Same: Structural sources of anaphora and relativization

This paper offers a unified structural analysis of anaphora and relative clauses licensed by same within definite descriptions. Taking as a point of departure the proposal that indices occupy syntactic positions in anaphoric DPs (Schwarz 2009; Simonenko 2014, i.a.), I examine the open issue of how anaphoric modifiers, particularly same, interact with this proposed structural complexity. Based on the morphosyntactic behavior of definites with same, I argue that indices may be introduced via different positions within the DP. I argue moreover that the behavior of same in both anaphoric and non-anaphoric contexts supports the view that same is syntactically an equative head (Alrenga 2007; Oxford 2010), whose selectional properties are shared across equative constructions. I also propose an analysis of as-relatives that accounts for their alternation with anaphoric interpretations, and offer a comparison with restrictive relatives.


Introduction
This paper contributes to the study of anaphora by examining the interaction between DP structure and nominal modifiers that support anaphoric interpretations. The point of departure for this investigation is the relatively recent attribution of anaphoric interpretations in definite descriptions such as the recipe in (1) to the presence of an index introduced within the functional structure of the DP (Elbourne 2005, Schwarz 2009. (1) I cooked with a new recipe for pancakes yesterday. I followed the recipe again today.
On the view that anaphora is structurally encoded, definite descriptions giving rise to anaphora do so by virtue of containing an index-hosting head in their structure that is otherwise lacking in non-anaphoric (i.e., solely unique) definites. A proposal along these lines is illustrated in (2) Given this analytical backdrop, the aim of this paper is to investigate how anaphoric modifiers interact with this proposed complexity within the structure of the DP. While the relationship between DP structure and modification has gone largely unaddressed in this line of work, the claim that indices are structurally encoded leads to predictions about the ways in which they might interact with nominal modifiers. The present paper takes same (Dowty 1985;Carlson 1987) as a case study to probe this question.
On the view that anaphora has a structural source, which component of the structure is responsible for introducing the anaphoric meaning -the modifier or the index head -is at this point an open question. Consider the definite description 'the same recipe' in (4), whose indefinite antecedent is introduced in the clause preceding it.
(4) I cooked with a new recipe for pancakes yesterday. I followed the same recipe today.
In (4), it is not immediately clear whether same itself is anaphoric or, in the present line of inquiry, whether it is merely an NP modifier that is compatible with the semantics resulting from a structure along the lines of (2).
In what follows, I argue against the null hypothesis that same appears in an otherwise unchanged index-containing DP structure such as (2). Based on seemingly unrelated morphosyntactic behaviors, I argue instead that same encodes anaphora through distinct structural means by selecting for its own index-hosting head. I argue moreover that this selectional behavior results from the fact that, syntactically, same is an equative 'degree' head (Heim 1985;Alrenga 2007;Oxford 2010). Below, the structures in (5)-(6) offer a preview of the proposed difference underlying simple anaphoric definites and those modified by same. The crucial distinction is where idx is introduced: In (5) it is in the extended projection of N, while in (6), it is selected by Deg.
(5) Anaphoric definite DP idxP … NP idx [id:n] D the (6) 'Same'-modification DP NP woman NP DegP idxP idx [id:n] Deg same D the Beyond the morphosyntactic differences between definite descriptions with and without same in anaphoric contexts, I argue that the treatment of same as an equative head is further supported by a broader selectional alternation observed across equative expressions, namely one between an implicit argument that gives rise to anaphora, and an overt standard in the form of an as-relative (Carlson 1977b), in which an anaphoric reading need not obtain (Carlson 1987). Consider (7): 'the same pancake' is not anaphoric in this case, and can be used in out of the blue contexts (a 'first mention' or 'referent-establishing' definite, in Hawkins's (1978) terms), thus distinguishing this environment from the 'second mention definites' found in cross-sentential contexts such as (4).

