## Supplementary Materials A. Additional Examples: Classifier-Loci Generalization and Viewpoint Dependency

We provide below additional data about (1) the Classifier-Loci Generalization, and (2) the behavior of viewpoint variables (with cases of existential quantification, and examples in which two non-coreferring viewpoint variables co-occur in the same sentence).

### 1. The Classifier-Loci Generalization

The Classifier-Loci Generalization predicts that if a classifier predicate 'touches' arbitrary loci, these become iconic. As a result, in the presence of three arbitrary loci, a classifier that connects just two of them iconically situates them with respect to each other, but not necessarily with respect to third arbitrary locus. On the other hand, a classifier predicate that connects three loci that are initially introduced as arbitrary turns them all into iconic loci evaluated with respect to a single viewpoint. It is this dual prediction that we test in the paradigms below.

#### □ Partial iconicity: two loci out of three

In (143), we consider sentences with three loci, one to represent an American student, and two to represent foreign students. There is no classifier in (143)a: the three loci are arbitrary, and the sentence just implies that the two foreign students paint together. In (143)b, the three loci are initially arbitrary, but two classifiers are then added to represent the two foreign students coming together and rotating toward the front. Information about the position of the American student appears to be optional, giving rise only to a weak inference that the American student is behind the foreign students. This sharply contrasts with (143)c,d, where the three loci are introduced by classifier predicates and are thus interpreted iconically: they provide strong iconic information to the effect that "the foreign students always sit apart toward the front while the American is between and behind them".<fnref n="66" />

(143) *Context:* In the presence of American students, foreign students tend to bond together—even with hesitations due to Covid.

**POSS-1 CLASS ALWAYS HAVE**

'In my class, there are always

a. ⁷FOREIGN PERSON<sub>a</sub> PERSON<sub>c</sub> AMERICAN PERSON<sub>b</sub>. ALWAYS THE-TWO-a,c PAINT TOGETHER.

two foreigners and an American. The two foreigners always paint together.'

b. ⁷FOREIGN PERSON<sub>a</sub> PERSON<sub>c</sub> AMERICAN PERSON<sub>b</sub>. ALWAYS THE-TWO-a,c PERSON-move-cl-c--->|<--- PERSON-move-cl-a+rotation

two foreigners and an American. The two foreigners always come together in the middle of the room and turn to face the front of the class.'

c. ⁷FOREIGN PERSON-Cl<sub>a</sub> PERSON-Cl<sub>c</sub> AMERICAN PERSON-Cl<sub>b</sub>, ALWAYS THE-TWO-a,c PAINT TOGETHER

two foreigners apart and an American behind them. The two foreigners always paint together.'

d. ⁷FOREIGN PERSON-Cl<sub>a</sub> PERSON-Cl<sub>c</sub> AMERICAN PERSON-Cl<sub>b</sub>, ALWAYS THE-TWO-a,c PERSON-move-cl-c--->|<--- PERSON-move-cl-a+rotation

two foreigners apart and an American behind them. The two foreigners always come together in the

<footnote n="66">⁶⁶ One might object that the framework developed here leads us to expect that in (143)b there should be precise iconic information about the initial position of the two foreigners relative to each other, since classifier predicates start from their initial positions and meet halfway between them. But without the specification of a viewpoint and a scale, this is very unspecific, in the sense that when two individuals move towards each other, it's always possible to find a viewpoint from which the scaled movement would develop as displayed by the classifiers. By contrast, when three individuals are situated relative to each other, the information is much richer. To make an analogy: without a specification of the scale, a map that just situates two points relative to each other is rather uninformative by contrast, a map that situates three points relative to each other is far more informative.</footnote>
(144) Inferential judgments for (143) (3 judgments)

<table><thead><tr><th>It can be inferred that...</th><th>(i) the class always has two foreign students and an American student, <strong>without further information about their initial position.</strong></th><th>(ii) the class always has two foreign students and an American student, <strong>and the three are initially in a certain configuration</strong></th></tr></thead><tbody><tr><td>a. 3 normal nouns - 1 normal verb</td><td>6.7</td><td>1.7</td></tr><tr><td>b. 3 normal nouns - 2 classifiers</td><td>5.7</td><td>3</td></tr><tr><td>c. 3 classifiers - 1 normal verb</td><td>2</td><td>6</td></tr><tr><td>d. 3 normal nouns - 2 classifiers</td><td>1</td><td>7</td></tr></tbody></table>

Here it is worth noting that our second consultant partly disagreed with these judgments: he found that (144)b was iconically stronger than indicated here, and (144)c weaker. Importantly, he still agreed that (144)c was iconically stronger than (144)b. From the perspective of the present theory, such disagreements need not be surprising because (some) normal predicates have the *option* of being interpreted iconically, and so it could be that our second consultant treats the normal nouns *PERSON* in (143)c as carrying viewpoint variables in this case.<fnref n="67" />

The Logical Forms in (145) can account for our main consultant's judgments; for simplicity, we assume that some repeated elements are elided (the assumption that conjunction can be unexpressed is standard in ASL).

