Crossing and stranding at edges: On intermediate stranding and phase theory

This paper investigates the distribution of stranding in intermediate positions under A′-movement, which I show obeys a cross-linguistically robust word order generalization: leftward movement of a phrase α can only intermediately strand an element β if β can be ordered rightward of α before stranding occurs. I argue that this generalization emerges naturally from the Cyclic Linearization theory of spell-out, and its interaction with independently supported constraints on movement in syntax. I go on to consider some reasons why a particular position may or may not be a viable location for stranded material.


Introduction
Moved phrases can sometimes leave material behind at an intermediate point in the path of movement, as numerous works have shown. If the syntactic derivation is bounded by phases (at least vP and CP), which movement from must successive-cyclically pass through the edge of (Chomsky 2000;a.o.) then the possibility of such stranding is expected. This is because the intermediate landing sites forced by phases provide positions where, in principle, we predict that stranding might occur. In this paper, I examine the nature of such intermediate stranding.
The schema in (1) illustrates the basic form of an intermediate stranding derivation. Here successive-cyclic movement of a phrase α intermediately strands an element β in the edge of the phase YP, in the following way. First, α moves to the YP edge while simultaneously pied-piping β. Second, α moves on alone, leaving β behind in the edge of YP. Thus movement of α through the edge of the phase YP feeds intermediate stranding of β. (1) Intermediate stranding under successive-cyclic movement Intermediate stranding under successive-cyclic movement In this paper, I show that such stranding obeys a cross-linguistic generalization about word order, stated below: (2) Intermediate Stranding Generalization (ISG) Leftward movement of a phrase α can only intermediately strand an element β if β is (or can be) ordered rightward of α before stranding occurs.
I argue that this generalization stems from a particular proposal concerning the nature of spell-out, along with independent constraints on movement in syntax.

Preview of results
Assuming that intermediate stranding typically occurs in phase edges for the reasons outlined above, I argue that the ISG in (2) holds because only those derivations that obey it avoid a fatal crossing problem. This problem is illustrated in (3a) below. Here β precedes α before intermediate stranding occurs. In this situation, when α strands β in the edge of the phase YP, movement of α from YP must cross over β. By contrast, in (3b) α originally precedes β. Thus here movement of α will not cross over β when β is stranded at the YP edge. In this paper, I argue for a theory which rules in only non-crossing intermediate stranding derivations like (3b). Since (3b) corresponds to what the ISG describes, the ISG will thus be derived.
(3) a. * Intermediate stranding with crossing at the edge b.  Intermediate stranding without crossing at the edge Intermediate stranding without crossing at the edge In particular, I argue that the ISG arises naturally under the Cyclic Linearization (CL) theory of phase spell-out (Fox & Pesetsky 2005a;2005b;Ko 2007;Sabbagh 2007;Podobryaev 2009;Fanselow & Lenertová 2011;Jenks 2011;Overfelt 2015;Erlewine 2017;Davis 2019). CL derives successive-cyclic movement (and certain exceptions to it) from the logic of linearization, the operation that maps syntactic structures to pronounceable linear strings at spell-out. As we'll see, CL interacts with the impossibility of movement within phrase edges (Ko 2007;a.o.) and with anti-locality (Bošković 1997;Ishii 1999;Grohmann 2003;Abels 2003;Erlewine 2016;a.o.) to constrain intermediate stranding in precisely the way the ISG describes.

Road map of the paper
Next, section 2 provides the empirical basis for the ISG, describing all intermediate stranding patterns that I am currently aware of. Section 3 overviews phase theory and the CL approach, and shows how CL derives the ISG. Section 4 demonstrates how independent constraints on movement interact with CL to accurately rule out various alternative derivations that would violate the ISG. Section 5 goes on to consider some factors that constrain the set of possible landing sites for stranded material. Section 6 compares this paper's approach to that of Bošković (2018), who predicts a result that is similar to the ISG, but different in several details.

The cross-linguistic distribution of intermediate stranding
This section provides the empirical motivation for the ISG, reporting all patterns I currently know of that may constitute intermediate stranding. Most of these patterns come from previous literature. While some of these scenarios may indeed be clearer than others, it will nevertheless be evident that a straightforward word order generalization can be stated about patterns of this nature. McCloskey (2000) discusses what is likely the most well-known case of intermediate stranding, involving the post-nominal quantifier all in West Ulster English, a dialect of Ireland. In this English variety, A′-movement can pied-pipe all, strand it in its base position, or strand it in a clause edge: Based on these facts, McCloskey argues that A′-movement from CP pauses in the CP edge, and that the punctuated nature of such movement provides an intermediate landing site in the clause edge where this dialect's strandable all can be left behind. A clear piece of evidence that such patterns truly involve stranding is the fact that stranded all can only appear in positions within the A′-movement path of the associated phrase:

Stranding in West Ulster English and a puzzle about prepositions
(5) all-stranding in West Ulster English must occur within the movement path (McCloskey 2000, ex. 19) a. What k did she buy t k all in Derry yesterday? b. *What k did she buy t k in Derry all yesterday? c. *What k did she buy t k in Derry yesterday all?
Decades earlier, Postal (1972;1974) argued for the opposite of McCloskey's conclusion, based in part on the fact that English prepositions cannot be stranded in clause edges (6) The same constraint is found in Norwegian, which like English allows a preposition to be either stranded in its base position or totally pied-piped, but not stranded in a CP edge, as (7) shows:

Stranding of adjuncts to wh-phrases in English
English allows an interrogative wh-phrase to be modified by exactly/precisely and similar elements, which Zyman (2019b) argues should be considered adjuncts. As is often the case for English adjuncts, these elements can attach on either side of the phrase they merge to: (9) Variable order of wh-adjoined exactly / precisely a. (Exactly / precisely) [how many cakes] k (exactly / precisely) did you say that we ate t k ? b. Who said that you ate (exactly / precisely) [how many cakes] (exactly / precisely)?
Such adjuncts can be stranded in their base position or in a CP edge by wh-movement of their host phrase (Urban 1999;Stroik 2009;Zyman 2019b): (10) Adjunct stranding under wh-movement What k did you suppose t k (exactly / precisely) (that) they wanted t k (exactly / precisely)?
Since these adjuncts are able to be adjoined to the right side of their host phrase, the possibility of stranding them in a CP edge fits the ISG. The same basic pattern holds for adjuncts of quantity like to the nearest pound in (11)

Q-stranding in Wolof
Torrence (2018) examines a variety of elements that appear in the periphery of clauses crossed by wh-movement in Wolof (Niger-Congo, Atlantic). Torrence reports that there are at least two morpho-syntactic classes of such elements. He argues that one of these classes, which he terms 'Q-like', has a distribution indicative of stranding under movement. According to Torrence, these quantificational elements obligatorily follow the NP they merge with. This fact is evident when they are not stranded by movement, as in (13) below, where total pied-piping occurs: (13) Full pied-piping of Q-like element in Wolof a. Torrence (2018, ex. 38a) [Ñ-an ñ-epp] k l-a Ayda wax ne l-a-a dóór t k ? who every cop Ayda say that cop.1sg hit 'Who all did Ayda say that I hit?' b. Torrence (2018, ex. 38b) [F-an f-eeneen] k l-a Ayda wax ne l-a-a dem t k ? Where other cop Ayda say that cop.1sg go 'Where else did Ayda say that I went' These elements need not necessarily be pied-piped by wh-movement, but can also be stranded in situ (14), as well as in the edge of an embedded CP (15). Since these strandable elements originate to the right of NP, their ability to undergo intermediate stranding in the CP edge corresponds with the ISG.   Torrence (2018, ex. 29b) F-an k l-a-nu foog [t k f-eeneen] j ne la-a togg-e ceeb t j ? where cop.3pl think other that cop.1sg cook rice 'Where else do they think that I cooked rice?' Torrence states that the stranding of these elements is parasitic on A′-movement. It is, for instance, not possible to insert such an element into the edge of a CP that is c-commanded by a relevant noun phrase that did not move from that CP, as we see in (16) below. This is expected if the appearance of such elements in a clause-peripheral position, as in examples like (15) above, is indeed derived by intermediate stranding.

(16)
Intermediate stranding in Wolof requires A′-movement of host phrase (Adapted from Torrence 2018, ex. 31) *Xale b-i defe-na b-oo-b-u ne lekk-na-a ceeb b-i. child the think aforementioned that eat.1sg rice the 'The aforementioned child thinks that I eat rice' Barbiers (2002) shows that long-distance A′-movement from an embedded clause in Dutch can strand adpositions and various other elements in the matrix spec-vP, as demonstrated below:

Stranding in spec-vP in Dutch
(17) Stranding in spec-vP in Dutch (Barbiers 2002 Scrambled phrases in Dutch are generally 'frozen' and hence behave like islands (see Corver 2017 and references therein), suggesting that these examples are not derived by first scrambling a phrase into the matrix spec-vP, and then sub-extracting from it. It is conceivable that the freezing effect is circumvented in these examples by first performing sub-extraction, and then scrambling the remnant of that extraction from the embedded clause and into the matrix spec-vP. However, Barbiers shows that long-distance A′-movement cannot normally be combined with long-distance scrambling in Dutch. Barbier's conclusion is that the facts in (17) are best analyzed as stranding under successive-cyclic movement.
Most of the elements that Barbiers shows undergoing such intermediate stranding in spec-vP originate to the right of what strands them, as in (17a-b). The exception is (17c), involving a stranded maar ('only'), which Barbiers shows as originating to the left of the moving element that stranded it. This example thus appears to violate the ISG. However, in other work, Barbiers (1995) shows that such configurations where maar has a numeral as its focus associate allow maar to be either pre-or post-nominal. We see this in (18) below, where maar may appear either on the left or the right of the NP containing the numeral twee 'two' that it focuses: Dutch maar in pre-or post-nominal position (Adapted from Barbiers 1995, ex. 31c-d) [(Maar) twee jongens (maar)] weten het antwoord.
(only) two boys (only) know the answer 'Only two boys know the answer.' Since maar can be ordered rightward of NP in these contexts, (17c) is not an exception to the ISG.
Further Dutch stranding facts also fit the ISG. In Dutch, inanimate pronouns within PPs take on a special form (termed R-pronoun) with which many prepositions are inverted to alternative postpositional forms. While prepositions in Dutch cannot be stranded by A′-movement, their postpositional forms used with R-pronouns can be (van Riemsdijk 1978), as exemplified by (19)(20)  where cut you the bread with 'What are you cutting the bread with?' Importantly, the P 'with' in (19-20) above is realized as met when it is a preposition, and mee when it is a postposition. Example (17a) above showed that the postposition mee is capable of intermediate stranding. As expected given the ISG, its prepositional variant met cannot be intermediately stranded. Hence an example analogous to (17a) that uses met instead of mee such as (21) below is unacceptable: No preposition stranding in spec-vP in Dutch (Coppe van Urk, p.c.) *[Welk mes] k had jij dan [met t k ] j gedacht dat je de vis t j zou which knife had you then with thought that you the fish would moeten snijden? must cut 'Which knife did you think then that you would have to cut the fish with?'