(7)
I followed the same pancake recipe today [ as-rc as I always do ].
Building on earlier proposals in Matushansky (2010a;, I argue that this alternation is straightforwardly captured by the fact that idx and the as-relative both compete for the same syntactic position, which in the present analysis is the complement of Deg: As-relativization Narrowly, this paper offers arguments for the existence of more than one structural path to anaphora within the DP, which follows naturally upon comparison with the selectional requirements of equative heads more generally. As a result, new evidence is provided for the previously proposed idea that indices may occupy structural positions, and, novel to this paper, that these positions may vary. This study sheds light moreover on the characteristics of as-relatives embedded by same, which, unlike other types of as-relatives, are not well-studied in the literature. More broadly, this paper offers an account of the relationship between anaphora, modification, and relativization that ultimately offers a unified view of how these components interrelate in equative constructions. The structure of this paper is as follows. Section 2 reviews previous arguments that indices are syntactically reified as heads in the structure of anaphoric definites, and introduces the open questions posed for this view by same-modification. Section 3 lays out the observed alternation between anaphora and as-relatives, and Section 4 introduces the proposal that same is syntactically an equative head that is part of a larger family of equative constructions. Section 5 applies the proposal to account for the morphosyntactic behaviors of definite descriptions with same, and offers a comparison to other (anaphoric) relational terms. Section 6 gives a matching analysis of as-relatives selected by same, and offers a brief comparison to thatrelatives, thereby situating same within a larger family of equative and relative constructions.

Indices and modification in anaphora
I offer in this section a brief review of previous claims that syntactically-encoded indices are responsible for giving rise to anaphora (Elbourne 2005;Schwarz 2009;Arkoh & Matthewson 2013;Simonenko 2014;Patel-Grosz & Grosz 2017;Schlenker 2017;Jenks 2018, i.a.). I then lay out the particular implementation of this view that I adopt, in which an index-hosting head idx projects its own functional phrase within an extended nominal projection (Simonenko 2014;Hanink 2018). I then turn to the questions posed by the availability of same in anaphoric definites for such a representation of indices.

