L

Actual Plane

Actual Plane figure 8.12. Conditionals.

1985,1996,1997; Sweetser, 1996; Dancygier & Sweetser, 1997). The import of a conditional construction ifP (then) Q is that, upon examining the space containing P, one will also encounter Q. In other words, the construction incorporates a kind of mental scanning, sketched in Figure 8.12: starting from an imagined situation where P is observed, further inspection of the same situation leads to the observation of Q. The occurrence in this construction of then, whose basic value is temporal, can thus be related to the temporality of the scanning process (as noted previously for still and already).

It is generally accepted that a negative sentence presupposes the consideration of its positive counterpart. We can describe this in terms of the relation between a virtual and an actual plane, as sketched in Figure 8.13. The positive situation is given as X [F] Y, F being the focus of negation, i.e., the element that fails to correspond to actuality. This positive situation is not only explicitly coded, but even functions as the expression's profile. Nonetheless, it is virtual in nature, being conjured up just for purposes of describing actuality. Negation serves to specify how this virtual situation maps onto actuality: namely, the actual situation is obtained by cancelling out substructure F. This operation of mental cancellation is inherently dynamic, as indicated by the arrows. It is only by first evoking the virtual situation that one can cancel out F to arrive at the actual one.

In some cases, e.g., (22)(a), the entire proposition is focused and thus cancelled, so that nothing is left (hence X and Y are vacuous). In others, not

Virtual Plane not

Virtual Plane figure 8.13. Negation.

figure 8.13. Negation.

only a portion of the profiled situation constitutes the focus (or "target") of negation, generally marked in English by unreduced stress (small caps):

(b) I didn't eat the ZUCCHINI.

(c) She didn't PASSIONATELY embrace me.

Since the uncancelled portion is not specifically excluded from actuality, if conceptually coherent it can be taken as real. Thus (22)(b) cancels the notion of zucchini from the description of my eating, but it leaves open the possibility that I did eat something. And in (22)(c), the absence of passion is still compatible with her having given me a friendly hug. Indeed, limitation of the focus of negation to the elements in question suggests that the remainder is in fact valid.

We turn now to a classic issue in logic and formal semantics, namely quantifier scope. This too is a matter of conceptual structure in which fictive entities play a crucial role (Langacker, 1991, 3.3,1999b). Let us take just one example, which is ambiguous between a scopal and a non-scopal interpretation:

(23) Three boys lifted two chairs.

On the nonscopal interpretation, (23) simply profiles an interaction between a group consisting of three boys and a group consisting of two chairs, all construed as actual individuals.10 This is diagrammed in Figure 8.14(a).

Of more interest here is the scopal interpretation. Under normal circumstances the quantifier on the subject is interpreted as having wide scope, and that on the object, narrow scope (i.e., three has two "in its scope").11 This is where fictivity enters the picture, since, on this reading, direct reference is made to three actual boys, but not to any actual chairs. As shown in Figure 8.14(b), the import is rather that each of the three actual boys participated in one instance of the event type boy lift two chairs. That is, the two chairs referred to are virtual chairs, conjured up to characterize an event type (boy lift two chairs), one instance of which is ascribed to each actual boy.12

On the scopal interpretation, no actual chairs are directly mentioned, although it can be inferred that between 2 and 6 actual chairs were involved. Note the infelicity of (24)(a), where by default the second sentence is taken as describing actuality. The problem is that the antecedent two chairs

10 There is vagueness about how many atomic lifting events there were, and how many members of each set participated in each atomic event, but that is not pertinent here.

11 In formal logic, the contrast is represented by different nestings of quantifiers in a logical formula.

12 On the less likely interpretation where two has wide scope, reference is instead made to two actual chairs, each of which participates in one occurrence of the event type three boys lift chair.

figure 8.14. Quantifier scope.

occupies the virtual plane, whereas the anaphoric both is actual - since no actual chairs were directly mentioned, anaphoric reference to them is conceptually inconsistent (see Langacker, 1996a). However, we can rescue the discourse by making it clear that the second sentence also pertains to the type description (boy lift two chairs), as in (24)(b). Here the antecedent and the anaphor are both construed as referring to virtual entities.

(24)(a) Three boys each lifted two chairs. *Both were metal.

(b) Three boys each lifted two chairs. In each case, both were metal.

Obviously, this is not a full account of logical scope, but only an example of an approach to it. I believe, however, that it is basically the correct approach and that the phenomenon hinges crucially on the evocation of Active entities. This also proves to be the case when we examine the meanings of individual quantifiers (Langacker, 1991, 3.2).

quantifier meanings

Whereas logicians have often been content to posit a single universal quantifier (V), English, quite strikingly, has no less than six means of quantifying over all members of a class:

(25)(a) All cultures are worth preserving. (b) Cultures are worth preserving.

