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In: Journal of Logic, Language and Information 22 (2013), 195-230.
Paraconsistency and Plausible Argumentation in Generative Grammar: A Case Study
András Kertész and Csilla Rákosi
Abstract
While the analytical philosophy of science regards inconsistent theories as disastrous, Chomsky allows for the
temporary tolerance of inconsistency between the hypotheses and the data. However, in linguistics there seem to
be several types of inconsistency. The present paper aims at the development of a novel metatheoretical
framework which provides tools for the representation and evaluation of inconsistencies in linguistic theories.
The metatheoretical model relies on a system of paraconsistent logic and distinguishes between strong and weak
inconsistency. Strong inconsistency is destructive in that it leads to logical chaos. In contrast, weak
inconsistency may be constructive, because it is capable of accounting for the simultaneous presence of
seemingly incompatible structures. However, paraconsistent logic cannot grasp the dynamism of the emergence
and resolution of weak inconsistencies. Therefore, the metatheoretical approach is extended to plausible
argumentation. The workability of this metatheoretical model is tested with the help of a detailed case study on
an analysis of discontinuous constituents in Government-Binding Theory.
Keywords: generative syntax, inconsistency, paraconsistency, plausible argumentation
1. Introduction
Since the advent of Government-Binding Theory, Chomsky has continuously emphasised the
necessity of dealing with inconsistencies in generative linguistics. For example, in On
Binding he writes that
“[a]pparent counterexamples and unexplained phenomena should be carefully noted,
but it is often rational to put them aside pending further study when principles of a
certain degree of explanatory power are at stake. How to make such judgements is not
at all obvious: there are no clear criteria for doing so. […] But this contingency of
rational inquiry should be no more disturbing in the study of language than it is in the
natural sciences.” (Chomsky 1980: 2)
During the past three decades none of the claims made here have been thought over in the
generative literature as systematically as they should have been. We still do not know –
despite the long period of Government-Binding Theory and the rise of minimalism which
also presupposes the same idea of inconsistency tolerance (see e.g. Chomsky 2002: 95) –
which criteria decide whether a certain inconsistency may or must not be tolerated. The
present paper focuses on this issue and sets out to suggest a novel approach to the problem of
inconsistency in linguistics.
To begin with, let us remind the reader of the role which the standard view of the
analytical philosophy of science attributed to the law of non-contradiction in scientific
theories:
“Internal inconsistency of a theory was anathema to the positivists – the mark of
irrationality, the complete breakdown of logic and reason. For in standard logic and
epistemology […] a single inconsistency is logically and epistemically disastrous: an
inconsistency anywhere instantly propagates to generate inconsistency everywhere.
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[…] Accordingly, for the positivists, and for most traditional logicians and
philosophers, consistency was not one constraint on rational inquiry among others, to
be balanced in cost-benefit tradeoffs with those others. Rather, it was an absolute, sine
qua non for rational inquiry.” (Nickles 2002: 9; emphasis as in the original)
This view has prevailed for decades among linguists, too. Thus, theoretical linguistics seems
to be characterised by the presence of incompatible principles in relation to the treatment of
inconsistencies.
However, the topic of inconsistency has attracted increased attention over the last few
years in the philosophy of science. There have been serious attempts at its re-evaluation:
“Today, it is generally recognised that almost all scientific theories at some point in
their development were either inconsistent or incompatible with other accepted
findings (empirical or theoretical). A growing number of scholars moreover
recognises that inconsistencies need not be disastrous for good reasoning.” (Meheus
2002: VII; emphasis added)
How can the consequences of this general tendency in the philosophy of science be related to
Chomsky’s claims quoted above? Obviously, what is needed is the elaboration of
metatheoretical criteria for the detection and evaluation of inconsistencies which,
nonetheless, are not alien to and, therefore, applicable to the practice of linguistic research.
However, the comprehensive discussion of such a methodology at a general level would be
beyond the scope of the present paper. Therefore, we will restrict our considerations to an
instructive and illuminating example by relativising them to a particular case study.
Moravcsik (2006, 2010) outlined a systematic typology of inconsistencies and their
resolution in syntax by analysing a great number of examples. Her main hypothesis is that the
differences between syntactic theories result basically from different strategies of
inconsistency-resolution. Another approach was put forward in, among others, Kertész
(2004), and Kertész & Rákosi (2006, 2012). In the present paper we want to relate the two
approaches in the following way: the starting point for our case study will be one of
Moravcsik’s (2006: 47 ff.) central examples, namely, Baltin’s (1987) account of
discontinuous constituents, and we will present a detailed metascientific analysis of this
example by making use of the framework developed in Kertész & Rákosi (2012).
Baltin’s paper applies a particular version of Government-Binding Theory as conducted
in the late 1980s. In our study, it serves merely as an object-scientific example which is
expected to illustrate our metascientific approach to the structure and function of
inconsistency in syntax; we do not dispute his findings and it is not our aim to criticise his
analyses.
Thus the present paper will focus on the following problem:
(P) (a) How are inconsistencies treated in Baltin’s account of discontinuous
constituents?
(b) Which metatheoretical framework is capable of representing these
inconsistencies?
(c) How can the treatment of inconsistencies in generative syntax be evaluated?