Stranding by left branch extraction in Polish
Wiland (2010) (25) below. Assuming that Polish V moves to v, Wiland argues that the stranding positions shown in (25) are the specifiers of VP, vP, and CP. Wiland thus assumes that these three phrases are all phases, 2 which movement must pass through the edges of: 1 Rackowski & Richards (2005) and den Dikken (2009) both argue that this Afrikaans pattern actually involves stranding in a clause-medial position. What matters for the present paper is not where exactly these elements end up, but only that their word order properties fit the ISG. 2 Wiland's assumption that VP is a phase is not shared by most work on phase theory, but this concept has some precedent, as discussed in section 5.3 of this paper (particularly footnote 23). For the most part, the present paper assumes with Chomsky (2000;a.o Wiland notes that prima facie it is possible to analyze these examples as scrambling followed by sub-extraction of the wh-element from the scrambled phrase. However, Wiland goes on to show that unlike wh-movement, Polish scrambling is clause-bounded. From this, he argues that at least (25c) above and (26)  Since the Polish NP is ordered to the right of the wh-element undergoing sub-extraction in the above examples, these stranding configurations fit the ISG. Podobryaev (2009) compares two types of adpositions in Russian. First Podobryaev shows that, as is well known, prepositions in Russian cannot be stranded: (27) No preposition stranding in Russian (Podobryaev 2009

Interim summary
In this section I have reported all instances of intermediate stranding that my research so far has uncovered. All of these facts fit the ISG, repeated below: Intermediate Stranding Generalization (ISG) Leftward movement of a phrase α can only intermediately strand an element β if β is (or can be) ordered rightward of α before stranding occurs.
The remainder of this paper focuses on demonstrating how CL, plus certain independently proposed constraints on movement, straightforwardly derives the ISG. 7

Two phase theories and their predictions
This section compares the predictions about intermediate stranding made by the phase theory in Chomsky (2000;a.o.) against those of Cyclic Linearization (CL). I will argue that the latter theory is better equipped to account for the word order generalization about intermediate stranding illustrated in the previous section.

Phases in Chomsky (2000; 2001)
Chomsky argues that syntactic derivations are mapped to phonology (PF) and interpretation (LF) incrementally, phase by phase. Minimally, vP and CP are phases. Chomsky hypothesizes that when the operation spell-out performs this mapping, the content of the spelled-out constituent becomes inaccessible to the rest of the syntactic derivation. Chomsky argues that spell-out applies to only the complement of phase heads. Consequently, this theory predicts that moving from a phase directly from its complement isn't possible, since the material in the phase's complement will undergo spell-out before such movement can apply (32a). However, movement to the edge (specifier) of the phase before its complement spells-out is predicted to allow further movement from the phase (32b).
(32) Must exit phase complement via the phase edge In this way, Chomsky's theory of phases predicts that moving phrases must pass successive-cyclically through the specifier of each phase crossed, in order to avoid being prematurely trapped by spell-out.
(ii) Intermediate stranding of numeral quantifier in Korean (Ko 2011, ex. 24) Kong-ul k amato [ vP [t k sey-kay] j haksayng-tul-i t j patassulkesita]. Ball-acc probably 3-thing student-pl-nom received 'The students probably received three balls' Similar strings are possible in Japanese (Shigeru Miyagawa, Takashi Morita, p.c.), whose syntax is highly similar to that of Korean. Ko shows that the numeral quantifier constructions in Korean/Japanese that allow stranding involve the numeral quantifier being ordered rightward of NP. Thus if examples like (ii) are indeed instances of intermediate stranding, they fit the ISG. A reviewer points out that the great productivity of scrambling in Korean/Japanese makes it difficult to determine whether such examples actually constitute intermediate stranding rather than a more complex derivation involving something like remnant movement, however.

Predictions for intermediate stranding
Under the phase theory described above, anything which is in (or can reach) a complement-external position within a phase should, in principle, be available for further movement. Word order should not be at issue here, only structure. Therefore unless more is added to this theory, it predicts that both of the hypothetical intermediate stranding scenarios in (33) below should be licit. 8 These two scenarios are structurally comparable, but differ in word order. In reality, we've seen that in all attested intermediate stranding patterns the stranded material originally was (or could have been) ordered to the right of what stranded it. This fact is described by only the ISG-matching schema in (33b) b. Intermediate stranding without crossing at the edge (ISG-obeying) The linear nature of the ISG is thus not captured by a theory of movement cast purely in structural terms. As we'll see, the connection between linear word order and the availability of intermediate stranding emerges naturally under CL, for which syntactic movement is constrained by the linear ordering information that phase-by-phase spell-out generates.

Cyclic Linearization (CL)
CL proposes that successive-cyclic movement, and related effects, emerge as a consequence of the information-preserving nature of spell-out. For CL, spell-out applies to entire phases, not just their complements. A phase spells-out as soon as it is done being built up by successive applications of (internal and external) Merge. Since for this theory phase-level spell-out applies to everything within the phase, not even elements in the phase edge escape spell-out. Therefore in order to avoid predicting the absence of movement from phases, CL hypothesizes that spelled-out material remains accessible for the entire syntactic derivation. Since this hypothesis is incompatible with the explanation for successive-cyclic movement in Chomsky's work, CL proposes an alternative. In particular, CL argues that successive-cyclic movement is necessary to ensure that the ordering information generated by phase-by-phase spell-out remains consistent throughout the derivation.
To understand the logic of CL, first consider a derivation like (34)  Later, what moves in one step to spec-CP. Spell-out of CP produces the ordering information shown in (36) Notice that in (35), what was determined to follow everything in vP. However, in (36) what was established to precede everything in CP, and thus to ultimately precede everything in vP. Here we have a contradiction: this derivation has established that the moved phrase what must simultaneously follow and precede the content of vP. CL posits that such contradictory results yield a derivation that is deviant at PF. Importantly, successive-cyclic movement through the linear edge of vP, as in (37), prevents such an ordering contradiction from arising.