(145) a. $∃_{a,b,c} [[\text{foreign person}]_a \text{ and } [\text{foreign person}]_c \text{ and } [\text{American person}]_b \text{ and } \text{pro}_{a,c} \text{ paint-together}]$

b. $∃_{a,b,c} [[\text{foreign person}]_a \text{ and } [\text{foreign person}]_c \text{ and } [\text{American person}]_b \text{ and } [\text{person-move-cl}_τ^π]_a \text{ and } [\text{person-move-cl}'_τ^π]_c]$

c. $∃_{a,b,c} [[\text{foreign person-cl}^π]_a \text{ and } [\text{foreign person-cl}^π]_c \text{ and } [\text{American person-cl}^π]_b \text{ and } \text{pro}_{a,c} \text{ paint-together}]$

They key example is in (145)b: it involves a mixed representation in which loci *a* and *c* are initially introduced by normal nouns, but then receive an iconic interpretation because they are arguments of the classifier predicates. By contrast, the third locus *b* (corresponding to the American person) can remain arbitrary. Without going into full details, the key is that relative to an assignment function *s'*, whose details are determined by the unrestricted quantifier $∃_{a,b,c}$, the conjunct $[\text{person-move-cl}_τ^π]_a$ will impose the following condition:

(146) Assuming that $s'(a) ≠$ #:
$$
\begin{align*}
& [[\text{person-move-cl}_τ^π]_a]]^{c, s', t, w} = [[\text{person-move-cl}_τ^π]]^{c, s', t, w}(s'(a)) \\
& = [λ_{x_e} . \# \text{ iff } x = \#; \text{ otherwise, } 1 \text{ iff } \text{person}'_{t,w}(x) = 1 \text{ and } \text{proj}(x, s(π), t, w) = \text{walk-cl}_τ](s'(a)) \\
& = 1 \text{ iff } \text{person}'_{t,w}(s'(a)) = 1 \text{ and } \text{proj}(s'(a), s(π), t, w) = \text{walk-cl}_τ
\end{align*}
$$

Now the crucial formal observation is that the beginning of the movement of the classifier *person-walk-cl*<sub>*τ*</sub> originates in locus *a*, and as a result the (dynamic) projection rule will require that at the time of evaluation *t* and in the world of evaluation *w*, *s*'(*a*) should be in a position that projects to that locus.

By parity of reasoning, an iconic condition will equally be imposed on locus *c*, as it appears in the beginning of the movement of the second classifier predicate. By contrast, no such condition is imposed on the third locus, *b* (associated with the American), as it is not 'touched' by any classifier predicate. If the three loci *a*, *b*, *c* are initially arbitrary, the classifiers touching *a* and *c* will situate their

<footnote n="67">⁶⁷ This might make sense on pragmatic grounds: if the signer goes through the trouble of using classifier predicates to situate the movement of the two foreign students, this might be with the intention of conveying information about the position of all three individuals relative to each. Such pragmatic pressure might be absent in (143)a, which does not involve classifier predicates.</footnote>
denotations with respect to each other,<fnref n="68" /> but not with respect to the American. (If the normal nouns PERSON carry a viewpoint variable, they will in essence behave like classifier predicates and will thus be interpreted iconically. But for them this is just an option, whereas for classifier predicates this is an obligation.)

Unsurprisingly, in (145)c,d, the three person classifiers that appear at the beginning of the sentence force all three loci to be interpreted iconically.

A shorter paradigm appears in (147):

(147) *Context:* In the presence of American students, foreign students tend to bond together – even with hesitations due to Covid.

CLASS WHEN HAVE ____, SOON THE-TWO-a,c PERSON-move-cl-c--l-><--l-- PERSON-move-cl-a<fnref n="69" />.