Indices in the DP
Recent work on anaphora engages with the nature of indices, and particularly with the way in which they are formally represented in the syntax of definite descriptions. Broadly speaking, this line of research questions the idea that indices are merely subscripts on D or N, as they are often schematized in syntactic representations (following e.g., the Binding Theory of Chomsky 1981: Chapter 3, according to which each NP must be indexed by a single numerical index value at LF; see Fiengo & May 1994 for an overview).
More specifically, building on Elbourne (2005), Schwarz (2009) argues that German morphology provides evidence that indices occupy structural positions within anaphoric definites to the exclusion of their non-anaphoric (i.e., solely unique) counterparts: In German, the form of the definite article in anaphora differs from its form in non-anaphoric contexts, providing a morphological distinction that makes a cut along Heim's (1982) notion of familiar vs. unique definites. 1 This is observed through the fact that non-anaphoric definites allow for contraction with a preceding preposition (the 'weak' form of the article, in Schwarz's terminology), as in (9), while 'familiar' definites whose reference must be resolved via an antecedent may not participate in this contraction (10), exhibiting the so-called 'strong' form instead.
(9) Der Empfang wurde vom/#von dem Bürgermeister eröffnet. the reception was by.the/by the mayor opened 'The reception was opened by the mayor. ' Schwarz 2009: 40 (10) Hans hat einen Schriftsteller i und einen Politiker j interviewt. Er hat Hans has a writer and a politician interviewed. He has #vom/von dem Politiker j keine interessanten Antworten bekommen. from.the/from the politician no interesting answers gotten 'Hans interviewed a writer and a politician. He didn't get any interesting answers from the politician. ' Schwarz 2009: 30 The crucial distinction is that in (9), 'the mayor' is a solely unique definite, uttered in a context in which world knowledge dictates that a given town has just one mayor (cp. Hawkins's (1978) typology), while 'the politician' in (10) has already been introduced into the discourse, making it familiar. 2 Based on this distinction, Schwarz reaches the generalization that the definite article may not contract when a definite description is anaphoric (see also Hartmann 1978, Haberland 1985, and Cieschinger 2006. 3 1 I use the term 'familiar' rather than 'anaphoric', as the strong form also has a demonstrative use.
2 I refer to such contexts as cross-sentential anaphora, cf. the notion of second-mention definite descriptions in Hawkins 1978: 86. 3 Schwarz (2009 points out that the distributions of the strong and weak forms overlap in some cases. My focus is however on the syntactic underpinnings of these forms, and so I do not address this issue. To capture the morphological reflex of this generalization, Schwarz proposes that the definite determiner may not contract with a preceding preposition in case an anaphoric index (notated as '1') intervenes in the structure of the DP, which D selects as its specifier, as in (11)  Schwarz then attributes the interpretational differences to the meanings for the definite article in (13)-(14), which differ in whether anaphoricity is hardwired in. The denotation in (13)  The anaphoric (strong) form then differs in that D must take an index as an argument (in addition to its nominal complement), as schematized in (14). This index introduces a free variable that picks out an antecedent via an assignment function according to the Pronouns and Traces rule of Heim & Kratzer (1998). 4 Certain phonological restrictions likewise prohibit contraction, see Schwarz 2009: 15-17. 5 Schwarz's proposal uses the situation semantics of Kratzer (1989 Going forward, I follow the spirit of Schwarz's (2009) analysis, but I adopt the revised implementation in Simonenko 2014 andHanink 2017;, in which syntactic indices head their own phrase (see also Hanink 2021). Hanink (2018) argues in particular that the structure of the anaphoric DP is instead as in (15), in which idx is not a specifier, but a head within the extended projection of N, on a par with other functional layers such as NumP (Ritter 1991;1993; see Alexiadou et al. 2007 for an overview). 6 (15) Revised structure for anaphoric definites DP idxP … NP idx [id:n] D the As argued by the above authors, one benefit of this implementation is that it allows for a single denotation for D across both anaphoric and non-anaphoric interpretations (cf. (13)-(14)), as anaphoricity within the DP is divorced from D itself and placed entirely on idx. Idx is not a semantic argument of D but instead a nominal modifier that has undergone the ident type shift (Partee 1986) from type e to the property meaning in (16) (as also in Elbourne 2005, though in a different syntactic position).
(16) [[idx [id: i] ]] g : λy e [y = g(i)] This modifier of type ⟨e, t⟩ then undergoes Predicate Modification (Heim & Kratzer 1998) with the NP, and we arrive at precisely the DP meaning proposed by Schwarz (2009), though in this case by different means: In order to more explicitly explain the contraction contrast, Hanink (2018) adopts an analysis couched in Distributed Morphology (Halle & Marantz 1993). Hanink argues that P-D contraction 6 As a head, idx not only projects but also hosts featural information about the value of the semantic index it hosts, represented as a value n on the feature id, which refers to the set of natural numbers. This assumption is in line with a range of arguments for the treatment of indices as features (Rezac 2004;Hicks 2009;Kratzer 2009 is the result of postsyntactic Lowering (Embick & Noyer 2001: 561), a type of merger that applies hierarchically to head-complement sequences, after all syntactic operations, but prior to linearization. This process is schematized in (18).
Similar to variation in head movement, whether or not a head triggers Lowering is specified on a head-by-head basis in a given language. For instance, Embick & Noyer (2001) analyze "affix hopping" in English tense marking as a case of T lowering to v (20): Adopting this idea, Hanink (2018) argues that P-to-D lowering is a specified process in German, resulting in contraction in the general case, as schematized in (20) Crucially, the structure of anaphoric DPs is more complex than (20) in that it includes idx. In this case, Hanink (2018) argues that idx itself triggers lowering of D. Adopting a bottom-up, cyclic approach to postsyntactic operations (e.g., Embick 2010), D-to-idx lowering (21) precedes P-to-D lowering. This then bleeds the environment for contraction, as D, itself having lowered, is no longer present within the relevant domain to trigger lowering of P (22). (This particular approach will be further motivated in Section 5.1, which evaluates the behavior of same in contraction environments.) 8 7 Cf. Embick's (2010) and Svenonius's (2012) on P-D contraction in French, which is licensed differently.  Going forward, I adopt the proposal laid out above that the head of idxP is the locus of anaphoricity in the DP, and that P-D contraction is contingent on whether D-to-idx Lowering is able to apply first.