(37)
Successive-cyclic movement through the linear edge of vP Spell-out of the vP in (37) generates the ordering information in (38) The grammaticality of this sample derivation depends on the moving phrase reaching (and thus being linearized at) the left linear edge of the intermediate phase before moving on. In this way, CL predicts that movement from any phase must successive-cyclically pass through its linear edge. This is because if movement exits a phase from a position that is not at the linear edge, hence crossing over some material in the phase on the way out, incoherent ordering information is generated. 10

Why CL predicts the ISG
Recall the generalization about intermediate stranding that this paper argues for: 9 The notation '<' encodes the relative linear order of two elements, not strict adjacency. Thus the establishment of an ordering [α < β] is compatible with α moving on, with the result that other material ultimately intervenes between α and β, as in [α γ β]. 10 However, later movement of material that is crossed over by a phase exit from a non-edge position is predicted to be able to rescue the derivation, as I discuss further in section 5.1 below.
(40) Intermediate Stranding Generalization (ISG) Leftward movement of a phrase α can only intermediately strand an element β if β is (or can be) ordered rightward of α before stranding occurs.
The ISG is an automatic consequence of CL only permitting movement from a phase via its linear edge. If a successive-cyclically moving phrase intermediately strands material that precedes it, then that phrase illegally crosses over the material it strands in the edge as it moves on into the next phase (41a). In contrast, if the material being stranded at the edge follows the phrase that strands it by moving on (41b), then such problematic crossing at the phase edge doesn't occur: (41) a. * Intermediate stranding with crossing at the edge b.  Intermediate stranding without crossing at the edge To see concretely why this is so, compare the ordering information generated in the derivation of (41a) with that of (41b). In (41a), the constituent βα first moves to the edge of the phase YP. In this situation, when YP undergoes spell-out, the result is the ordering β < α < Y < X. Next, the element α is extracted into spec-ZP. Spell-out of ZP then generates the ordering information α < Z < YP. Here a contradiction arises: within YP, it was previously established that β precedes α. However, after movement of α from YP, α is linearized as preceding the content of YP, including the element β which YP contains. Because α cannot both precede and follow β, this configuration is not pronounceable. In contrast, this linearization problem does not arise in (41b). Since in this derivation α precedes β in the first place, no contradiction is caused by extraction of α from YP after α pied-pipes β to the YP edge: α simply precedes β for the entire derivation. In this way, CL accurately permits only non-crossing intermediate stranding derivations like (41b), which corresponds to what the ISG describes. Importantly, the crossing problem that derives the ISG applies only at phase edges. Thus base position preposition stranding in languages like English and Norwegian, for instance, is correctly permitted. To my knowledge, the closest analogue to this proposal in preceding work comes from the examination of quantifier float in Jenks (2011;, who focuses on numeral classifiers in East Asian languages. Jenks argues that quantifier float is (at least in some languages like Thai) derived by rightward extraposition of the quantifier, which he argues obeys the following generalization: Quantifier Float Generalization (paraphrased from Jenks) Rightward float of a (numeral) quantifier/classifier is only attested in languages which allow the DP-internal order N < #/Q.
Jenks argues that this generalization may in fact apply to all rightward extraposition, and proposes that this result is a consequence of CL. While Jenks' generalization differs from the one proposed in the present paper since it is not about intermediate stranding per se, Jenks' findings are convergent with this paper in that they show how independent word order facts constrain movement. This is precisely as expected, if CL limits the set of licit movement configurations.

The role of locality constraints on movement
In this section, I argue that CL interacts with independently proposed locality constraints on movement in a way that correctly rules out several potential ISG-violating derivations. This section will also clarify why the ISG contains the disjunction that if β is or can be ordered rightward of α, then α can intermediately strand β. I adopt from Ko (2007; the hypothesis that movement from one specifier to another of the same phrase is banned. As Ko points out, such a ban is a direct consequence of the concept that movement to the specifier of a given head requires that head, or more specifically an 'edge feature' or EPP feature on that head (Chomsky 2005), to c-command the goal phrase to be moved (Chomsky 2000;a.o.). Thus since heads don't c-command their specifiers, it is not possible for a head to target and move a phrase from one of its specifiers to another. 11 The impossibility of such movement correctly rules out circumventing the ISG by re-arranging the content of the phase edge before stranding occurs, as described below.
If intermediate stranding fails when a moving phrase crosses what it strands while exiting the phase, then ISG-violating intermediate stranding should be permitted if the moving phrase can reach a higher position within the phase edge, above any pied-piped material that initially preceded it. In (43) below, this hypothetical configuration is illustrated with pied-piping wh-movement of a prepositional phrase into spec-CP (43a), followed by extraction of the wh-phrase from the complement of the prepositional phrase and into a higher specifier of the same CP (43b):
Step 1: Pied-piping into phase edge Step 2: Extraction to second specifier of the same phase Since the edge-internal movement in (43b) brings the wh-phrase to a position within CP preceding the pied-piped preposition, then this movement, if available, should allow the wh-phrase to subsequently extract from CP without crossing P. Such movement would thus strand the preposition in spec-CP. As we've seen, such ISG-violating stranding is not possible in reality. However, if following Ko the edge-internal movement required for this hypothetical derivation is independently ruled out, then we correctly avoid predicting the possibility of such derivations. 12 A related constraint on movement in syntax is anti-locality, the concept that movement must not be too short (Bošković 1997;Ishii 1999;Grohmann 2003;Abels 2003;Erlewine 2016;a.o.). Many formulations of anti-locality at least partially subsume the ban on phrase-bounded specifier-to-specifier movement just discussed. Additionally, Abels' version of anti-locality also bans movement of a head's complement to its specifier. I adopt this constraint on movement as well, since it correctly rules out the possibility of deriving certain ISG-violating configurations via movement within the pied-piped constituent.
For instance, a wh-phrase complement of a prepositional phrase might conceivably move to spec-PP prior to pied-piping the PP into spec-CP, as diagrammed in (44) below. 13 In the resulting configuration, the wh-phrase occupies the left linear edge of PP and of the containing CP: Hypothetical movement internal to pied-piped PP

