WO L F R A M H I N Z E N
. Introduction
What in syntax do so-called “interface conditions,” in current minimalist con-ceptions of the language faculty, explain? Virtually everything, to the extent that the Strong Minimalist Thesis (SMT) holds, which stipulates that language is an optimal response to interface conditions externally imposed on the language faculty prior to its insertion into a language-ready but prelinguistic brain. The idea is that prior to and independent of the evolution of language, systems of “thought” or semantics were in place that the emerging language system had to “interface” with. Clearly, then, the language system will have to satisfy certain minimal conditions on usability imposed by these non-linguistic systems (“bare output conditions”): conditions the language system has to satisfy to be usable at all.
It is hard to see—and I will here concur—that such usability conditions could fail to be met. Yet, I will argue that this particular conceptual necessity is a very different demand from another and much stronger one, to the effect that there are richly structured non-linguistic systems of thought on the other side of the interface (so-called “Conceptual-Intentional” or “C-I”-systems), whose structures mirror and explain the syntactic forms that we find on the inner, linguistic side of this interface.
To illustrate how minimalist explanation by appeal to conditions imposed by the interface (the semantic one, to which I largely confine my discussion here) work, consider the question why adjunction should exist as an operation in the grammar. Chomsky (a) suggests that at least prima facie there is no principled ground for such an operation to exist in addition to the operation standardly called Merge, which combines lexical items into binary sets. The
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suggestion is that Merge is conceptually necessary, hence does not need to be especially justified, and hence that adjunction, if it exists additionally, needs to be so justified. Why is Merge conceptually necessary? Because any combi-natorial system exhibiting discrete infinity needs an operation putting some primitive items together into larger, complex units containing the former as parts. Merge as currently defined is meant to achieve exactly that and nothing more. If Merge is defined so as to capture what is minimally needed—it simply includes the items in question into unordered binary sets, giving rise to a relation of containment—Merge can be viewed as coming for free and as having found a “principled explanation.” How then is adjunction to find such an explanation, too? Answer: The C-I-systems “require an operation of predicate composition,” as Chomsky (a) puts it, and adjunction (“pair-Merge”) provides just that.
At the heart of this explanation is the positing of a certain functional need, whose existence rationalizes a given computational operation. Inevitably, for such an explanation to work there needs to be evidence for the functional need in question which is independent of the operation to be motivated itself. But as Chomsky himself has often emphasized, such evidence is not in general to be expected, given the evolutionary and conceptual entanglement of language (on the inner side of the putative interface) and “thought” (on its outer side). We don’t have much independent grasp—if indeed grasp at all—of the semantic systems or systems of “thought” on the non-linguistic side of the semantic interface. Therefore, any attempt to explain language from interface conditions imposed on it will have to figure out the nature of those conditions by looking at how narrow syntax satisfies these very conditions.
A circularity problem thus looms, though one that is not necessarily either vicious or unfamiliar from other areas in biology (e.g. the adaptationist pro-gram in biology) or cognition (e.g. the study of neural nets). On the other hand, there is a danger of mistakenly assuming that as we pile up explanations of features of language in terms of “interface conditions,” we have actually provided independent evidence for what these interface systems are like—
instead of merely getting results that are artefacts of our research methodology.
The problem of merely providing “just-so” stories arises in the biolinguistic program as much as it does in evolutionary thinking at large.
The problem worsens if we add to this a rather simple-minded conceptual point. Any textbook introduction to linguistic minimalism repeats that the very existence of a “C-I”-interface is a “virtual conceptual necessity.” But it isn’t: It goes beyond conceptual necessity. By a merciless minimalist logic it
The Successor Function + LEX
would have to go for this reason alone. All that’s conceptually necessary is that language is used. This weaker statement does not entail, firstly, that there is an interface where linguistic representations arrive tuned to (independently given) requirements of some “outside systems of thought”: Language and thought could be more entangled and could obviously have co-evolved in such a way that no conceptual distinction between the two can be drawn (and none of the two “answers” any conditions imposed by the other). Secondly, there is no entailment that the language system will be anything more than usable by the outside systems. That is, it may as well be no more than partially used, hence not meet conditions on expressive potential optimally or in full.