Anaphoric modification in the DP
We now turn to the relationship between structurally-encoded indices and anaphoric modifiers within the DP. While there has been a good deal of work on anaphoric modifiers such as same and different (i.a. Alrenga 2007;Dotlačil 2010;Brasoveanu 2011;Bumford & Barker 2013;Charnavel 2015;Hardt & Mikkelsen 2015; see also Dowty 1985;Carlson 1987;Moltmann 1992;Beck 2000), these works focus by and large on various aspects of interpretation, leaving structural questions unaddressed (though see Oxford 2010). As a testing ground for investigation, I focus on the modifier same, as in (23): (23) I cooked with a new recipe for pancakes yesterday. I followed the same recipe today.
On what can be taken as the null hypothesis in the current view, same is a modifier within an idxP-hosting DP structure, just as in any unmodified anaphoric definite (e.g., (15)). If this is correct, then the morphosyntactic behaviors of anaphoric DPs with and without same should be identical. I argue however that this is not the case: Instead, same has a distinct syntax and encodes anaphora in its own way. On this view, we expect to see morphosyntactic differences between definite descriptions with and without same. I briefly introduce data supporting this prediction below before offering an analysis that accounts for the observed differences in Section 3.
Our starting clue to the structural difference between anaphoric definites with and without same comes from an apparent anomaly in P-D contraction behavior in German. Recall Schwarz's generalization that the definite article may not contract with a preceding preposition in anaphora.
As Schwarz points out however, anaphoric same appears to contradict his generalization, a puzzle that he leaves for future work. 9 The puzzle is exemplified in (24) These data constitute evidence against the null hypothesis: If same appeared in an otherwise unchanged DP structure, contraction should be blocked: idx should trigger lowering of D to idx (see (21)) on Hanink's account (or 1 would intervene between P and D as in (11), on Schwarz's account), thus bleeding the environment for P-D contraction. This prediction is crucially not borne out, and we therefore find evidence that distinct structures underlie anaphoric definites with and without same.
Beyond P-D contraction in German, another more general and well-established clue to this proposed structural distinctness is that only definite descriptions with same license an as-relative 9 Schwarz (2009) in fact shows this with the antiquated form selbig (attributed to Angelika Kratzer), but the facts remain the same with the more contemporary selb, at least in cross-sentential anaphora (cf. fn. 23). 10 The data from German here and throughout the paper have been discussed and corroborated with at least 5 native speakers, all of whom prefer contraction with selb. 11 As diagnosed by stress patterns, dasˈselb does not form a complex word, cf. 'derjenig- (Blümel 2011). (Carlson 1987) as in (26a) (cf. 26b), a characteristic that has long been attributed to same's selectional properties (Heim 1985).
(26) a. I followed the same pancake recipe today [ as-rc as I always do ]. b. *I followed the pancake recipe today [ as-rc as I always do ]. 12 While this is by no means a new observation, I argue in what follows that understanding the ability of same to introduce an as-relative can shed light both on the structure in which it occurs as well as the way in which it gives rise to an anaphoric interpretation.
Looking forward, the core of the analysis relates the availability of both anaphora and as-relatives to the selectional properties of equative heads more broadly, in a way that can explain the seemingly unrelated puzzle from German contraction. As previewed in Section 1, I contend that, unlike anaphoric definites without same, anaphoric definites with same have an underlying syntax in which same is an equative head that selects for idx as an implicit argument (Baker et al. 1989, see Williams 2015 Chapter 5 for overviews). Crucially, I propose, building on Matushansky (2010a; b) and Charnavel (2015), that idx and the as-relative compete for the same position ((27)-(28)) -as the complement of Deg -explaining why they alternate with one another.

The alternation between anaphora and as-relatives
In this section, I argue that the selectional behaviors of same follow naturally if same realizes an equative head. Below, I motivate this syntactic proposal on the basis of a comparison between same and the equative heads as and such, which likewise alternate between an anaphoric interpretation and one in which an as-relative is present.
Recall the two seemingly distinct uses of same discussed at the end of Section 2.2: a crosssentential anaphoric use as in (29), and one with an as-relative, as in (30).

