The propositional calculus approach to coordination can be traced back to Becker (1832) and the work of other logical grammarians from the 19th-century, and was also adopted by early generative grammarians including Chomsky (1957); we refer the reader to Bakker (1968:§I.5), Dik (1968), and Van Oirsouw (1987:§1) for extensive critical reviews of these two periods. Becker conjectures that coordinators link sentences and not parts of sentences: “Konjunktionen verbinden Sätze, und nicht eigentlich einzelne Glieder des Satzes” (p.141-2). In current terminology, this amounts to saying that coordinators should be translated as logical connectives in a propositional calculus, which are used to form complex formulas from simpler ones: this is illustrated in (9) for some cases where the input of the logical operation consists of one or two atomic formulas indicated by the proposition letters p and q; other cases will be discussed in the following subsections.

Propositional calculus is recursive in the sense that the complex formulas in (9) can be used as the input for further logical operations: the operands of the logical operation can therefore be represented more adequately by the letters φ and ψ, which stand for well-formed (atomic or complex) formulas. Note that negation differs from the other logical connectives in that it has a single operand; it can therefore also be considered as an operator with a formula in its scope.

The meaning contribution of the four logical connectives in (9) is defined by the truth tables in Table 1, which specify the truth conditions on the complex formulas in (10); the digits 0 and 1 stand for “false” and “true”, respectively. The truth of a complex formula depends on the input of the logical operation by which it was formed; ¬φ is true only if φ is false; φ ∧ ψ is true only if both φ and ψ are true; φ ∨ ψ is true unless φ and ψ are both false; and φ → ψ is true unless φ is true while ψ is false.

input		output
φ	ψ	¬φ negation	φ ∧ ψ conjunction	φ ∨ ψ inclusive disjunction	φ → ψ material implication
1	1	0	1	1	1
1	0	0	0	1	0
0	1	1	0	1	1
0	0	1	0	0	1

This subsection has discussed the four basic logical connectives from propositional logic. Subsection B will show that these are not sufficient to describe the coordination of clauses in a one-to-one fashion; therefore, we will introduces a larger set of logical connectives to cover the remaining cases.

The assumption that the coordinators function semantically as logical connectives usually leads to a classification as of the kind given in (11).

Conjunction and disjunction can easily be expressed by means of a coordinator, although the latter seems to come in two subtypes with slightly different truth conditions: the propositional calculus meanings of these types of disjunctive coordinators are given in Table 2. We will use the connective ⊻ for exclusive disjunction, although it can also be expressed quite adequately in the more primitive terms of conjunction and disjunction: (φ ∨ ψ) ∧ ¬(φ ∧ ψ).

input		output
φ	ψ	φ ∧ ψ conjunction	φ ∨ ψ inclusive disjunction	φ ⊻ ψ exclusive disjunction	¬( φ ∨ ψ) logical nor
1	1	1	1	0	0
1	0	0	1	1	0
0	1	0	1	1	0
0	0	0	0	0	1

There are various logical connectives that have no corresponding coordinator in Dutch (or any other natural language); these include material implication, material equivalence, and logical nand. The truth conditions for these connectives are given in Table 3; mote that logical xnor is logically equivalent to material equivalence, so that we can ignore this option in what follows.

input		output
φ	ψ	φ → ψ material implication	φ ↔ ψ material equivalence	¬( φ ∧ ψ) logical nand	¬( φ ⊻ ψ) logical xnor
1	1	1	1	0	1
1	0	0	0	1	0
0	1	1	0	1	0
0	0	1	1	1	1

We have expressed the meanings of logical nand and nor in the tables above by means of negation with the more familiar connectives ∧ and ∨ in its scope, but they are sometimes also expressed directly by means of symbols such as ⊼ and ⊽. This is an arbitrary decision immaterial to the main issue here, viz. that logical nor can be expressed in Dutch by the coordinator nochnor while logical nand cannot be expressed by a coordinator (although it can of course be expressed by more elaborate descriptions; cf. Het is niet zo dat φ ∧ ψ It is not the case that φ ∧ ψ).

An important argument for assuming that coordinators should be translated as logical connectives in a propositional calculus is related to the commutative laws in (12), which show that the logical connectives in Table 2 allow the operands to swap places without affecting the truth conditions of the formula as a whole. The commutative rules in (12) express this by the symbol ≡ (is logically equivalent to): (12d) follows from (12b), but we give it here anyway for convenience.