Thirdly, and relatedly, it doesn’t follow that the language system will actually be explained by the outside systems or the conditions imposed by them. To conclude from the system’s being used that we can explain it by reference to systems that use it, is a non sequitur.
Ludwig Wittgenstein, when proposing a “use-theory of meaning,” stayed clear of this last error. His thesis that “meaning is use” does not suggest that we can explain the meaning of an expression from its use. Indeed, obviously this very use is what does itself need to be explained (in part by conditions that may be internally imposed). Transferred to the context of the MP, a use theory of meaning would not assume that language answers to independently given thoughts or semantic contents that we somehow “grasp” in our C-I systems and that the linguistic system is somehow designed to “express.” Instead, the workings of the computational system and how its productions are being executed by systems of use could be all there is. That these productions are used implies that other cognitive systems using linguistic structures must be rich enough in themselves to be able to use these structures somehow, but not that they “rationalize” them or impose conditions on which structures need to be delivered by the syntax in order to meet certain independent semantic con-ditions. The importance of this distinction will be clarified through examples later on.
If human syntax is to essentially boil down to Merge, as on the stan-dard minimalist view, it is natural to attempt to blame as much as possible on “bare output conditions.” Accordingly we may expect that the current tendency to deflate phrase structure and linguistic structure-building will correlate with an inflated conception of what conditions of language the extra-linguistic “semantic systems” impose. And indeed it seems to me that the more minimal the syntax has become in recent years and the more flatter and thinner our trees, the more maximal the conditions imposed by the semantic interface have become. Current empirical evidence in comparative
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cognition, I will argue, does not support this asymmetry and in fact suggests pursuing the opposite strategy: inflating our notion of syntactic categorial hierarchy and deflating the role of the interfaces, particularly the semantic one.
(), below, is a long list of linguistic properties that have been said to be motivated from interface conditions—this is virtually all of the theory of syntax except Merge and principles of efficient computation (giving rise to locality effects):
() a. adjunction
b. the A/Adistinction c. displacement
d. the binary nature of Merge e. the EPP-principle
f. the relation Agree g. phases
h. hierarchy
I will here conclude that what can be motivated from interface conditions may as well reduce to (a), alone, and that, moreover, an “I”(ntentional) interface, in the sense of something that could motivate LF-like structures, likely does not exist. Empirical differences between conceptual (C) and intentional (I) structures or information, and the dependence of the lat-ter on the former (which does not hold the other way around), suggest that at least the intentional ones are narrowly linguistic and likely originate with the very syntactic structures that are often said to merely “express”
them.
In the following section I will turn to the “deflated” conception of Merge or combinatoriality that has been thought to yield human language, after being added to (i) a lexicon, (ii) interface conditions, and (iii) language-independent economy principles, in the way that the title of this chapter suggests. Section
. turns to some available evidence from comparative cognition regarding thought in non-linguistic animals. Section. turns to adjuncts specifically and argues that the very reason why adjunction perhaps can be motivated from semantic interface conditions also reveals why probably little else in syn-tax can. I also sketch a hypothesis for where the actual locus of hierarchy in the linguistic system lies, and why, in particular, it cannot be based algebraically on the kind of structures that the successor function in arithmetic yields.
Section. concludes.
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. Deflating Phrase Structure
.. Arithmetic and Merge
Chomsky (: ) argues as follows:
() Merge
“Suppose that a language has the simplest possible lexicon: Just one LI, call it ‘one’. Application of Merge to the LI yields {one}, call it ‘two’.
Application of Merge to {one} yields {{one}}, call it ‘three’. Etc. In effect, Merge applied in this manner yields the successor function. It is straight-forward to define addition in terms of Merge (X,Y), and in familiar ways, the rest of arithmetic. The emergence of the arithmetical capacity has been puzzling (. . . ) and it has often been speculated that it may be abstracted from FL [the faculty of language] by reducing the latter to its bare minimum. Reduction to a single-membered lexicon is a simple way to yield this consequence.”