(29)
Anaphora I used a new recipe for pancakes yesterday. Today, I used the same recipe.
(30) As-relative Today I used the same pancake recipe [ as-rc as I used yesterday ].
Both constructions encode identity; the difference is that (29) involves an anaphoric dependency, while (30) is not anaphoric, and instead involves the introduction of an as-relative. Crucially, this alternation demonstrates that the presence of an as-relative obviates the need for an antecedent, which is obligatory with same on its cross-sentential use. 13 That is to say, the use of same is felicitous in out-of-the-blue contexts/first-mention definites just in case an as-relative is introduced; unlike in (29), there is no antecedent in (30), but the use of same is felicitous nonetheless. 14 It is crucial for our purposes that precisely this alternation is attested for other equative heads. For example, it is observed in degree equatives introduced by as (31) (Landman 2006;Umbach 2007;Anderson & Morzycki 2015) as well as in kind equatives introduced by such 13 I do not address the internal reading of same here, though see Barker (2007), who proposes that this use is unrelated, and Matushansky (2010b) and Charnavel (2015) for opposing views. 14 The facts are the same in German. That same with an as-relative does not require resolution via an antecedent is consistent with the behavior of P-D contraction in as-relatives, which exhibit contraction whether an antecedent is present (i) or not (ii). However, because contraction is predicted with same whether an antecedent is present or not, I do not discuss such examples further. (ii) Topinambur gehört zur/#zu der selben Gattung wie die Sonnenblume.
Jersualem.artichoke belongs to.the/#to the same genus as the sunflower 'Jersualem artichoke belongs to the same genus as the sunflower.' (32) (e.g., Bolinger 1972;Bresnan 1973;Carlson 1977b;Siegel 1994 (31) Degree equatives a. Anaphora Fresh fruit is good in smoothies, but frozen fruit is just as good.

b. As-relative (standard of equation)
Frozen fruit is just as good in smoothies [ as-rc as fresh fruit is ].
(32) Kind equatives a. Anaphora Dogs with long hair are quite difficult to bathe. Floyd here is such a dog.

b. As-relative (standard of equation)
Such a dog [ as-rc as Floyd ] is quite difficult to bathe.
Drawing on previous proposals for these constructions, I argue that a unified syntactic analysis can be achieved if equative heads share the same selectional requirements, and if same is a member of this class alongside as and such.

Degree equatives
Beginning with degree equatives, the examples in (31)  (33) Comparatives a. Anaphora Apples are interesting, but pomegranates are more interesting.

b. Than-clause (standard of comparison)
Pomegranates are more interesting [ than-pp than apples are ].

Alrenga et al. account for this contrast by proposing that an implicit degree argument competes
for the same syntactic slot as the than-clause, that is, in addition to a gradable adjective, Deg selects either for an overt standard, or for an implicit degree argument, giving rise to an anaphoric interpretation. The parallel to equatives is then as follows: While in (34) the as-relative provides the overt standard of equation, as on its anaphoric use selects for an implicit degree argument Both the implicit degree argument and the as-relative are of the same type -d -making sense of this syntactic alternation. Adopting the view that gradable predicates denote relations between degrees and individuals (Creswell 1976;von Stechow 1984;Heim 1985;Kennedy 1999), a standard semantics for degree equatives (with an overt as-relative) is as in (36) (Horn 1972;Seuren 1984;von Stechow 1984;Schwarzschild & Wilkinson 2002). As imposes a weak linear ordering between maximal degrees, in this case contributed by the matrix and embedded clauses, respectively: In anaphoric equatives, where an as-relative is lacking (35), the standard is instead supplied by the implicit degree argument (see Umbach 2007 for a similar, but slightly different semantic analysis of the German counterpart to as, 'so'): 15 Alrenga et al. (2012) propose that the than-clause in comparatives is related to the degree head in a different way than presented here, occupying a position outside DegP (see also Bhatt & Pancheva 2004). The exact relation between Deg and its standard is not crucial here. Following Guéron & May (1984), surface word order is derived by extraposition of the standard.

Kind equatives
Beyond degree equatives, a similar state of affairs has been observed moreover by Anderson & Morzycki (2015) for kind equatives, who treat such as a degree head in its own right. Building on with one key result being that such is analyzed syntactically as a degree head.
These authors present evidence for the unification of degrees and kinds from the fact that such has a degree use in addition to its better-studied kind use. For instance, (38a) shows such as a degree exclamative (Bolinger 1972;Bresnan 1973;Carlson 1977a); (38b) shows such on an extent reading (Meier 2003;Castroviejo-Miró 2011). 16 (38) a. That man is such an idiot. b. He is such a tall man that he might not fit in the car.