The truth conditions for conjunction in Table 2 state that p ∧ q is true only if both p and q are true. This is a proper description of example (13a) with the coordinator enand, which is true only if Jan is in Utrecht and Marie is in New York. The same holds for example (13b) with the coordinator wantbecause.

If the coordinators enand and wantbecause are to be translated as logical conjunctions, we would predict that the coordinated clauses in (13a&b) can swap places, as in (14), without affecting the truth conditions of the coordinate structure as a whole. The coordinate structures in (13a) and (14a) are indeed logically equivalent in the sense that they both entail the truth of both coordinands.

Although the same holds for the coordinate structures in (13b) and (14b), it seems unlikely that these examples will be construed as fully equivalent expressions in discourse, which is reflected in the fact that different conditions are imposed on their use. The reason for this is that want does not only have a conjunctive meaning but additionally expresses that the truth of the second conjunct in some sense explains the truth of the first conjunct: the truth of (13b) is thus not only based on the truth of p and q, but rather on the truth of q and the material implication q → p, cf. Lagerwerf (1998:20), Van der Heijden (1999:202-3) and Verhagen (2005:192ff.).

input			output
p (J is in U)	q (M is in NY)	q → p	q ∧ (q → p)
1	1	1	1
1	0	1	0
0	1	0	0
0	0	1	0

By inverting the two coordinands, as in (14b), we get the output given in Table 5, which is based on the truth of p and the material implication p → q. The two truth tables show that (13b) and (14b) have the same truth conditions, but that they are computed in a largely different way, which is reflected in the actual interpretation and the concomitant use conditions on these coordinate structures.

input			output
p (J is in U)	q (M is in NY)	p → q	p ∧ (p → q)
1	1	1	1
1	0	0	0
0	1	1	0
0	0	1	0

We can provide a similar account of the fact that the two examples in (15) with the coordinator dusso do not obey the same use conditions in discourse. The difference is again due to the fact that conjunctivity does not exhaustively describe the meaning of dus, and that we have to postulate additionally that the truth of the first conjunct explains the truth of the second conjunct, cf. Verhagen (2005:199ff.). The truth of (15a) is thus not only based on the truth of p and q, but rather on the truth of p and the material implication p → q.

This means that (15a) is synonymous with (14b) in the relevant respects, and its interpretation can therefore be described as in Table 5. Example (15b), on the other hand, is synonymous with (13b), and its interpretation is therefore correctly described by Table 4. The purpose of discussing the use conditions on wantbecause and dusso is to show that their lexical meanings cannot be described exhaustively in terms of the truth values of the coordinands alone; they do have conjunctive semantics but impose the additional restrictions on the operands of the conjunction indicated by (16). We use the symbol ≅ to indicate the logical translation of the coordinate structure, while the Greek capitals are used as convenient symbols for syntactic objects that translate as propositional formulas indicated by the corresponding Greek letters in lower case.

The disjunctive coordinators ofor and of ... of ...either ... or ... do not seem to pose the same problems as the conjunctive coordinators: they behave in full accordance with the commutative law in (12b) by allowing inversion of the coordinands without any truth-functional effects: these coordinators can be easily translated as inclusive and exclusive disjunction, respectively.

Note, however, that it is sometimes difficult or even impossible to interpret ofor as inclusive disjunction; examples such as (17a) are interpreted as exclusive disjunction in many contexts. That of should nevertheless be translated as inclusive conjunction is clear from the answers to question (18a) given in the (b)-examples: the available answers nicely reflect the truth table for disjunction in Table 1. We postpone further discussion of the question why of is often interpreted as exclusive disjunction in examples such as (17a) to Section 38.4.1, sub II.

The primed examples in (19) show that nochnor and noch ... noch ...neither ... nor ... cannot be used to coordinate full main clauses. However, the fact that (19a') entails that the two propositions Jan/Marie is in Utrecht are both false suggests that these coordinators can nevertheless be translated as logical nor. The same follows of course from the fact that (19b') entails that the propositions Jan/Marie is in New York are both false.