... t j
After these movements occur, the wh-phrase could be extracted from CP without crossing over P on the way out, thus undesirably deriving intermediate stranding of the preposition. However, since the required movement from complement to specifier of PP is banned by anti-locality, a configuration like (44) cannot be derived, and thus cannot serve as the input for an ISG-violating derivation. 14,15 12 The problematic configuration in (43b) could also be derived by first performing wh-movement to spec-CP without pied-piping PP, and then moving the remnant PP from its base position and into a lower specifier of the same CP via tucking-in (Richards 1997;a.o.). Given that this wh-movement and subsequent PP remnant movement would both be A′-movement to the same position, the possibility of such a derivation is likely excluded by the finding of Müller (1998) that it is impossible to extract from a given constituent and also move the resulting remnant, when both the extraction and remnant movement would be movements of the same type. See Takano (1993) and Kitahara (1994) for discussion of similar considerations. 13 Any PP-internal movement occurs before PP moves, not after, if syntactic derivations are governed by the Strict Cycle Condition (Chomsky 1973). 14 The ruling-out of the PP-internal movement in (44) that this paper requires is in correspondence with Abels (2003), who argues that in languages where PP is a phase, P-stranding does not occur because anti-locality prevents the needed movement via spec-PP. In contrast, Abels (2003) hypothesizes that in languages like English P-stranding is available because PP is not a phase, so extraction from PP need not illegally pass through its edge. Abels (2012) seeks to remove the variability in phasehood inherent to Abels (2003) by taking PP to be a phase in all languages, and hypothesizing that in P-stranding languages PP is more structurally complex, such that extraction via the PP edge is possible. Abels (2012) is not compatible with the present paper, for which the possibility of movement to the edge of PP in languages like English would wrongly rule in intermediate preposition stranding. Abels notes that there is not much direct evidence favoring his (2012) approach over his (2003) one. The arguments of the present paper, if correct, can be taken as evidence that Abels (2003) is in fact on the right track. 15 Abels' anti-locality as applied here raises a question about swiping, which inverts P and its wh-complement under sluicing: I know John went somewhere, but I don't know where to (Ross 1969;Merchant 2002). This paper does not allow swiping to be derived by movement of the wh-phrase within PP, or from PP to a second specifier of the embedded CP. Since the inversion characteristic of swiping is not possible without ellipsis, maintaining that such movements are unavailable appears tenable: I know John went somewhere, but I don't know (to) where (*to) he went. The fact that swiping is generally exclusive to single-word wh-phrases may provide evidence that swiping is derived by a PF process available under ellipsis rather than by usual syntactic movement: *I know John read about a few languages, but I don't know how many languages about.
This anti-locality constraint is predicted to be irrelevant if the pied-piped constituent is structurally larger, however. For instance, in the schema in (45) below, a wh-phrase piedpipes ZP and the containing phrase YP into a CP edge. Since movement of the wh-phrase from ZP to the edge of YP does not violate anti-locality, such movement to the linear edge of this two-layered pied-piped constituent is possible. After such movement as well as pied-piping into the CP edge occur, the wh-phrase ultimately occupies the linear edge of the pied-piped phrase and of the containing CP phase, as (45) shows: Legal movement within larger pied-piped constituent In principle the wh-phrase could subsequently move from the CP in (45), intermediately stranding the pied-piped YP in the CP edge. Since the wh-phrase would not cross any material as it exits this structure, such stranding is predicted to be licit. This prediction provides an analysis for intermediate stranding of material that can be ordered on either side of what it merges with, as we saw in section 2 for certain adjuncts of wh-phrases in English, maar ('only') in Dutch, and ambivalent adpositions in Russian. If the word order variability these elements display stems from the possibility of movement within the relevant constituent, then such movement should provide a means of deriving ISG-obeying intermediate stranding. This expectation is connected to the disjunction in the definition of the ISG that if an element β is or can be ordered rightward of α, then α can intermediately strand β. For the account developed here, this aspect of the ISG emerges from the fact that if a given phrase can move to the left edge of a containing constituent, then such movement should be available to feed later intermediate stranding of that constituent.
To see precisely how the derivation of such an instance of intermediate stranding would proceed, let's consider Russian ambivalent Ps once more. Podobryaev (2009) argues that anti-locality bans movement within typical Russian PPs, but that the strandable variably ordered Ps discussed in section 2.6 are more structurally complex, such that movement within them is possible. Podobryaev suggests, consistent with the diachronic facts, that such PPs are derived from nouns via the N to P incorporation in (46) below. If these adpositions indeed involve two phrasal layers, then anti-locality respecting A′-movement to the edge of such an adposition should be licit, as we see with a moved wh-phrase in (46) Thus the possibility of moving to the left edge of the complex adposition provides the means for intermediate stranding of this constituent to succeed. 16,17,18 In contrast, this 16 The same concerns lead to an understanding of configurations in English involving A′-extraction from a constituent that has undergone topicalization or wh-movement to an embedded spec-CP, like (iii) below. Such patterns have been discussed by at least Pesetsky (1982), Chomsky (1986), Lasnik & Saito (1999), and Sauerland (1999): (iii) Sauerland (1999, 24c) ?
The present approach can derive (iii), in the following way. First, the inner wh-phrase what student j moves to the spec-DP of the outer wh-phrase what picture of k . This movement from the complement of NP to spec-DP does not violate anti-locality. The outer wh-phrase then moves to the embedded spec-CP. The inner wh-phrase is then the leftmost phrase in the embedded CP since it occupies the specifier of the outer wh-phrase, which in turn occupies the specifier of the embedded CP. From this peripheral position, the inner wh-phrase can move on into the matrix clause. 17 While pied-piping a constituent large enough to permit movement through its edge is one predicted way to yield legal intermediate stranding, the same result is predicted for a constituent whose internal order is simply free due to optionality (or under-specification) of linearization rules. This alternative could be correct for the stranding of the English adjuncts discussed in sub-section 2.2 above: given that English adjuncts can often be freely ordered either left or right of the phrase they adjoin to, this may simply be a matter of free ordering feeding intermediate stranding. 18 Heck (2009)