'In class, whenever there are ____, the two foreigners soon come together.'

a. normal nouns

⁶⁷FOREIGN PERSON_a PERSON_c AMERICAN PERSON_b

two foreigners and an American

b. finger classifiers facing the addressee (student's perspective on the scene)

⁷FOREIGN PERSON-cl_a PERSON-cl_c AMERICAN PERSON-cl_b

two foreigners behind an American

c. finger classifiers facing the signer (teacher's perspective on the scene)

⁷FOREIGN CL-person_a CL-person_c AMERICAN CL-person_b

two foreigners in front of an American

(ASL, 35, 2078; 3 judgments; https://youtu.be/8M-CtR-xVuA)

(148) Inferential judgments for (147) (3 judgments)

<table><thead><tr><th>It can be inferred that the two foreign students move closer together whenever...</th><th>(i) the foreign students are in the presence of an American student.</th><th>(ii) the foreign students are in the presence of an American student <strong>and the three are in a certain configuration.</strong></th></tr></thead><tbody><tr><td>a. 3 normal nouns</td><td>6</td><td>2.7</td></tr><tr><td>b. 3 classifiers facing the addressee</td><td>1.7</td><td>6.3</td></tr><tr><td>c. 3 classifiers facing the signer</td><td>1.7</td><td>6.3</td></tr></tbody></table>

In (147)a, the three loci representing the three students can be construed as arbitrary, and thus the *when*-clause quantifies over all situations in which there are (at least) two foreign students and an American student in class. Nonetheless, due to the presence of a classifier predicate, the main clause provides iconic information about the two foreign students: they move toward each other, hesitate, and then end up next to each other. By contrast, in (147)b,c, the three students are represented by three person classifiers, and correspondingly the *when*-clause quantifies over situations in which two foreign students and an American student stand in a particular spatial relation. In (147)b, the three finger classifiers are seen 'from the back' (as they are facing the addressee), so that the viewpoint is probably that of a student, and the situations quantified over involve two foreigners behind an American. In (147)c, the three person classifiers face the signer and thus the viewpoint is probably that of the teacher, and now the *when*-clause quantifiers over situations in which two foreigners are in front of an American. (Our second consultant agreed with our main consultant on this paradigm.)

Let us add that the mixing of iconic and arbitrary loci can be found in further examples, sometimes with less clear results. Be it across signers or examples, this variation is unsurprising since normal nouns can optionally carry viewpoint variables and thus behave like classifiers with respect to iconic interpretation. In (149), the main clause uniformly involves two classifier predicates originating in loci a and c. The *when*-clause includes either three normal nouns for an airplane (in (149)a,b), or

<footnote n="68">⁶⁸ As noted in fn. 66, if the viewpoint is underdetermined, this provides little information, e.g. that they should be sufficiently far apart that they could move closer together.</footnote>

<footnote n="69">⁶⁹ The classifier predicate involves a movement of the two indexes towards each, with a pause before they finally meet.</footnote>
three minimally different airplane classifier predicates (in (149)c, d). The latter clearly provide positional information about the three airplanes. For (149)a,b, positional information about the American plane, corresponding to locus *b*, is far more open, but there is variation across (149)a and (149)b, and across judgment tasks. Still, a contrast between (149)a,b on the one hand and (149)c, d on the other hand is preserved: the latter are more iconically specific than the former. (Here our second consultant agreed with our main consultant's judgments given below.)

(149) *Context:* Space is severely limited at DC airport.

DC AIRPORT WHEN HAVE

'At the DC airport, when there are

a. ⁷FOREIGN PLANE<sub>a</sub> PLANE<sub>c</sub> AMERICAN PLANE<sub>b</sub>, CONTROLLER ASK THE-TWO-a,c
PLANE-cl-c--->|<--- PLANE-cl-a.

two foreign planes and an American plane [2/3 judgments]

or: two foreign planes behind an American plane [1/3 judgment],
the controller asks the two foreign planes to move closer together.'

b. ⁷FOREIGN PLANE<sub>a</sub> PLANE<sub>c</sub> AMERICAN PLANE<sub>b</sub>, CONTROLLER ASK THE-TWO-a,c
PLANE-cl-c---\--- PLANE-cl-a.

two foreign planes behind an American plane,<fnref n="70" /> the controller asks the two foreign planes to line up
behind each other.'

c. ⁷FOREIGN PLANE-cl<sub>a</sub> PLANE-cl<sub>c</sub> AMERICAN PLANE-cl<sub>b</sub>, CONTROLLER ASK THE-TWO-a,c
PLANE-cl-c--->|<--- PLANE-cl-a.

two foreign planes behind an American plane, the controller asks the two foreign planes to move closer
together.'

d. ⁷FOREIGN PLANE-cl<sub>a</sub> PLANE-cl<sub>c</sub> AMERICAN PLANE-cl<sub>b</sub>, CONTROLLER ASK THE-TWO-a,c
PLANE-cl-c---\--- PLANE-cl-a.

two foreign planes behind an American plane, the controller asks the two foreign planes to line up
behind each other.'