Let us now return to Becker’s conjecture that coordinators link sentences and not parts of sentences, which entails (i) that the apparent coordination of non-clausal phrases results from clausal coordination followed by conjunction reduction and (ii) that the meaning of coordinate structures can be exhaustively described by propositional logic. Although this subsection has shown that there is data to support the second entailment, it should be emphasized that the lexical meaning of some coordinators cannot be exhaustively described in terms of the truth values of their coordinands. This was illustrated for the coordinators wantbecause and dusso, which are lexically specified as indicated in (16) above; they do not only have a conjunctive meaning but also express a lexically specified material implication in the sense that the truth of one of the coordinands explains the truth of the other coordinand. Note that there is also a problem with the first entailment of Becker’s conjecture, according to which the primed examples in (19) should be derived from a coordinate structure with two clauses by conjunction reduction, because the unacceptability of the primeless examples suggests that nochnor and noch ... noch ...neither ... nor ... cannot be used in such structures. For this reason, this entailment will be discussed in more detail in Subsection C.

This subsection investigates in more detail the entailment of Becker’s conjecture that apparent coordination of non-clausal phrases, as in the examples in (20), should result from clausal coordination followed by conjunction reduction: “Wenn jedoch einander beigeordnete Sätze dasselbe Subjekt oder Prädikat [...] mit einander gemein haben; so wird das beiden Sätzen gemeinsame Glied des Satzes ein Mal ausgelassen” (Becker 1832:142).

According to Becker’s conjecture, the examples in (20) must be assigned the representations in (21) with two coordinated clauses; the parts with strikethrough are left unpronounced.

This subsection will show that there are strong reasons to reject the representations in (21) in favor of the simpler representations in (22) without conjunction reduction, derived by coordination of the predicative/adverbial phrases.

Another kind of problem for Becker’s conjecture that apparent coordination of non-clausal phrases results from clausal coordination followed by conjunction reduction can be illustrated by the examples in (37), where (37b) should be derived by coordination of the two main clauses in the (a)-examples.

If Becker’s conjecture were correct, the apparent coordination of noun phrases by en should categorically lead to the conjunction of the propositions expressed by the (a)-examples, i.e. ψ = p ∧ q. This is reasonable because it seems valid to infer from the truth of the two (a)-examples that (37b) is also true, in accordance with the valid argument schema in (38a), which expresses that the truth of the formulas to the left of the sign ⊫ entails the truth of the formula to the right of the sign. However, the validity of the argument schemas in (38b&c) also leads to the expectation that the truth of (37b) entails the truth of the (a)-examples, but this seems questionable.

The reason for doubt is that example (37b) is ambiguous between two readings, often referred to as the distributive and the cumulative (or collective/corporate) reading; see Dik (1968/1997) and, for a more recent review, Winter (2001a:§2/6). The examples in (39) show that the two readings can be easily distinguished by means of the modifiers allebeiboth and samentogether.

The distributive reading ψd is conjunctive in the sense that we can infer from the truth of the two (a)-examples in (37) that (39a) is also true, and conversely from the truth of (39a) that the two (a)-examples in (37) are both true. The cumulative reading ψc, on the other hand, is not conjunctive in this sense; we cannot infer from the truth of the two (a)-examples in (37) that (39b) is true, nor from the truth of (39b) that the two (a)-examples in (37) are true. This leads to the tentative conclusions in (40), which take the edge off Becker’s conjecture: the cumulative reading of (37b) cannot be derived by assuming coordination of sentences followed by conjunction reduction.

In the primeless examples in (41), the cumulative reading is the only one available, as is clear from the fact that the nominal coordinate structures in the primed examples cannot be replaced by their coordinands. The unacceptability of the primed examples makes it quite unlikely that the primeless examples are derived from them by coordination and conjunction reduction.

One possible way to account for (40) is to assume that the coordinator enand has two distinct meanings: the distributive meaning arises when en coordinates clauses, while the cumulative meaning arises when en coordinates noun phrases. We could represent the latter meaning as in (42), where the connective ⊕ expresses that x and y do not function as discrete entities (“singular individuals”) but as a “plurality” or “a plural individual” in the sense that they are thought of as a set of individual entities.