Independently from Alrenga et al. (2012), Anderson & Morzycki (2015) account for this alternation
with the now familiar proposal that such selects either for an overt standard of equation in the form of an as-relative (39), or an implicit kind variable instead, giving rise to an anaphoric interpretation (40) (see also Carlson (1977b), who argues that the as-relative itself supplies the anaphoric relation): 17 The semantics that Anderson & Morzycki propose is also such that both complements of such are of the same type -k. Such itself has the meaning in (41), which takes a kind k as its first argument (where ∪ is Chierchia's (1985) up operator, shifting kinds to properties) and returns a property of individuals instantiating that kind.
In cases where the standard is provided by an as-relative (39), the embedded clause is propertydenoting (following λ-abstraction) (42a), but then undergoes the existential closure type shift (Partee 1986) (42b), as previously proposed for free relatives by Caponigro (2003;. 18 The embedded clause then undergoes QR, rendering the meaning of the matrix clause that in (43), with abstraction over a kind variable of type k: The property in (43) then composes with (42b), resulting in (44), which states that the kind of dog that Floyd instantiates is also instantiated by the dog that barked: In cases of anaphora on the other hand (e.g., (32a)), such selects syntactically not for a CP, but for an implicit kind argument instead, on a par with anaphoric comparatives à la Alrenga et al. 2012 and the current proposal for degree equatives. The resulting meaning may then undergo another type-shift depending on its argument position, again resulting in a similar derivation in both cases. 19

Interim summary
Taken together, a parallel emerges between same, as, and such on the view that they are all equative degree heads that show a common selectional alternation: one between an implicit argument and an as-relative. Same makes a natural addition to the paradigm: while as equates degrees and such equates kinds, same equates individuals. The proposal that all of these morphemes take as-relatives to establish identity meanings is moreover in line with Bacskai Atkari's (2016) 18 The 'as' element is treated on a par with a wh-element, resulting in a property-denoting free relative. 19 Anderson & Morzycki (2015) assume that DegP and NP compose via Predicate Modification.
observation that the general purpose of as-relatives is to establish identity, regardless of the type of matrix material they compose with.

same as an equative head
I now turn to a more explicit analysis of same, making sense of same's selectional requirements through a comparison with those discussed above for as and such. The proposal predicts that anaphoric definites with and without same should display distinct morphosyntactic behaviors, which I return to in Section 5.

Previous work on same as Deg
The claim that same is a degree head goes back to Heim (1985), who notes that degree constructions do not only target positions on a dense scale, but can also target binary values on a scale of [0,1], i.e., the scale of (non-)identity. More recently, Alrenga (2007) has argued that same is a degree head based on its gradable behavior in what he calls similarity comparatives. Alrenga shows that the gradability of same is observed in that both degree equatives and similarity comparatives may be modified by the same set of closed-scale approximating modifiers (Huddleston & Pullum 2002), as in (46a-b): (46) a. Degree equative Frozen fruit is {almost, nearly, just about, not quite} as good as fresh fruit. b. Similarity comparative Frozen fruit is {almost, nearly, just about, not quite} the same as fresh fruit.
To capture this distributional equivalence, Alrenga argues that -beyond its identity readingsame may make reference to degrees on a measurement scale of similarity, where same encodes a relation expressing the grade of similarity between two objects. This is what unites similarity and degree equatives, explaining why both are able to occur with the set of modifiers in (46).
Crucially, on Alrenga's (2007) account, same is not an adjective, but a degree expression on a par with matrix as in degree equatives.
As Alrenga points out however, the modifiers in (46) are not possible in identity cases where the equative establishes a relation between individuals, rather than degrees, as illustrated with their badness in (47) where token identity holds between dogs: 20 20 Barker (2007) treats same an adjective partly on the basis that it can be modified by very (i).
(i) I saw the very same dog as you.
I argue that this very is not in fact a gradable modifier, but is a slack regulator in the sense of Lasersohn 1999. As on its use in superlatives (iia) and demonstratives (iib), it serves as a precision device. In this use very has a meaning similar to exactly.
(ii) a. The Himalayas have many peaks, but Everest is the very tallest.
b. I wore that very same dress just last week.
(47) You saw *{almost, nearly, just about, not quite, roughly} the same dog as I did.
On this basis, Alrenga draws the conclusion that same is polysemous between a gradable and non-gradable use; similarity same encodes an ordering between degrees in a fashion similar to as in degree equatives, while identity same encodes identity between individuals. In both cases, the purpose of this head is to express the absence of dissimilarity. Notably however, beyond the modifiers that Alrenga discusses in (46), we find a similarity between degree equatives and even non-gradable same. For instance, both may be modified by exactly, which in Lasersohn's (1999) terms effectuates an identity mapping: (48) a. Degree equative I am exactly as tall as Mary is.
b. Same-equative I saw exactly the same dog as Mary did.
I therefore take Alrenga's work one step further and argue that individual-equating same is also syntactically an equative head, not an adjective. 21 While Oxford (2010) reaches the same conclusion based on same's ability to take an as-relative, I show that such cases can be unified with the anaphoric use of same on the present approach.
Before moving on, I clarify that I am using the term degree head purely syntactically, making reference to the shared selectional properties of this head across equatives and comparatives.
Another possible label for DegP in this case is for example 'EquatP', proposed by Brandner (2016) and discussed by Bacskai-Atkari (2016). I note that while I do not assign identity-same a degree semantics here (see below), it might well be the case that this head may be analyzed with reference to degrees, related to its gradable use (see e.g., Alrenga 2007: Chapter 4 for discussion). 22 I must leave this matter aside, focusing instead on the syntactic properties of degree heads related to their selectional behavior.