(ASL, 35, 2084; 3 judgments; https://youtu.be/DGI36jPTx4w)

(150) **Inferential judgments for (149)** (3 judgments)

<table><thead><tr><th>The two foreign airplanes move closer together in the airport whenever...</th><th>(i) the foreign airplanes are in the presence of an American plane.</th><th>(ii) the foreign airplanes are in the presence of an American plane <strong>and the three are in a certain configuration.</strong></th></tr></thead><tbody><tr><td>a. 3 normal nouns - 2 classifiers moving closer</td><td>5<br>(3, 6, 6)</td><td>3<br>(5, 2, 2)</td></tr><tr><td>b. 3 normal nouns - 2 classifiers lining up behind each other</td><td>3.7</td><td>4.3</td></tr><tr><td>c. 3 classifiers - 2 classifiers moving closer</td><td>1.7</td><td>6.3</td></tr><tr><td>d. 3 classifiers - 2 classifiers lining up behind each other</td><td>1.3</td><td>6.7</td></tr></tbody></table>

□ Regaining full iconicity

Following the same logic, we expect if the three arbitrary loci that are introduced in the first clause are
all 'touched' by classifier predicates in a later clause, they will *ipso facto* acquire an iconic interpretation.
This is the case in (151)b, which minimally differs from (143)b: in the second clause, classifier
predicates start from loci *a* and *c* and move toward the center (as was the case in (89)b), but in addition
a classifier predicate moves from the *b* locus toward the center. Since now all three loci have been
'touched' by a classifier predicate, they all acquire an iconic interpretation, and the sentence provides
information about the original position of the two foreign students relative to the American student.

<footnote n="70">⁷⁰ The inferential judgment about (149)b should be qualified. As seen in the Supplementary Materials B, in 2 judgment tasks out of 3, the consultant wrote that the foreign planes were probably/likely behind the American plane. And upon proofreading the glossed examples he mentioned that this is what he would 'guess' if asked, a weaker inference than in (149)b,c.</footnote>
(Here our second consultant finds that (151)b is iconically stronger than (151)c: he would give a higher endorsement of the inference in (152)(ii) for b than for c.<fnref n="71" />)

(151) *Context*: Some students tend to bond together – even with hesitations due to Covid.

POSS-1 CLASS ALWAYS HAVE

'In my class, there are always

a. ⁷FOREIGN PERSON<sub>a</sub> PERSON<sub>c</sub> AMERICAN PERSON<sub>b</sub>. ALWAYS END THE-THREE-a,b,c PAINT TOGETHER.

two foreigners and an American. The three of them always end up painting together.'

b. ⁷FOREIGN PERSON<sub>a</sub> PERSON<sub>c</sub> AMERICAN PERSON<sub>b</sub>. ALWAYS END THE-TWO-a,c PERSON-move-cl-a+c->center PERSON-move-cl-b->center.

two foreigners in front of American. In the end, it's always the case that the two foreigners come together in the middle and are then joined by the American.'

c. ⁷FOREIGN PERSON-cl<sub>a</sub> PERSON-cl<sub>c</sub> AMERICAN PERSON-cl<sub>b</sub>, ALWAYS END THE-THREE-a,b,c PAINT TOGETHER.

two foreigners standing in front of American. The three of them always end up painting together.'

d. ⁷FOREIGN PERSON-cl<sub>a</sub> PERSON-cl<sub>c</sub> AMERICAN PERSON-cl<sub>b</sub>, ALWAYS END THE-TWO-a,c PERSON-move-cl-a+c->center PERSON-move-cl-b->center.

two foreigners standing in front of American. In the end, it's always the case that the two foreigners come together in the middle and are then joined by the American.'

(ASL, 35, 2098; 3 judgments; https://youtu.be/4AcnqwYUP9E)

(152) **Inferential judgments for (151)** (3 judgments)

<table><thead><tr><th>It can be inferred that...</th><th>(i) the class always has two foreign students and an American student, <strong>without further information about their initial position.</strong></th><th>(ii) the class always has two foreign students and an American student, <strong>and the three are initially in a certain configuration</strong></th></tr></thead><tbody><tr><td>a. 3 normal nouns - 1 normal verb</td><td>6</td><td>2</td></tr><tr><td>b. 3 normal nouns - 3 classifiers</td><td>2</td><td>6</td></tr><tr><td>c. 3 classifiers - 1 normal verb</td><td>2</td><td>6</td></tr><tr><td>d. 3 normal nouns - 3 classifiers</td><td>1</td><td>7</td></tr></tbody></table>

The contrast between (143)b and (151)b is captured by the Logical Forms in (153); the key point is that only two loci are 'touched' by classifier predicates in the former case, whereas all three loci are in the latter case (owing to the addition of the boldfaced classifier).