We refer the reader to Winter (2001a:§2) for a discussion of various formal semantic approaches to the cumulative reading, but for our more limited descriptive purposes the informal distinction between the connectives ∧ and ⊕ suffices. It is unclear, however, whether the distinction between a distributive and a cumulative meaning for the coordinator en is really necessary in order to account for (40). One reason for doubt is that plural definite descriptions such as de meisjesthe girls can give rise to a similar ambiguity as nominal coordinate structures with en. If the noun phrase de meisjesthe girls refers to Els and Marie, example (43a) is ambiguous in the same way as Els en Marie hebben de rots opgetildEls and Marie have lifted the rock in (37b): both examples can be disambiguated by means of the modifiers allebeiboth and samentogether, as will become clear by comparing the (b)-examples in (43) with the examples in (39). This strongly suggests that the distinction between distributive and cumulative readings cannot be reduced to an ambiguity of enand.

Cumulative readings are (cross-linguistically) restricted to conjunctive coordinate structures. We will illustrate this by means of the examples in (44).

Suppose that the contextually determined set of cats consists of c1 and c2 and that the contextually determined set of dogs consists of d1 and d2 and consider the situations depicted in Figure 19. The distributive readings of the examples in (44) can be described by the situations in I and II: example (44a) claims that both are true, (44b) claims that at least one is true, while (44c) claims that neither is true. The only example with an alternate, i.e. cumulative, reading is (44a): it can also refer to situation III, in which all entities denoted by the definite descriptions de katten and de honden are fighting with each other. Although this is not immediately relevant for our present discussion, we want to note that (44a) can also refer to situation IV, if the definite descriptions refer to collectives themselves (as indicated by the subscript C on the nouns).

The main conclusion of the discussion above is that Becker’s conjecture that coordinators link sentences and not parts of sentences cannot be maintained on semantic grounds because propositional calculus cannot account for the cumulative reading of nominal coordinate structures with the conjunctive coordinator en. There are also morphosyntactic reasons to be skeptical about Becker’s conjecture. One reason is related to subject-verb agreement. The representation in (45a) shows that coordination and conjunction reduction are not sufficient to derive (37b) from the examples in (37a&a'): since the former has plural agreement while the latter have singular agreement, we need an additional ad hoc mechanism that changes the singular finite verb into the plural one when conjunction reduction has been applied. This mechanism is not needed for the alternative representation in (45b) if we assume that nominal coordinate structures with en trigger plural agreement on the finite verb.

The examples in (46) show that more ad hoc mechanisms are needed to maintain Becker’s conjecture: an example such as Els en Marie houden van elkaarEls and Marie love each other needs not only an adaptation of the finite verb form, but also an additional stipulation to allow the violation of the condition on reciprocal elkaareach other that it should have a plural antecedent within its own clause; the structure in (46b), on the other hand, satisfies this condition in a trivial way.

The necessity of accepting these ad hoc stipulations strongly suggests that even if adopting Becker’s conjecture were tenable from a semantic point of view, it would still have to be considered undesirable because it would lead to considerable complications in the syntactic description of coordination.

The examples so far deal with clausal constituents (arguments, adverbials or complementives), but the collective and distributive readings can also occur with smaller constituents: cf. Haeseryn et al. (1997:1460). Example (47) is ambiguous between a collective and a distributive reading: according to the first reading Jan and Peter submitted several joint proposals, which were all rejected; according to the second reading, Jan and Peter each submitted at least one proposal, and their proposals were all rejected.

Haeseryn et al. (1997:1460) claim that nominal conjunctions can be collective even when used as the first member of a compound. Consider the examples in (48), where strikethrough is used to indicate conjunction reduction. Haeseryn et al. claim that (48a) has only a distributive reading: we are dealing with one or more Christmas cards and one or more New Year’s cards. Example (48b), on the other hand, has a distributive reading: we are dealing with cards that can be used to send end-of-year greetings. Although the semantic intuitions about the examples in (48) are correct, we leave it to others to decide whether the distributive-collective distinction is indeed the most appropriate one to account for them.

We conclude this subsection by noting that cumulative readings seem to be restricted to the simple conjunctive coordinator en: the examples in (49a&b) show that the correlative coordinators en ... en ...and ... and ... and zowel ... als ...both ... and ... are distributive. This is clear from the fact that the coordinate structures they head trigger singular agreement and cannot be used as the subject of the predicate bijeen komento come together; cf. the (a)-examples in (41). Example (49c) further shows the same for the disjunctive coordinator ofor. De Vries & Herringa (2008:§3) suggest that the obligatoriness of the distributive reading of these coordinate structures is reflected in the fact that they usually trigger singular agreement on the finite verb when their coordinands are both singular.