Arithmetic, that is, is the “minimal language,” and iterating the operation “set-of ” generates the natural numbers:
() Enumerating a series I
Ø =
Merge () = {Ø} = Merge () = {{Ø}} = Merge () = {{{Ø}}} = etc.
The broader idea is: If we generalize the generative principle of the series (), i.e. Merge, and add the full set of lexical features characterizing FL, language-specific properties will emerge. On the other hand, the successor function is standardly defined as the transitive closure of the “immediate successor”
function defined in ():
() Immediate successor Succ(X) =defX∪ {X}
Note that applying this definition yields not the sequence generated by Merge in (), but the full ordinal sequence in (), in which every number is the set of its predecessors:
() Enumerating a series II
Ø =
Merge() = {Ø} = {} =
Merge() = {Ø, {Ø}} = {, } = Merge() = {Ø, {Ø}, {Ø, {Ø}}} = {, , } = etc.
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Once Succ/Merge is defined, algebraic operations + (addition) and (.) (multi-plication) are definable, and if these conform to relevant axioms, we obtain a mathematical space that is a group. I will here think of a space like that as pro-viding the mind with a particular “ontology”: Any structured mathematical space, having elements in certain structural relations (including entailments), contains objects of a particular kind and formal nature. In geometric terms, the particular space built by the generative principles above can be represented as a line; in algebraic terms, as a vector space, every element of which can be expressed as a linear combination of the vectors in its base. In this particular case, there is one single vector in the base, namely, , scalar multiplications of which suffice to span the entire space in question (they yield all of its elements). By consequence, the dimension of the space so constructed is one:
Merge as conceived in () yields a one-dimensional vector space. If Merge in language and Merge in arithmetic are species of the same operation, as per Chomsky’s quote above, linguistic objects will be of the same mono-dimensionality as the natural numbers. That this is so is an empirical claim about the productions of the human faculty of language, right or wrong. In principle, syntactic objects could vary across more than one dimension.
Note that the space of the numbers as such (which of course includes more than the naturals) is not one-dimensional in this sense. That is, if the successor function was the only generative principle the human mind could employ, our mind would be mathematically impoverished in a way it is factually not. To characterize all the other numbers that exist, from the whole numbers to the rational, real, complex, and hypercomplex numbers, the dimensionality of the vector space involved has to be steadily increased. Since a higher-dimensional system cannot evolve from a lower-dimensional one in a linear fashion, the mathematics/language capacity must involve non-linear operations alongside a linear Merge-operation. These operations are needed to as it were catapult us from one dimension to the next containing different kinds of objects, as our mathematical insight grows and we discover that one number system can be recursively employed as a basis for constructing another one. It is interesting to ask whether this process might find a reflection in human language: Whether, in short, non-linear operations are generative for certain aspects of linguistic objects as well, generating more and other hierarchies than those that linear and one-dimensional Merge as applied in the language system can. If arithmetic evolved from language, this is perhaps what we would expect.
There is an interesting consequence of the potential fact that human lan-guage may, in a relevant sense, be “multi-dimensional,” relevant to the prob-lem with which we began. The consequence, if indeed we wish to motivate
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language from interface conditions, is that either the extra-linguistic systems are multi-dimensional too, in which case we have simply shifted the explana-tory problem, or they are not, in which case we must essentially give up the whole project of principled explanation, to whatever extent it is tied to the idea of motivating syntax from interface conditions. On the latter option, it must have been narrow syntax itself, in evolution, which helped to boost the dimensionality of the human mind and the thoughts or objects it can recursively generate: “thought” wasn’t multi-dimensional before these specific computational operations of language (or arithmetic) evolved. Put differently, the language system was creative for the kinds of thoughts we can think (Uriagerekaa; Hinzen & Uriagereka ).