(153)a. Logical Form of (143)b

∃<sub>a,b,c</sub> [[foreign person]<sub>a</sub> and [foreign person]<sub>c</sub> and [American person]<sub>b</sub> and [person-move-cl<sub>τ</sub>]<sub>a</sub> and [person-move-cl<sub>τ</sub>]<sub>c</sub>]]

b. Logical Form of (151)b

∃<sub>a,b,c</sub> [[foreign person]<sub>a</sub> and [foreign person]<sub>c</sub> and [American person]<sub>b</sub> and [person-move-cl<sub>τ</sub>]<sub>a</sub> and [person-move-cl<sub>τ</sub>]<sub>c</sub> and [person-move-cl<sub>τ</sub>]<sub>b</sub>]]

In sum, in some cases at least, there are mixed cases in which some loci introduced by normal nouns become iconic because they have been 'touched' by classifier predicates, while other loci remain arbitrary. More work would be needed, however: all we have done is provide an argument that *sometimes* one can mix arbitrary and iconic loci. Since any locus can in principle be interpreted as iconic, there should be variation across examples, as we saw in (149).

<footnote n="71">⁷¹ As seen in the Supplementary Materials B, "he feels b is stronger than c and would perhaps make c 2;5 instead of 2;6".</footnote>
## 2. Viewpoint Variables

We provide below additional examples that can be analyzed with Logical Forms involving (i) existential quantification over viewpoints (to complement Section 5), and (ii) distinct viewpoint variables (to complement Section 6). The same alternative theoretical analyses could be considered as in Appendix I-C, D.

### □ Existential quantification over viewpoints

In (154)b,c, a plane classifiers veers right or left, giving rise to an iconic meaning in the scope of negation. What is understood isn't that there is a viewpoint relative to which the plane won't have a similar movement (with existential quantification scoping over negation); rather, it is that there is no viewpoint relative to which the plane will have such a movement (with existential quantification over viewpoints scoping under negation). There is a complication relative to (115) in Appendix I-C, however: movement to the right or to the left need not be interpreted literally, but may be taken to encompass diverse ways for the plane to veer away from its course (see Supplementary Materials B for details). Still, in both cases there is a strong intuition that the movement is viewed from the back of the airplane. Our second consultant mostly agreed with these judgments, except that he saw the camera angle as being in front of the plane, not behind the plane. As explained in Section 7 of the main text, within the Puppet Model such disagreements are unsurprising as one may equally view the 3D scene from the signer's or from the addressee's position.

(154) *Context:* The signer is a pilot chatting with another pilot.
TOMORROW WEATHER GOOD. POSS-2 PLANE WON'T
'Tomorrow the weather will be nice. Your plane won't
a. ⁷FLY ROUGH.
have a rough flight.'
b. ⁷PLANE-veer_right-cl.
veer off course.'
c. ⁷PLANE-veer_left-cl.
veer off course.'
(ASL, 37, 2564; 3 judgments; https://youtu.be/La4NWeG7p5c)

(155) Inferential judgments for (154) (3 judgments)

<table><thead><tr><th rowspan="2"></th><th colspan="3">One infers that tomorrow's the addressee's plane won't...</th><th rowspan="2">If some movement is represented iconically, from which perspective is it represented, i.e. where is the 'camera position'?</th></tr><tr><th>(i) fly roughly, without further specification.</th><th>(ii) fly as iconically depicted, from a fixed spatial viewpoint.</th><th>(iii) fly as iconically depicted, no matter what the viewpoint.</th></tr></thead><tbody><tr><td>a. FLY ROUGH</td><td>7</td><td>1</td><td>1</td><td>n/a</td></tr><tr><td>b. FLY-upwards-bumpy-cl</td><td>2</td><td>1</td><td>7</td><td>from behind the plane</td></tr><tr><td>c. FLY-downwards-bumpy-cl</td><td>2</td><td>1</td><td>7</td><td>from behind the plane</td></tr></tbody></table>

As was the case for (115)b,c and (119)a (in Appendix I-C), (154)b,c can be analyzed by way of the simplified Logical Form in (156).