One of the reasons for claiming a relation between (obligatory) distributivity and singular agreement is that conjunctive coordination of noun phrases with the distributive quantifiers iedereevery and elk(e)each also triggers singular agreement on the verb: this is illustrated by the examples in (50). De Vries & Herringa (2008) suggest that this hypothesis may account for more “exceptional” cases of singular agreement; see the discussion in Section 38.4.1, sub IB.

The fact that the examples in (51) trigger plural agreement regardless of their interpretation (as distributive/cumulative) shows that this hypothesis can only be maintained if it is restricted to distributive readings due to the inherent properties of the coordinands or the coordinator, i.e. it excludes distributive readings due to some property of an element external to the coordinate structure (e.g. the presence of the adverbial allebeiboth); see De Vries & Herringa (2008) for more discussion.

This subsection discusses a number of problematic cases of predicate conjunction with enand. First, consider the familiar type of example in (52), and assume that the definite description de jongensthe boys refers to the same set of persons as the coordinate structure Jan en Peter in the relevant domain of discourse.

Subsection C3 has shown that examples such as these are true only if the entities referred to by the subject are all part of the intersection of the sets denoted by the predicative coordinands (A∩B). Figure 20 illustrates this for six possible situations: the informal formulas above the Venn diagrams, in which Sb stands for the relevant set of boys referred to by the subject, indicate the situations in which speakers would consider the examples in (52) to be true/false.

Sb ∈ A∩B = 1	Sb ∈ A∩B = 0	Sb ∈ A∩B = 0
Sb ∈ A∩B = 0	Sb ∈ A∩B = 0	Sb ∈ A∩B = 0

A complicating factor is that Winter (2001a/2001b) has argued that in some cases sentences with coordinated predicates behave in an unexpected way. Consider the examples in (53).

The discussion of (52) leads to the expectation that predicate conjunction by enand requires that the entities referred to by the subject de eenden are located in the intersection of the sets denoted by the coordinated predicates. Examples such as given in (53) should therefore be true if all the entities referred to by the subject (indicated by S) are located in the gray areas in the Venn diagrams in Figure 21, where A, B and C stand for the predicates used.

type (53a): S ∈ A∩B = 1	type (53b): S ∈ A∩C = 1	type (53c): S ∈ B∩C = 1	type (53d): S ∈ A∩B∩C = 1

Winter claims that this does not correspond to the actual interpretation the actual interpretations of the examples in (53). He illustrates this with the situation represented by the Venn diagram in Figure 22, where each represents a duck. Since the contextually determined set of ducks is not contained by any of the intersections marked in Figure 21, we expect that all examples are inappropriate for describing this situation. However, this does not seem to be borne out, since example (53a) is accepted by many (if not all) speakers as a description of this situation; see Dik (1968:217-8) for similar examples/judgments.

situation

This surprising fact is not the only one raised by the set of examples in (53) with respect to the situation in Figure 22. Since ducks that fly also quack, and vice versa, the predicates fly and quack denote the same subset of ducks and we might therefore expect the two examples in (53a&b) to be logically equivalent. Winter claims that this expectation is not borne out either: unlike example (53a), example (53b) is semantically well-behaved in the sense that it cannot be used to refer to the situation sketched in Figure 22. Graphically, we can illustrate the difference in interpretation between (53a) and (53b) as in Figure 23, where the gray areas indicate the regions that should contain the contextually-defined set of ducks.

(53a) is applicable	(53b) is not applicable

One way of describing the unexpected reading of (53a) in the first Venn diagram in Figure 23 is to assume that the conjunctive coordination enand can give rise to two different readings, similar to that found in the case of the coordination of two noun phrases discussed in Subsection D. The first reading would be the regular reading, where the coordinate structure denotes the intersection of the sets denoted by the coordinands. The second reading would be a more special reading, in which the coordinate structure refers to a collection of properties. This description of the more special reading correctly predicts that the set of ducks must be included in the union of the sets denoted by fly and quack in order for (53a) to be considered true; (53a) cannot be used to describe the situation sketched in Figure 24.