(c) A culture is worth preserving.

(d) Every culture is worth preserving.

(e) Each culture is worth preserving.

(f) Any culture is worth preserving.

It is also striking that some universally quantified nominals are singular, despite their apparent reference to a class with indefinitely many members. From the cognitive semantic perspective, this variation is obviously symptomatic of different ways of conceptualizing the process of making generalizations reaching to all members of a set. These conceptual differences constitute different linguistic meanings and in large measure account for differences in form and grammatical behavior.

These kinds of universal quantification represent alternate strategies for making and expressing generalizations by means of fictive entities. A first observation is that the generalization in question need not be truly universal, applying globally to all instances of a type, but can also apply locally to a restricted set of instances relevant in a particular context. The statements in (26), for instance, apply just to the students attending the campus in question:

(26)(a) On this campus, all students are encouraged to think independently.

(b) On this campus, students are encouraged to think independently.

(c) On this campus, a student is encouraged to think independently.

(d) On this campus, every student is encouraged to think independently.

(e) On this campus, each student is encouraged to think independently.

(f) On this campus, any student is encouraged to think independently.

There are, then, limitations on the scope of the generalizations made, with fully generic statements constituting the extreme case where no restrictions whatever are imposed. This parameter has to be distinguished from the meanings of the quantifiers per se. Rather it pertains to the conceptual configuration with respect to which the quantifiers are employed. In terms of the previous discussion, it pertains to the nature of the plane (or mental space) constructed to represent the generalization, and how the structure represented on that plane maps onto actuality.

Consider first the indefinite articles in (25)(c) and (26)(c). These are simply cases of evoking a virtual instance of a type in order to make a local or global generalization, as previously exemplified in (i2)-(i3). In (i2)(b) [Three times, a student asked an intelligent question], diagrammed in Figure 8.4, the generalization made is local in character, so the plane bearing the fictive profiled event is constructed on an ad hoc basis just for that purpose. In (13) [A cat plays with a mouse it has caught], diagrammed in Figure 8.5, the fictive event occurs in a plane conceived as representing the world's inherent nature, its stable structure; this is how I will understand the term generic. But the indefinite article in these examples - (i2)(b), (13), (25)(c), and (26)(c) - has its normal value. What is special is simply that the thing instance it evokes is virtual, occurring in a virtual plane constructed by abstraction from actuality to capture a generalization valid within some range.

Universal quantification with a zero determiner, as in (25)(b) and (26)(b), is quite similar. The zero determiner is the mass-noun counterpart of the indefinite article a (mass nouns include plurals as a special case). Hence the contrast is primarily a matter of whether the mental model conjured up to represent this generalization contains just a single virtual instance of a type (the minimum needed to capture the regularity) or multiple instances (reflecting more directly the multiplicity of instances all exhibiting the property in question).13

That leaves us with the true quantifiers all, every, each, and any. They divide into two groups, which I call proportional and representative instance quantifiers. All belongs in the first group, along with the nonuniversal most and some. One distinguishing property of this group is their occurrence with plurals (all cats, most cats, some cats). Naturally, all occurs as well with nonplural mass nouns (all beer). The representative instance quantifiers are every, each, and any, which combine with singular nouns (every cat, each cat, any cat). Additionally, any quantifies both plural and nonplural masses (any cats, any beer).

I refer to all, most, and some as proportional quantifiers because they designate some proportion of the relevant instances of the type in question. For a given type (t), we can speak of the contextually relevant extension, Et, consisting of the maximal set of instances invoked for some purpose, notably as a basis for generalization.14 A proportional quantifier - like the quantified nominal it derives - profiles a subpart of this extension (the type being determined by the quantified noun and its modifiers). As shown in Figure 8.15(a), all profiles a set coextensive with the maximal extension. Hence only one ellipse shows up in the diagram, since the profile, P, coincides with the maximal extension, Et. The two are distinct in the case of most, which profiles a set that comes close to exhausting Et without actually doing so. Some profiles a set of indeterminate size, being specified as nonempty. If we represent the full expanse of Et as a scale, in the manner of Figure 8.15(d), then all falls at the positive endpoint of the scale, most lies in the vicinity of the endpoint, and some can be anywhere else (except at the zero point).

What should be noticed about this characterization is that everything is fictive. Consider (27):

(27) Most cats are lazy.

13 For more details, and for some consequences of this difference, see Langacker 1996b, 1997b.

14 In Langacker (1990) I called this the reference mass for the type.

figure 8.15. Proportional quantifiers.
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