On quantifier float under A-movement
It is in the context of A′-movement that the type of stranding this paper focuses on emerges most clearly. However, many languages also allow the apparent stranding of quantifiers under A-movement, a phenomenon often referred to as floating quantification, exemplified in (48): The students have all had lunch.
b. French (Sportiche 1988, ex. 2b) Les enfants ont tous vu ce film. the kids have all seen this film Some such patterns may present exceptions to the ISG at first glance, given the ban on movement within phrase edges adopted earlier in this section. To illustrate the potential problem, it will suffice to consider the English example in (48a). Here the subject DP is separated from its associated quantifier all by an intervening auxiliary. If all was originally merged to the subject which then A-moved to spec-TP, then the fact that all cannot follow a DP that has not moved, like the object in (49) below, suggests that all originally preceded the subject in (48a) prior to A-movement.
(49) Unmoved DP must be preceded by all I saw (all) the cats (*all).
Sentences like (48a) have a word order consistent with all having been stranded in spec-vP by A-movement of the subject from its θ-position, as illustrated in (50)  Given the ban on phrase-bounded specifier-to-specifier movement, it is not possible for the subject to move to a higher spec-vP above the quantifier to avoid this crossing problem. Thus movement of the subject to spec-TP must cross the stranded quantifier in the linear edge of vP. Therefore the possibility of sentences like (48a) appears to constitute a violation of the ISG, if the right analysis for them is (50). 19 However, if the floated quantifier in (48a) was not derived by stranding, then this sentence does not constitute an exception to the ISG. A non-stranding approach to quantifier float has been explored by a variety of works (Dowty & Brodie 1984;Bobaljik 1995;Doetjes 1997;Fitzpatrick 2006;a.o.). Fitzpatrick (2006) in particular follows preceding works in taking quantifier float under A-movement to be essentially adverbial, involving an adjunct containing the quantifier and a pro co-indexed with the A-moved phrase (51). Importantly for the present paper, Fitzpatrick goes on to argue that while stranding under A′-movement is genuine sub-extraction, apparent stranding under A-movement is always adverbial in this way.

On when an edge is available for stranding
So far, this paper has focused on understanding what sorts of elements can be stranded in intermediate positions.
Another relevant topic in this domain is the question of what positions are, in principle, available to be stranded in. While the present paper cannot provide a full understanding of this issue, this section will discuss several relevant predictions and possibilities.

Stranding in spec-vP by A′-movement is blocked by A-movement
As described in section 3, CL derives successive-cyclic movement through phase edges from the logic of non-contradiction in linearization: movement through the linear edge of each phase crossed ensures the coherence of the orderings that phase-by-phase spellout generates. As we'll now see, the same logic also predicts that certain exceptions to successive-cyclicity are possible, as long as additional movements occur that keep linearization coherent. In (52) below, we see a schema for non-successive-cyclic movement and its repair. In (52a), the element α initially precedes β within the phase XP. β then moves from XP without stopping in its edge, thus crossing α on the way out. As discussed above, such a scenario is predicted to result in a linearization contradiction. This is because such crossing of α by movement of β creates an ordering which requires pronouncing β both before and after α. CL predicts that this problem is avoided, however, if α also moves into the next phase, to a position above β, as in (52b). The result of this movement is that α precedes β within the subsequent phase just as it did within the first.

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This prediction, which Fox & Pesetsky (2005a;b) originally defended in the context of object shift in Scandinavian, leads us to expect that any phase edge crossed over by such non-successive-cyclic movement should not be a viable position for intermediate stranding. Rather, we expect that such positions must be vacated. We find a verification of this prediction in the distribution of exactly and other adjuncts to wh-phrases in English, which as introduced in section 2.2 above, can be stranded at clause edges: Adjunct stranding at clause edge by wh-movement a. What k did you suppose t k (exactly / precisely) (that) they wanted t k ? b. How much saffron k did the chef say t k (to the closest gram) (that) we need t k ?
If vP is a phase in addition to CP, then we also in principle expect these adjuncts to be able to be stranded in spec-vP, and thus appear in a position between the subject and verb. However, this linear position is also a possible location for adverbs. For this reason I focus on strandable adjuncts like that in (53b), which can't be parsed as adverbs. Example (54) below attempts to strand such an adjunct in spec-vP, which proves to be unacceptable: The impossibility of such stranding in spec-vP is expected, given the prediction of CL discussed at the beginning of this section. To see why, consider the interaction of successive-cyclic A′-movement with A-movement of the subject. CL requires an A′-moving non-subject argument to temporarily land in the most peripheral position of the vP phase on its way to spec-CP. This will be a spec-vP above the external argument (EA) in situ in its θ-position. No linearization problem arises when the subject later A-moves to spec-TP across that outer spec-vP formed by successive-cyclic A′-movement, provided that the content of that outer specifier moves to spec-CP. After such movements, the relative order of the moved phrases established in vP and CP are the same, yielding a coherent linearization, as (55) exemplifies with movement of an object wh-phrase: (55) WH < EA order maintained in vP and CP However, if this wh-movement strands something in that outer spec-vP, then movement of the subject across that position encounters a crossing problem. This is shown in (56), where we see that while there is no issue if the moving wh-phrase pied-pipes the element α to spec-CP, there is a problem if α is stranded in vP and is thus crossed by A-movement of EA: (56)

Conflict between EA movement and stranding in the vP edge
This problem could be avoided if it were possible to rearrange the specifiers of vP before movement from it occurs. However, given the ban on phrase-bounded specifier-to-specifier movement discussed in section 4, this is not an option. Thus stranding in spec-vP cannot be permitted. The same concerns lead to a solution for a puzzle from McCloskey (2000), who notes that if vP is a phase, West Ulster English should allow all-stranding in its edge, contrary to fact, as we see in (57)  The impossibility of such stranding follows directly from the concerns just discussed, given A-movement of the subject from vP. The movement of V from vP that McCloskey posits for West Ulster English provides a second reason why such stranding should be banned: there is no position in vP where V can precede the specifiers of vP. Hence movement of V from vP will necessarily cross over any specifiers of vP, forcing them to be evacuated. For further examination of how CL affects movement from and stranding in vP, see Davis (2019).

