, because we have nothing but fragments at any point (by finiteness). Could we improve the situation by making claims of the form: there is a fragment of English such that ...? But this is highly unsatisfying:
we can also easily find a fragment of English where utterance length grows exponentially, if choose it appropriately. What we rather want to say is: the fragment is somehowcoherent, we have not ignored any strings which naturally belong to it. That of course does not entail that there are no strings which are relevant, but of which we are not aware yet. And this seems to be the best we can do: we can sayto the best of our knowledge, which means we have chosen the relevant data for projection without deliberately ignoring anything. So there remains still a further condition on which statements of the form: natural
194 CHAPTER 7. CONCLUSION AND OUTLOOK languages are not regulardepend, and there is nothing we can do about it.
An issue which I should also mention is the following: in some discussions on this work,1 we discussed the question whether linguistic metatheory can simply take over linguistics; that is: the classical tasks of linguistics (with the cognitive commitment) should be solved by linguistic metatheory, or at least with its methods. My position is the following: I think this goes too far. I have stressed for all possible positions that there is a proper difference between linguistic theory and linguistic metatheory.
In the classical approach, this difference is as follows: the linguist takes a certain dataset, andchooses to project it into the infinite. If we want to use this as a model how the speaker learns his language, we immediately encounter a problem: the speaker does not have this choice. He has to stay open; more concisely: he cannot just define his subject, as does the linguist – he has to respect all external constraints. As linguists, it is inevitable that we always work with fragments; for the speaker – in the classical perspective – this is impossible:
a speaker by definition learns his language, so by definition he must have all relevant data and succeed on all possible (or plausible) presentations of the relevant data, at least in the usual idealized paradigm (see [10] for criticism and alternatives). The linguist on the other side is free in his decision, because he can possibly be wrong: he need not succeed in reconstructing the unique language a speaker knows, though this is what he strives for. So the (classical) speaker is in a much weaker position than the metalinguist; and if our methods are sufficient for metalinguistics, it is not said at all that they will also do for linguistics. That is, in short, my position: I will not say my methods are useless for linguistics, as say, for a theory of learning of the speaker. But I am not convinced they are sufficient. Just consider in how far our projections deviate from classical learning in the limit, which gives much weaker results, exactly because we cannot choose the point of projection.
In the finitist approach, there is an obvious difference between pre-theory and theory: this is because the meta-theory is basically inexistent – it is just a philosophical position, nothing more. What we have described in the above section was rather already theory.
What is maybe most delicate is the separation of linguistics and metalin-guistics in the intensional meta-theory; for this reason we have discussed this issue separately. In the intensional approach, we can assume an arbitrary set of pre-theories as given from the metalinguist. From what we have seen, inten-sional linguistics mostly consists in in fixing i-language and defining acceptable sublanguages, as they correspond to inferences speakers can perform on the spot.
In this sense, there is a very sharp boundary between meta-theory (defining the whole intensional language) and theory (e.g. defining sublanguage). The whole point of the intensional approach is: we do no longer fix “language” as what speakers actually know, but rather: as what theycanknow, if they reason. What they do reason in a sufficiently immediate and intuitive sense is an empirical question, and that is linguistics. So there is a sufficiently sharp distinction between linguistic theory and linguistic metatheory also in this approach.
There is also a principled concern I have regarding the idea of using the techniques of linguistic metatheory (say pre-theories) for linguistics within the
1Mostly with Udo Klein.
7.2. THINGS THAT SHOULD BE DONE 195 cognitive commitment. Metalinguistics as a discipline in its own right is only meaningful as long as we believe in the priority of the epistemological point of view. As soon as we convince ourselves that language is in the “mind” and we just have to see what it is like, there is no place for it. Now, if we do linguistics with the cognitive commitment, it is clear that we want to describe something in the mind of the speaker. But that in turn leads to the working hypothesis that linguistic metatheory can be neglected, if it has any meaning at all. If linguistic metatheory is irrelevant at best, that does not necessarily mean its techniques are. Still, I do not see why we should have pre-theories if we do not share the basic assumptions of linguistic metatheory. Just consider the strictly language-theoretic ontology of all metatheories. Adopting the cognitive commitment, one is quickly led to the (Chomskyan) conclusion that the part of language which we observe (that is, strings) is actually the most uninteresting of it. What is interesting from this perspective is rather the representation of language in the mind. It is immediately clear that this focus is diametrically opposed to any epistemological perspective: in the latter, we have a strong focus on the observable objects; in the former, we consider the observable objects negligible from a theoretical point of view. But why should we use pre-theories if we consider strings to be of minor interest?
So I see there is a dissonance between my approach and the commitment to a cognitive ontology, as it is prominent not only in the Chomskyan approach, but in most modern approaches to linguistics. I know that some researchers will see my major points very clearly, yet they will not easily be convinced to abandon their cognitive ontology. So as a very last point, let me stress that I do not think that the two cannot be unified: in fact, once we adopt a metatheory and construct “language”, nothing prevents us from conceiving of that object as something “cognitively real”. What is impossible to unify with our approach is the absolute priority of the “hard reality” of “language” in the brain over any epistemic concern.
196 CHAPTER 7. CONCLUSION AND OUTLOOK
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