(156) not FUT ∃π [your airplane] plane-move-clπ

### □ Multiple viewpoint variables

The paradigm in (157) parallels that in (77) in the main text, but with entirely different lexical choices, pertaining to airports and airplanes rather than classrooms and students. Here too, our second consultant sees the camera angle to be from the front of the plane rather than from behind the plane (the same
remark applies as in our earlier discussions: within the Puppet Model, the 3D scene may be viewed
from the signer or from the addressee position).

(157) *Context*: The signer is a part-time air traffic controller in New York and in Boston. Depending on air traffic, pilots use different runways, i.e. no pilot is assigned to a specific runway.

HAVE ONE PILOT NEW-YORK<sub>a</sub> ALWAYS __, BOSTON<sub>b</sub> ALWAYS ...

'There is one pilot who in New York always __ and in Boston always ... '

a. ⁷__ = a-PLANE-roll_right-cl ... = b-PLANE-climb_steeply-cl

rolls to the right after take-off climbs steeply after take-off

b. ⁷__ = a-PLANE-climb_steeply-cl ... = b-PLANE-roll_right-cl

climbs steeply after take-off rolls to the right after take-off

c. ⁷__ = a-PLANE-roll_right-cl ... = b-PLANE-roll_left-cl

rolls to the right after take-off rolls to the left after take-off

d. ⁷__ = a-PLANE-roll_left-cl ... = b-PLANE-roll_right-cl

rolls to the left after take-off rolls to the right after take-off

(ASL, 35, 2436; 3 judgments; https://youtu.be/_KofNCdwyNU)

In all examples, the take-offs are represented from the beginning of the runway (or from the front of the plane for our second consultant). But these correspond to different positions, as some are in New York while others are in Boston, and in any event each airport has several runways. Paralleling our analysis of (77)-(78), we can posit the Logical Form in (158), which involves two different viewpoint variables π and π'.

(158) there-is pilot λi [always<sub>T</sub> t<sub>i</sub> plane-fly-cl<sup>π</sup> and always<sub>T</sub> t<sub>i</sub> plane-fly'-cl<sup>π'</sup>]

There are potential objections, however. First, our analysis is correct only if we take the New York viewpoint to be fixed, and similarly for the Boston viewpoint. This is reasonable if we assume that the signer, who the context says is an air traffic controller, is always in exactly the same position while working in New York, and while working in Boston. But the context of (157) makes clear that pilots change runways, so it is unlikely that the representation of the New York take-off, or of the Boston take-off, could involve a fixed 'camera position'. Thus existential quantification might be needed for one or both viewpoint variables, as is represented in (159)a (where both variables are quantified).

(159) there-is pilot λi [always<sub>T</sub> ∃π t<sub>i</sub> fly-cl<sup>π</sup> and always<sub>T</sub> ∃π'<sub>i</sub> fly'-cl<sup>π'</sup>]

A second objection is that the data reported in (157) show that (for our main consultant) the 'camera position' is understood to be at the beginning of the runway, and thus one might think that an existential analysis is insufficiently specific. But given what is known about take-offs, it is clear if *some* viewpoint allows for the representations given, that has to be a viewpoint corresponding roughly to the beginning of the runway.
# Supplementary Materials B. Raw Data and Survey Results

## A. Raw data

Raw data can be found in the following folder: https://osf.io/3qnem/

They contain:

ASL data: 1. Raw data with the main consultant's judgments. 2. Averages for the main consultant's judgments. 3. Summary of the second consultant's judgments. 4. Anonymized ASL videos.

Gestures and onomatopoieas: 1. Anonymized version of the survey in pdf format. 2. Anonymized version of version of the results, in pdf format. 3. Anonymized version of the results, in xlsx format. 4. Anonymized gesture and onomatopoeia videos.

## B. Detailed results of the survey on pro-speech gestures and onomatopoeias

Here we provide further information about the judgments given by our 7 consultants (all of them linguists<sup>72</sup>) in the survey on pro-speech gestures and onomatopoeias mentioned in Section 8, and made available above. (Survey results pertaining to co-speech gestures co-occurring with *come* and *go* were discussed in Appendix II and are not repeated here.)

We describe our paradigms, with (i) average acceptability judgments as superscripts, and (ii) inferential questions and choices made by our consultants, as (rounded) percentages of consultants who selected the various options. We comment below on dominant or intended readings; in the latter case, some examples were unclear to our consultants and were not discussed in Section 8.