Unexpected absences of stranding in spec-CP
The previous subsection analyzed a circumstance under which stranding in spec-vP is banned. There are also patterns where material that appears to be capable of being stranded in situ fails to be stranded in the CP edge, even though such stranding would satisfy the ISG. Several such patterns are shown below:  (58), a lack of intermediate stranding in spec-CP is expected of these patterns: under the remnant movement analysis, an element that appears to have been stranded in its base position in fact was not. Rather, it evacuated the moving phrase at an earlier point. Since stranding is not involved in such a derivation, there is no pied-piping/stranding at issue in the first place, and hence, no expectation that stranding in spec-CP should be possible.

On possible landing/stranding sites and phase theory
The previous two subsections have discussed scenarios where stranding in a particular edge fails. While the analyses I have offered may apply to some such patterns, they are unlikely to be correct for all, since the cross-linguistic variance in intermediate stranding patterns is quite rich. For instance, recall that in West Ulster English as reported by McCloskey (2000), wh-adjoined all can be stranded in spec-CP, but not spec-vP. Henry (2012) (17) and Polish (25). Further variation within West Ulster English presents yet more puzzles. According to Henry, South Derry English allows base position all-stranding in addition to spec-vP all-stranding, but does not permit all-stranding in the CP edge. The Strabane variety is evidently even more restrictive, permitting all-stranding in only the base position. The least restrictive is East Derry English, which Henry shows allows all-stranding in the base position, spec-vP, and spec-CP. In response to these diverse facts, Henry argues that the set of positions in which a language permits stranding is simply a matter of choice. That is, while the syntactic principles endowed by Universal Grammar determine a consistent set of landing sites through which successive-cyclic movement passes, languages may opt to permit stranding in only some of them. While this could ultimately be the correct understanding, a more predictive theory is desirable if possible. 22 A different strategy is taken by Barbiers (2002), who analyzes stranding in a position consistent with spec-vP in Dutch, as described in section 2.4 above. As Barbiers shows, this stranding pattern is highly restricted: only stranding in the matrix spec-vP in a longdistance movement derivation is permitted. Stranding in the embedded spec-vP is banned, as is stranding in the embedded CP edge. Part of Barbiers' approach to these facts is to connect the distribution of stranding to the distribution of phases: if a constituent is not a phase, it is not a domain for successive-cyclic movement, and hence not a possible location for intermediate stranding. In general, relating the distribution of intermediate stranding and of phases in this way has the potential to lead to a more predictive theory of whether or not a given language will permit stranding in a particular position.
A difficulty for this analytic direction is that it likely depends on positing considerable cross-linguistic variation in the set of phases. This is a complex issue, since the current literature offers numerous proposals about where phases can be found. As Ko (2014) points out, beyond the original phases vP and CP, most constituents in the clause have been taken to be a phase at some point, including VP (Fox & Pesetsky 2005a;Wiland 2010;Ko 2011), Asp(ect)P (Bobaljik & Wurmbrand 2013;Bošković 2014;Harwood 2015), and TP (Deal 2016;Zyman 2019a). Further, some works argue that phasehood can change during a derivation, for instance, in response to movement of a phase head (den Dikken 2007;Gallego 2010;Alexiadou et al. 2014). While these possibilities can accommodate many different patterns of intermediate stranding, 23 pursuing a phase-centric approach to the cross-linguistic variance in stranding will require case-by-case analysis of each pattern and the language in which it is situated. Such a task is beyond the scope of this paper. Regardless, the present paper predicts that any instance of intermediate stranding must obey the ISG, an expectation that is confirmed by the known facts.

Comparison with Bošković (2018) on movement from moved phrases and labeling
As analyzed in this paper, intermediate stranding is a particular instantiation of movement from a moved phrase: a first step of successive-cyclic movement pied-pipes material into a phase edge prior to a second step of movement stranding it there. As Bošković (2018) notes, movement from moved phrases has been shown to be quite restricted by many works. While such sub-extraction is largely banned in many languages, others permit it to some extent. Working within the phase theory in Chomsky (2000; and the labeling framework of Chomsky (2013), Bošković (2018) makes a prediction about when movement from moved phrases is allowed. While his results partially overlap with the ISG, they differ in several details, as we'll see next.