Basic proposal
If same has the same equative degree syntax as both as and such, it immediately explains why same shows the same selectional alternation between an implicit argument and an overt standard 21 Corroborating historical evidence against the treatment of same as an adjective comes moreover from evidence in Breban 2010 that same did not develop historically as an adjective, but as an intensifier. This stands in contrast even to other elements expressing equation such as 'identical', as well as the anaphoric modifier 'different'. Breban argues that the grammaticalization path shifted same from an element "emphasizing identification to [one] establishing/ contributing to the identification" (p. 240). 22 Some authors have suggested that same is an adjective that obligatorily co-occurs with a null equative head (Oxford 2010;Sun 2020;. Relatedly, Bacskai-Atkari (2016) proposes that a DegP only has a degree semantics if a gradable predicate is in Spec, DegP; this semantics is not tied to Deg on its own. as those heads do. I therefore propose that identity same may select either for an overt standard of equation in the form of an as-relative (49), or for the implicit individual argument idx (50) Turning to interpretation, while the precise meaning of same has received a good deal of attention in recent literature (Alrenga 2006;Barker 2007;Charnavel 2010;Hardt et al. 2012;Hardt & Mikkelsen 2015), going forward, I adopt the modest proposal that it relates two individuals in a relationship of equation (Heim 1985 Adopting this meaning along with the structure in (49), composition with an as-relative proceeds as follows. (I return to a detailed analysis of the internal make-up as-relatives in Section 6.) The as-relative and implicit variable are both individuals of type e; while this is a straightforward enough meaning for the implicit variable, I treat as-relatives as properties of individuals that 23 The meaning of same is certainly more complex; it has been argued for example to have an additive component, and moreover to place a restriction on eventualities (Hardt et al. 2012;Hardt & Mikkelsen 2015). A reviewer also points out that definites without and without same appear to carry different presuppositions. These important questions are however beyond the scope of the present work.
undergo the iota type-shift (Partee 1986) to achieve the individual meaning, on a par with the treatment of definite free relatives proposed by Caponigro (2003;: The as-relative is then of the right type to saturate the first argument of same, as in (53) With this meaning for DegP in place, the interpretation of same on its anaphoric use is then as in (56)

A comparison to related proposals
Before moving on, I offer a brief comparison to previous analyses that the present proposal builds on, found in Matushansky 2010a; b and Charnavel 2015. The crucial similarity with these proposals is that they likewise aim to capture the fact that same is compatible with either an anaphoric interpretation or a comparative-type clause instead.  (57), Matushansky assigns same the category of an adjective and argues that it is the lexicalization of Partee's (1986) ident type-shift (with the same semantics adopted in the previous section, from Heim 1985). My proposal therefore differs from Matushansky's in the treatment of same as the equative head of an NP-modifying DegP, which offers a unified 25 Cp. Schwarz (2009: 266), who suggests that same might play the same role as the index. analysis with other equative degree heads such as as and such. 27 (I return to Matushansky's (2010a) analysis of as-relatives and empirical challenges for it in Section 6).
Second, Charnavel 2015 proposes a related account of same and particularly different in French according to which they are relational adjectives (see also Safir 1996). The meaning she proposes for même 'same' is shown in (58) Oxford 2010) rather than an adjective, in a way that makes sense of the relationship between identity-same and similarity comparatives, as well as the morphosyntactic differences between same and adjectival modifiers (see Section 5). The proposal also offers an explicit representation of same's implicit argument as idx, and unifies the selectional properties of same with those of other equative heads.