The structure of the paper is as follows. In Section 2, we will first offer a brief survey of the
structure, the function and the treatment of inconsistencies in Baltin’s paper with respect to
different analyses of degree word complement clauses. For lack of space, we will discuss
only those aspects of his account which are relevant for the solution of (P). In order to get an
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– at least relatively – direct and neutral picture of Baltin’s approach, in this section we will
not apply any specific metascientific model and will try to keep the descriptive apparatus
applied to a minimum. In this way, we will obtain our answer to (P)(a). Section 3 will be
devoted to showing how inconsistency in scientific theories can be reconstructed by the
application of Rescher & Brandom’s paraconsistent logic. Then we will apply this
paraconsistent logic to Baltin’s argumentation and thus obtain a solution to (P)(b). We will
see, however, that this result is not satisfactory, because paraconsistent logic can be applied
only to the reconstruction of single contradictions; it cannot grasp the process of the
continuous emergence and resolution of inconsistencies in Baltin’s argumentation. Therefore,
the treatment of inconsistencies cannot be evaluated on the basis of paraconsistent logic
alone. Consequently, in order to solve (P)(c), in Section 4 we will briefly show that the
dynamism of the emergence and solution of inconsistencies can be captured if paraconsistent
logic is supplemented by the tools of plausible argumentation. Finally, Section 5 will
summarise our findings.
2. On (P)(a): The emergence and the treatment of inconsistencies in Baltin (1987)
2.1. The basic inconsistency and four proposals to its solution
Baltin (1987) raises the problem of discontinuous constituents in generative grammar by
investigating sentences containing degree words and complement clauses such as
(1) (a) John was so tall that he hit his head on the overhead lamp.
(b) John worked on the problem too much to give up.
The syntactic analysis of examples like (1)(a) and (b) must account for two things. First,
sentential complements are selected by the degree word, i.e., they are complements of the
degree word.
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One of the principles of generative grammar says that complements have to be
generated within the phrase whose head is their selector. The adjective, however, is not the
complement of the degree word (because it can occur in a sentence without the degree word
but not vice versa). From this we obtain the following structure:
(2) [NP Infl [V [Q complement clause] A]]
Second, sentential complements always appear in clause-final position, i.e. we have the
order:
(3) NP Infl V Q A complement clause
Thus, in representing the structure of this sentence, the linear separation of the degree word
and the sentential clause as well as their syntactic relatedness should be accounted for.
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That
is, one has to resolve the following inconsistency which is one particular manifestation of the
general problem of discontinuous constituents:
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That is, without the degree word, sentential clauses cannot appear in the sentence. Moreover, the finiteness
of the complement clause depends on the choice of the degree word (so + that …; too + to …; enough +
that/to…).
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For evidence for this claim, cf. the examples (1)-(2) and (3)-(10), respectively, in Baltin (1987: 11f.).
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(I) (a) Sentential complements of too, so, etc. are located between the degree word
and the adjective.
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(b) Sentential complements of degree words may appear only in clause-final
position.
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The central problem of Baltin’s paper is how to handle the contradictory set (I)(a) and (I)(b).
(I)(a) is based on a very strong analogy between degree words and their sentential
complements on the one hand, and verbs, adjectives, nouns or prepositions and their
complements on the other.
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Therefore, (I)(a) is treated as a special case of a basic principle of
the theory which plays an important and indispensable role in generative grammar and has
been successfully applied to the description of a wide range of linguistic phenomena. (I)(b) is
an inductive generalisation accounting for a characteristic of English sentences supposed to
be of a specific structure. This hypothesis is characterised by Baltin as an “obvious fact that
any observationally adequate grammar of English must capture” (Baltin 1987: 11).
Baltin examines and compares four proposals which have been raised in the literature
in order to resolve the contradiction between (I)(a) and (I)(b).
Bresnan’s proposal to handle (I) – which we will call the Proposal Based on
Extraposition, (PEP) – supposes that the operation of extraposition is at work with degree
word complement clauses (cf. Baltin 1987: 12f.):
(PEP) Sentential complements are generated in the deep structure between the degree word
and the adjective in the case of too, so and after the degree word in the case of enough
as sisters of the degree word. Then they get moved rightward and adjoined to S’ in the
surface structure (i.e., they are ‘extraposed’).
S’
S’ S’
i
C S that he hit his head …
NP Infl VP
John was
V AP
QP A
Q S’
so e
i
tall
Figure 1
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In the case of enough, the adjective precedes the degree word.
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This formulation is vague because it does not specify in what kind of position the sentential complement
appears at the end of the clause. For example, it leaves open the question of whether we have to deal with a
position adjoined to S’ from outside of S or with a position within S, that is, within the internal structure of the
clause.
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Cf.: “[…] it seems that degree words combine with sentential complements to form linguistic units in
English (and in other languages) in exactly the same fashion as do verbs, adjectives, nouns, and prepositions.”
(Baltin 1987: 12)
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The representation of the sentence in (1)(a) is as in Figure 1. (PEP) resolves the conflict
between the two members of (I) by supposing that (I)(a) refers to the deep structure and (I)(b)
to the surface structure.
The second proposal – which will be dubbed the Proposal Based on Discontinuous
Constituency, (PDC) – is the following (cf. Baltin 1987: 15ff.):
(PDC) Degree word complements form deep- and surface structure discontinuous
constituents with degree words. This relationship is always clause-bounded.
On the basis of (PDC), the surface structure of (1)(a) presents itself as in Figure 2.
S’ S’
C S that he hit his head…
NP Infl VP
John was
V AP
QP A
Q tall
so
Figure 2
(PDC) resolves the conflict between (I)(a) and (b) by stating that degree word complements
are thematically linked to Q but in the linear ordering of the words, they are separated. Thus,
both their syntactic relatedness and their linear separation are accounted for, as witnessed by
their representation in Figure 2.
The third proposal (cf. Baltin 1987: 22) will be called the Proposal Based on
Multidomination, (PMD):
(PMD) Degree word complement clauses are multidominated: they constitute
discontinuous constituents with the degree word (and are dominated by QP),
and at the same time, they are dominated by the whole sentence.
This solution suggests representing both structures by combining them in a single tree (see
Figure 3).