.. Phrase Structure in Minimalist Syntax
Let us turn now to the conception of phrase structure (PS) that results (or perhaps rather fails to result), when we think of Merge as little more than a way of generating hierarchies in the way of Merge, as in (). If Merge is set-formation, there is no reason to restrict it to singleton sets. Thus, let Merge form n-ary sets, and let the restriction of n= follow from “interface conditions” (as is standardly assumed). The result of this is a label-free bare phrase structure in something like the sense of Collins (), with lexical items replaced by numbers, as before:
() Merge (, ) = {, }
Merge (, {, }) = {, {, }}
Merge (, {, {, }}) = {, {, {, }}}
etc.
As Collins points out, labels go beyond “virtual conceptual necessity”; hence they cannot be part of a system that is defined by this very notion. There are lexical items, there are (sets of) sets of them, and there are syntactic relations (Theta(X,Y), EPP(X,Y), Agree(X,Y), and Subcat(X,Y)), which hold between features or lexical items X and Y; and there is nothing else. Three explanatory factors for syntax therefore suffice:
() (i) the interaction of properties of lexical items (ii) economy conditions
(iii) interface (bare output) conditions.
Syntax on this construal is no longer about part-whole relations among syn-tactic categories or phrases, but lexical items and relations between them.
There is no such thing as projection, in particular. PS in this sense seems
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exactly as “flat” and one-dimensional as our number line above. It does exhibit hierarchy in a sense, but that is a deflated form of hierarchy, which, as Chomsky puts it, is “automatic for recursive operations, conventionally suppressed for those that merely enumerate a sequence of objects” (: ).
Does this view amount to a (i) “derivation,” “reduction,” or “naturalization”
of PS on the basis of barren Minimalist machinery, or (ii) its elimination? The question hasn’t been much discussed, but Chametzky () has extensively argued for the latter conclusion: Minimalist syntax is a non- or post-phrase-structural phase in the theory of grammar. If this is true, it is unclear whether the dismissal of PS has actually been widely noticed among practicing lin-guists, who may be under the impression that what one does using minimalist technology is what one did all along, though now the descriptive machinery has been “minimized” and “derived.” Let us go through some problems which arise when attempting to make phrase-structural syntax compatible with minimalism.
First, Chametzky argues that contrary to claims of e.g. Epstein et al. (), syntactic relations defined on traditional phrase-structure trees such as c-command actually don’t fall out naturally from the minimalist structure-building operation, Merge. This is in line with arguments of Chomsky () to the effect that all syntactic relations reduce to two, set-membership (a consequence of Merge) and probe-goal relations, leaving out c-command.
Second, Chametzky argues that minimalist theory has failed to give an argument for the fact that Merge should not be simply concatenation, where:
() Concatenate (A,B) =defA∧B, with A, B atoms
That is, there is no prima facie reason why a minimalist syntax, if indeed minimal, should be phrase-structural. Hornstein (), from where () is taken, argues that concatenation doesn’t yield phrase-structural hierarchies, and is a weaker notion. If it is more minimalist, preference should go to it, other things being equal. But he also argues that other things are not equal, given that the hierarchical organization of linguistic expressions is a basic assumption of modern syntactic theory. Hence a more PS-like system has to be reconstructed, by adding something to a bare concatenative system: categorial labels. In short, labels are needed to upgrade a purely concatenative system to a phrase-structural one. Against this particular line of reasoning one can object on several fronts, however:
(i) Why there should be such a hierarchy is precisely the question we have to ask in this minimalist context, and we can neither take it as a traditional assumption nor in particular appeal to some mysterious
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external “demand for the system to be hierarchical,” when giving an explanation of that fact.
(ii) Why could Concatenate defined as in () not yield hierarchy as Merge did, above, through a restriction to being binary?
(iii) Why is recursive set-formation not essentially simpler than concatena-tion, as it does not depend on principles of ordering?
(iv) If accepted as a foundation for the system, Merge qua recursive set-formation makes labels in Hornstein’s sense unnecessary for hierarchy:
A Collins-style system yields it as well, in the trivial and automatic sense described above.
(v) Adding labels to a concatenation-based system is also not sufficient for
(v) Adding labels to a concatenation-based system is also not sufficient for