(53a) is not applicable

However, according to Winter, this approach is problematic because it would not account for the fact that the more special reading is not available for (53b). Winter attributes this difference between (53a) and (53b) to the fact that the actions described by the predicates swim and fly are mutually exclusive while those described by swim and quack are not. The examples in (54) illustrate this fact by showing that the corresponding long forms differ in their usability: the number sign in (54a) indicates that this example cannot be used to describe a situation at one specific point in time simply because ducks cannot fly and swim simultaneously; (54b), on the other hand, can be used for this purpose because swimming and quacking can be done simultaneously.

The appeal to mutual exclusivity predicts similar contrasts between the more complex example in (53d), repeated here as (55a), and (55b) because walk differs from quack in that it is mutually exclusive with swim and fly. The number sign in (55a) again indicates that this example cannot be used for describing a situation at one particular point in time.

Indeed, the two examples seem to differ in the expected way, as is demonstrated by the situations sketched in Figure 25. In passing, note that all sets must contain at least one duck for (55b) to be felicitously used. This is due to pragmatics: if the speaker knows that none of the ducks flies, the cooperative principle will select the utterance De eenden zwemmen en lopen in de wei as the more informative and accurate expression.

(55a) is not applicable	(55b) is applicable

Although an appeal to mutual exclusivity is promising, we want to conclude with a potential problem for it related to examples of the type in (52b), repeated here as (56). We have seen that (56) is semantically well-behaved if the contextually determined set of persons referred to by the plural definite description is small, e.g. {Jan, Peter}; the complete set should be located in the union of the sets denoted by the predicative coordinands in order for (56) to be true (cf. Figure 20).

This is of course in line with the earlier discussion, since have danced and have sung are not mutually exclusive (which seems to be the case for all perfective verbal predicates). However, Subsection C3 has shown that the situation is less clear when the cardinality of the set of boys is somewhat greater, since (56) seems to be usable for describing all the situations depicted in Figure 26.

(56) is applicable	(56) is applicable	(56) is applicable	(56) is applicable

The fact that the use conditions become more lenient for (56) when the cardinality of the subject’s referent increases suggests that Winter’s conjecture is not entirely correct and that some other factors may (also) be involved: for example, it may be the case that the predicates must be part of the same semantic field (such as “recreation”) in order for relaxation of the use conditions to be possible. Since this takes us into unexplored territory, we leave this issue to future research.

We conclude this subsection by noting that the conclusion that conjoined predicates occasionally denote not the intersection but the union of the sets denoted by the coordinands may be relevant to solving the longstanding and persistent problem of interwoven dependencies triggered by the modifier respectievelijkrespectively illustrated in (57); see Zhang (2010:§6.4) for a historical review of the syntactic approaches to this problem as well as a proposal of her own. The entailment pattern shows that the first coordinands of the two coordinate structures must be paired with each other and that the same is true for the second coordinands.

This entailment pattern is surprising if predicative conjunctions denote the intersection of their coordinands, and for this reason it has been argued since the early 1970’s that (57a) is derived from the clausal coordinate structure [[Jan komt uit Duitsland] en [Marie komt uit Zwitserland]]. Figure 27 shows that the pattern is easier to understand if, under certain conditions, predicative conjunctions can also denote the union of their coordinands (marked in gray), because then the situation sketched in this figure would be true.

It is important to note that the “union” reading in Figure 27 is also possible in examples such as Ze komen uit Duitsland en ZwitserlandThey come from Germany and from Switzerland with the referential plural pronoun zethey; this part of the problem is therefore clearly something that cannot be dealt with in syntax. All that remains is to take into account of the fact that the presence of the modifier respectievelijk forces this reading. Whether this should be done in the syntax is again highly questionable, because the presence of this modifier is not necessary if the intended reading is clarified by other means. For example, the intended reading of example (58) is clear from our knowledge of the world, and the use of respectievelijk is therefore superfluous.

Van Oirsouw (1987:§1.2.4) claims that respectievelijk hardly ever occurs in spontaneous speech, which is confirmed by Uit den Boogaart (1975) and De Jong (1979), and that it is mainly used with bipartite coordinate structures, since its meaning in more complex examples is often difficult to work out without pen and paper. In fact, this suggests that respectievelijk is not an element of core grammar, and we will therefore refrain from discussing it in any further detail. The most important conclusion to be drawn from the discussion of the examples in (57) and (58) is that the independently established fact that conjoined predicates can sometimes denote the union of the sets denoted by the coordinands may help to solve the problem of interwoven dependencies; the correct solution may in fact not be syntactic at all, but rather of semantic and/or pragmatic in nature.