*Transcriptions:*

FLY-<sub>front</sub> transcribes a flat hand moving horizontally toward the speaker, and then abruptly upwards.

FLY-<sub>right</sub> involves the same movement on the speaker's right.

FLY-/// glosses a flat hand, representing an airplane, moving upwards in a bumpy fashion.

WALK-↑← transcribes a two-fingered gesture representing a person walking toward the speaker and then away on the speaker's left.

WALK-↓← transcribes the same movement going toward the speaker, but then away on the speaker's right.

### Pro-speech gestures

#### (160) Evaluation relative to a single viewpoint: airplane

a. *Context:* The speaker has just been hired as an air traffic controller at JFK airport.

⁵,³ Before my time, there was a pilot who upon take-off would always FLY-<sub>front</sub>. https://youtu.be/glZ9PFxOaig

Dominant reading: The pilot always took off toward the air control tower, and vertically.

b. In view of the context, what is the most accurate description of what the relevant pilot always did upon take-off?

0% The pilot always took off away from the air control tower, and vertically.

71% The pilot always took off towards the air control tower, and vertically.

29% The pilot always took off towards some point or other, and vertically.

#### (161) Evaluation relative to a single viewpoint: student

a. *Context:* The speaker is the Chair of the linguistics program, and he has just talked to the syntax

<footnote n="72">⁷² As noted in Section 8, one colleague who took the survey also gave feedback on an earlier draft of it.</footnote>
instructor about a recurring problem in the syntax class. This class always takes place in the same classroom.

⁵.¹ I have just talked to the syntax instructor. Apparently, there's a student who in the middle of class always WALK-↑←.

https://youtu.be/ScXW4z-rSaA

**Intended reading, but unclear from the data:** The student always walks toward the relevant teacher and then leaves from the left [from the teacher's perspective].

b. In view of the context, what is the most accurate description of what the relevant student always does in the middle of the syntax class?

29% The student always walks towards the teacher and then leaves from the left [from the teacher's perspective].

29% The student always walks away from the teacher and then leaves from the right [from the teacher's perspective].

43% The student always moves towards some point or other and then takes a right and leaves.

(162) **Viewpoints dependent on universal quantifiers: airplanes**

a. Context: The speaker is an airline pilot with prior experience in Crete, which has several airports.

⁵.⁷ In Crete, when the weather is bad, every hour there is a plane that FLY-////.

https://youtu.be/wmrNPppEW04

**Dominant reading:** Every hour, there is some point or other of space in which there is a plane that has a bumpy ascent.

b. In view of the context, what is the most accurate description of what always happens in Crete when the weather is bad?

0% There is some point of space in which, every hour, there is a plane that has a bumpy ascent.

100% Every hour, there is some point or other of space in which there is a plane that has a bumpy ascent.

(163) **Viewpoints dependent on universal quantifiers: students**

a. Context: The speaker is the chair of the linguistics program. Each 1st year student takes phonology, syntax and semantics, taught by three separate instructors in three separate classrooms.

⁵.¹ I have just talked to our three instructors. There's a student who in the middle of class always WALK-↑←.

https://youtu.be/3S0NqsqqIok

**Intended reading, but unclear from the data:** The student always walks toward the relevant teacher and then leaves from the left [from the teacher's perspective].

b. In view of the context, what is the most accurate description of what the relevant student always does in the middle of class?

43% The student always walks towards the relevant teacher and then leaves from the left [from the teacher's perspective].

29% The student always walks away from the relevant teacher and then leaves from the right [from the teacher's perspective].

29% For some fixed location at school, the student always moves towards that location and then takes a right.

(164) **Existential quantification over viewpoints in the scope of negation**

a. Context: The speaker is a pilot talking to another pilot.

⁵.⁴ Tomorrow the weather will be nice, so your plane won't FLY-////.

https://youtu.be/qHxsyRD74B4

**Dominant reading:** There is no point of space in which the plane will have a bumpy ascent.
b. In view of the context, what is the most accurate description of what will happen tomorrow?

0% There is some point of space in which the plane won't have a bumpy ascent [leaving open whether or not it will have a bumpy ascent in other parts of space].

100% There is no point of space in which the plane will have a bumpy ascent.

(165) **Evaluation relative to two viewpoint variables**

a. *Context:* The speaker works as a part-time air-traffic controller in New York and in Boston.

4.7 Before my time, there was a pilot who upon take-off in New York would always FLY-\_front, and in Boston would always FLY-\_right.

https://youtu.be/xbPxD9gfXh8

**Dominant reading:** 1. In New York, the pilot would take off toward the local air traffic control tower from the front. 2. In Boston, he would take off toward the local air traffic control tower from the right.

b. In view of the context, what is the most accurate description of what the relevant pilot always did upon take-off?