Labeling, phases, and movement from moved phrases
For Chomsky (2013), when a phrase XP is merged with another phrase YP, XP must move away unless Y agrees with XP such that the two share a common feature, based on which the mother of XP and YP is labeled. For this theory, successive-cyclic movement does not involve agreement and hence does not feed labeling, which is in part why successivecyclically moving phrases must keep moving until an appropriate landing site is found. Bošković (2018) argues that this system predicts a desirably restricted distribution of movement from moved phrases, when combined with two assumptions: that only phases may move (Rackowski & Richards 2005;Legate 2014;Harwood 2015;a.o.), and that unlabeled constituents cannot move. To illustrate how these concepts ban movement from moved phrases in some situations, let's first examine the ban on extraction from subjects in languages such as English: No sub-extraction from subject ?*I wonder [who k [friends of t k ] hired Mary].
Assuming that DPs are phases, and that the subject originates vP-internally, the unacceptability of (62) is derived as follows: prior to A-movement of the subject, the wh-phrase who does a first step of successive-cyclic movement to the edge of the subject DP that contains it. Because successive-cyclic movement does not feed labeling, this movement effectively de-labels the subject DP. This prevents it from moving to spec-TP, and hence the derivation fails: In general for this approach, successive-cyclic movement to the edge of any phase effectively de-labels it, preventing it from moving and thus automatically precluding the possibility of deriving movement from a moved phase. Bošković (2018) argues that for this reason, movement from moved constituents cannot usually occur. While specifiers formed by successive-cyclic movement yield the labeling problem just discussed, this issue should be irrelevant for specifiers that agree with the head of the phrase they merge to: such agreement should trigger labeling, and allow movement of the containing phrase. Bošković argues that this is correct. In particular, he argues that the ban on movement from moved phrases dissolves for specifiers that are externally merged in, and can remain in, the edge of a phase. This is because in the context of the labeling theory, any specifier that is able to remain in situ must have undergone agreement, or else it would have to move away.
Much of Bošković's supporting evidence for this claim comes from Serbo-Croatian. In this language the specifiers of the nominal phrase (and adjuncts, which Bošković assumes to be structurally equivalent to specifiers) agree with N in case and φ-features. Indeed, these elements can be extracted, as exemplified below with possessor extraction from a subject: (64) Possessor extraction from subject in Serbo-Croatian (Bošković 2018, ex. 25c) Jovanov i je [ NP t i prijatelj] j vjerovatno t j otpustio Mariju. John's.nom is friend.nom probably fired Mary.acc 'John's friend probably fired Maria' In general, Bošković (2018) makes the following prediction:

(65)
Prediction for movement from moved phrases in Bošković (2018) Movement from a moved phrase is possible only for a specifier that has agreed with the containing moved phrase.
Since specifiers are (at least in the basic case) linearized left of their sister, (65) predicts that left-adjoined phrases will be those that we see successfully extracting in scenarios of movement from a moved phrase. This prediction is thus partially overlapping with the ISG, since the ISG states that intermediate stranding is only possible when the extracted phrase was able to be initially linearized leftward of what it strands. The ISG and (65) differ in several respects, however.

Comparison
One difference between (65) and the ISG is that the former is concerned only with extraction of specifiers, whereas the ISG is only concerned with extraction of leftward-linearized elements. Many of the scenarios discussed in section 2 above do not, prima facie, involve extraction of specifiers. Since mere word order is all that the ISG is defined in terms of, it thus describes the facts with less analytical commitments than (65). More significantly, (65) predicts that movement from a moved phrase requires the extracted and stranded phrases to have an agreement relationship, while the ISG does not require this. Importantly, many of the intermediate stranding scenarios shown in section 2 do not involve any surface-evident agreement between the extracted phrase and stranded material, though it happens that some do, like quantifier stranding in Wolof. The ISG has a strong advantage on this issue if Preminger (2019) is right that there can be no agreement which is systematically morpho-phonologically null across its entire paradigm. The ISG is fully compatible with Preminger's results, since it has nothing to do with agreement. In contrast, Bošković (2018) frequently posits agreement where there is no independent evidence for it, given that the labeling theory requires it. This issue is relevant, for instance, to the examples of intermediate stranding in spec-vP in Dutch from Barbiers (2002), several of which we saw in section 2.4, exemplified once more below: (66) Intermediate postposition stranding in Dutch Waar j had jij dan [ vP [t j mee] k gedacht dat je de vis t k zou where had you then with thought that you the fish would moeten snijden]? must cut 'What had you thought to be forced to cut the fish with?' Here an adposition that was inverted in the context of an R-pronoun is intermediately stranded. Bošković suggests that since R-pronouns and their concomitant P-inversion occur with a restricted set of elements, some agreement relationship must be involved in such Dutch configurations. Bošković cites van Riemsdijk (1997) for a notion of R-feature that might be applicable, but it is not obvious whether such a feature can really be equated with agreement. We also saw in section 2.4 that this Dutch pattern is not exclusive to postpositions like mee in (66). For instance, in (17b) above the phrase voor ball ('for ball') is stranded, and in (17c) maar ('only') is stranded. Bošković's proposal requires claiming that these examples of stranding also involve agreement, which there is no independent evidence for.
This issue also arises for Serbo-Croatian. Bošković shows that this language allows an intensifier to be extracted from a scrambled adjective, as in (67)  The prediction in (65) requires Bošković to assume that there is agreement between the intensifier and adjective, since otherwise, this movement from the adjectival phrase should be impossible. Bošković notes that the intensifier can remain in situ in the adjectival phrase, which in the context of the labeling theory, implies that label-facilitating agreement occurred. There is, however, no direct evidence for such agreement in Serbo-Croatian. In contrast, notice that (67) obeys the ISG, given that the intensifier's base position is leftward of the adjective that it strands (though this example is of multiple scrambling rather than stranding per se).
Finally, it is unclear how Bošković (2018) would account for the movement from a moved phrase in spec-CP shown in footnote 16 above. Bošković briefly discusses such examples and assumes that they are ungrammatical, but as this footnote mentions, there are multiple works reporting the possibility of such sentences. As described above, such examples are correctly predicted to be possible under the proposals of the present paper. 24

Conclusion
This paper has proposed a generalization about word order in configurations with stranding in an intermediate position, and argued that this generalization emerges from the CL theory of phases, in combination with several independently supported constraints on the locality of movement.

(68)
Intermediate Stranding Generalization (ISG) Leftward movement of a phrase α can only intermediately strand an element β if β is (or can be) ordered rightward of α before stranding occurs.
Furthermore, this paper has considered how the set of positions available for intermediate stranding might be determined, though predicting the space of cross-linguistic variance in where such stranding can occur remains a task for future work. This concern is related to but logically separate from the ISG, however, which has so far proven to be robust.