The previous subsections have shown that the meaning of coordinators cannot be exhaustively described by propositional logic. Therefore, we have to replace Becker’s conjecture that coordination only links clauses by the generalization that coordinators link syntactic objects of the same semantic type; they create a new syntactic object of the same semantic type as the coordinands. Subsection B discussed cases in which the coordination of syntactic objects of the semantic type t (clauses expressing formulas with a certain truth value) results in a more complex object of type t; since the coordinands and the coordinate structure as a whole can all be assigned truth values, the semantic contribution of coordinators can be expressed by using truth tables. Subsection C discussed cases in which the coordination of syntactic objects of the semantic type <e,t> (predicates denoting a set of entities with a certain property) results in a more complex syntactic object of the type <e,t>: since the coordinands and the coordinate structure all denote sets, the semantic contribution of the coordinator can be expressed insightfully by means of Venn diagrams. This suggests the semantic generalization in (59).

It can be shown that generalization (59) is holds for cases in which nominal arguments or other syntactic objects are coordinated; we will not dwell on this here but refer the reader to Winter (2001a:§2) for a full discussion. The validity of generalization (59) suggests that the differences in the way we have chosen to represent the meaning contributions of coordinators in the subsections above (by truth tables and Venn diagrams) do not reflect differences in the meaning contributions of coordinators, but differences in the meaning of the coordinands and the resulting coordinate structures. Consequently, there is no a priori reason to assume that coordinators are polysemous in the sense that they express different meanings in different syntactic contexts. The proper formulation of the meaning contribution of coordinators is currently a much debated topic, but since discussing this issue here would lead us too far into formal semantics, we refer the reader to Zamparelli (2011:§4) for a brief introduction to this topic as well as relevant references. For our present purpose, it is sufficient to keep generalization (59) in mind, since it will account for some of the syntactic restrictions on coordination discussed in Section 38.3.

The main difference between the syntactic function of coordinators and subordinators is that the former link syntactic phrases of the same type, including main clauses, while the latter introduce an embedded clause. The fact that (66a) involves the coordination of two main clauses, while (66b) is a case of subordination, is reflected in the placement of the finite verb: it occupies the second position in the second (clausal) coordinand in (66a), but the clause-final position in the embedded clause in (66b).

The structures given in (66) indicate that the embedded clause in (66b) functions as a clausal constituent of the main clause, while the clausal coordinands in (66a) are syntactically independent of each other in terms of clause structure. The examples in (67) show that this is reflected in the fact that while the embedded clause can be moved leftward into the initial position of the main clause, it is impossible to move the second coordinand into the initial position of the first coordinand. For completeness, (67a') shows that leftward movement of the second coordinand is also impossible if the coordinator wantbecause is pied-piped.

The two clausal coordinands entertain different relationships in the two constructions with want and omdat, as shown by the fact illustrated in (68) that they exhibit differences in binding possibilities; while the quantified subject of the first coordinand cannot trigger a bound variable reading on the pronominal subject of the second coordinand in the coordinate structure with want, the quantified subject of the main clause can trigger such a reading on the subject of the embedded clause. The reason is that the bound variable reading is only possible if the pronoun is c-commanded by its quantified antecedent, a condition which is only met in the case of embedding; cf. Section N23.3. Note that the bound variable reading is indicated in italics.

The difference between conjunctive coordinators and subordinators can sometimes also be made visible by subordinators in embedded contexts. This does not apply to the pair in (66), since wantbecause cannot be used to coordinate embedded clauses, but it can be illustrated by means of the pair in (69a&b). First, note that the placement of the finite verb in the second clause already makes it clear that maarbut is a coordinator linking two main clauses, while hoewel is a subordinator. In addition, the primed examples show that in embedded contexts the coordinands of the coordinate structure in (69a') must both be introduced by the subordinator datthat, while this subordinator cannot be used in the second clause in (69b') due to the fact that embedded clauses can only be introduced by a single subordinator.

Note in passing that we have ignored the fact that some speakers do allow the complementizer dat immediately after hoewel in examples such as (69b'), probably as a result of contamination invoked by the complex complementizer ondanks datdespite that, which has more or less the same meaning.