0% 1. In New York, he would take off towards the local air traffic control tower from the right. 2. In Boston, he would take off towards the local air traffic control tower from the front.

86% 1. In New York, he would take off towards the local air traffic control tower from the front. 2. In Boston, he would take off towards the local air traffic control tower from the right.

0% Viewed from a single, fixed point of space, 1. in New York, he would take off towards that point from the right, 2. in Boston, he would take off towards that point from the front.

14% Viewed from a single, fixed point of space, 1. in New York, he would take off towards that point from the front, 2. in Boston, he would take off towards that point from the right.

(166) a. *Context:* The speaker is the chair of the linguistics program. Each 1st year student takes phonology and syntax, taught by two separate instructors in two separate classrooms.

4.9 I have just talked to our instructors. There's a first-year student who in the middle of the phonology class always WALK-↑←, and in the middle of the syntax class always WALK-↓←.

https://youtu.be/fi-q6O9JmR0

**Intended reading, but unclear from the data:** 1. In the phonology class, the student always walks toward the teacher and then leaves from the left [from the teacher's perspective]. 2. In the syntax class, the student always walks toward the teacher and then leaves from the right [from the teacher's perspective].

b. In view of the context, what is the most accurate description of what the relevant student always does in the middle of class?

43% 1. In the phonology class, the student always walks towards the teacher and then leaves from the left [from the teacher's perspective]. 2. In the syntax class, the student always walks towards the teacher and then leaves from the right [from the teacher's perspective].

29% 1. In the phonology class, the student always walks away from the teacher and then leaves from the right [from the teacher's perspective]. 2. In the syntax class, the student always walks away from the teacher and then leaves from the left [from the teacher's perspective].

29% Viewed from a single, fixed point of space, 1. in the phonology class, the student always walks towards that point and then takes a right, 2. in the syntax class, the student always walks towards that point and then takes a left.

Pro-speech onomatopoeias

(167) **Evaluation relative to a single auditory point**

a. *Context:* The speaker lives in France.

⁵On Bastille Day, I spend my time on my balcony. There are always fighter jets that sh<>sh.

https://youtu.be/AuDkVtAX9zM

**Dominant reading:** There are always jets that approach the speaker's balcony with increasing noise and
move away with decreasing noise.

b. In view of the context, what is the most accurate description of what happens on Bastille Day?
86% There are always jets that approach the speaker's balcony with increasing noise and move away with decreasing noise.

14% There are always jets that approach some point or other with increasing noise and move away with decreasing noise.

(168) **Auditory points dependent on universal quantifiers**

*Context:* The speaker is a journalist who used to be a correspondent in France.

⁵,¹ In France, on Bastille Day, there are always fighter jets that sh<>sh.

https://youtu.be/7htSTCEYhas

**Dominant reading:** There are always jets that approach some point or other with increasing noise and move away with decreasing noise.

b. In view of the context, what is the most accurate description of what happens on Bastille Day?

86% There are always jets that approach the speaker's past French neighborhood with increasing noise and move away with decreasing noise.

14% There are always jets that approach some point or other with increasing noise and move away with decreasing noise.

(169) **Auditory points dependent on two auditory points**

a. *Context:* The speaker lives in France.

⁴,⁷ On Bastille Day, in my neighborhood fighter jets always sh<>sh, whereas over the Champs-Elysées they shsh.

https://youtu.be/JmoKUc6HX3M

**Dominant reading:** 1. Fighter jets fly over the speaker's neighborhood with considerable and increasing noise before moving away. 2. Fighter jets fly over the Champs Elysées with less noise.

b. In view of the context, what is the most accurate description of what always happens on Bastille Day?

0% 1. Fighter jets fly over the Champs Elysées with considerable and increasing noise before moving away. 2. Fighter jets fly over the speaker's neighborhood with less noise.

100% 1. Fighter jets fly over the speaker's neighborhood with considerable and increasing noise before moving away. 2. Fighter jets fly over the Champs Elysées with less noise.

0% Heard from single, fixed point, 1. fighter jets that fly over the Champs Elysées make considerable and increasing noise before moving away, and 2. fighter jets that fly over the speaker's neighborhood make less noise.

0% Heard from single, fixed point, 1. fighter jets that fly over the speaker's neighborhood make considerable and increasing noise before moving away, and 2. fighter jets that fly over the Champs Elysées make less noise.
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