The morphosyntax of anaphora with and without same
With the analysis laid out, we now return to the puzzling behavior of German selb-introduced in Section 2.2. Section 5.1 revisits the unexpected behavior of same with respect to P-D contraction within the context of the present analysis, while Section 5.2 offers a comparison between selband other relational terms that have been argued to be anaphoric.

The German contraction facts revisited
The present proposal contends that anaphoric definites with and without same are structurally distinct, differing crucially in the position in which idx is introduced. Naturally, this claim leads to the prediction that we should find morphosyntactic reflexes of this difference. Section 2.2 introduced two morphosyntactic behaviors of same that appeared to support this prediction: i) the anomalous behavior of same in German contraction environments, and ii) the availability of 27 Cinque (2005) and Kayne (2005) suggest an intermediate view, that same is a functional adjective.

as-relatives only in definite descriptions with same. Having argued in Section 4 that the selectional
properties of same explain the alternation between anaphora and as-relatives, I now return to the contraction behavior of same in German and show how the present account accounts for this unsolved puzzle.
The anomaly presented in Section 2.2 is that P-D contraction is licensed in anaphoric environments just in case same is present, shown in the repeated example in (60). This is unexpected, as the presence of idx in anaphoric definites otherwise blocks contraction. Before presenting the analysis, I briefly rule out two alternative explanations for this behavior.
The first is the idea that the presence of any modifier licenses contraction, and that this behavior is therefore not particular to same. This is crucially not the case however, as seen for example in (61), in which same is replaced by the adjective blue. In this case, the definite article may not contract -much in accordance with Schwarz's generalization: (61) Gestern habe ich ein grünes und ein blaues Haus gesehen. #Am/An dem blauen yesterday have I a green and a blue house seen on.the/on the blue Haus gibt es eine Jareszahl, die man deutlich sehen kann. house gives it a date, rel one clearly see can 'Yesterday I saw a green and a blue house. On the blue house there's a date that one can see clearly.' Another possibility is that contraction is preferred because definites with same are not in fact anaphoric, but are unique uses of the definite article that are independently licensed in anaphoric contexts. Evidence against this idea comes from the observation that same may appear in covarying contexts, argued to be the sine qua non environment for diagnosing anaphoricity in languages with different definiteness-marking strategies (Schwarz 2009;Jenks 2018). 28 A covarying context is shown in (62) (adapted from a similar example without same in Schwarz 2009: 242): (62a) shows that, in definites without same, the strong article is preferred in such contexts, consistent with the idea that they involve anaphora. (62b) shows two things: First, same is likewise felicitous in anaphoric covarying contexts, and second, that contraction is observed in this environment as well (as in non-covarying contexts). 28 Interestingly, (Schwarz 2009: 266) reports examples such as (iv) as bad if antiquated selbig-is used, a judgement shared by the speakers I consulted with. There is therefore a contrast here with selb-.

(62)
Jedes Mal, wenn mir bei einer Gutshausbesichtigung ein Zimmer besonders gefällt, finde ich später heraus, dass eine berühmte Person … Every time I particularly like a room during a mansion tour, I later find out that a famous person … a. eine Nacht #im/in dem Zimmer verbracht hat. a night #in.the/in the room spent has 'has spent a night in the room.' b. eine Nacht im selben/#in demselben Zimmer verbracht hat. a night in.the same/#in the.same room spent has 'has spent a night in the same room.' From the above data we can conclude not only that same is exceptional in inhibiting contraction, but also that definites with same in cross-sentential anaphora are truly anaphoric. The emerging puzzle is therefore that P-D contraction is licensed in anaphoric definites just in case same is present, which is unexplained if same is simply an adjective, like blue, that co-occurs with the anaphoric index as on Schwarz's (2009) or Hanink's (2018) account. These contraction data are therefore a crucial clue that anaphoric definites with same involve a different underlying structure from those without this modifier.
On the current proposal, we can now make sense of this contraction anomaly as a result of the fact that DegP is present in the structure. One crucial characteristic of Lowering is that it may not result in the displacement of a head into an adjunct: A head X 0 may only lower to Y 0 iff Y 0 is the head of X 0 's complement (Embick & Noyer 2001: 561, see also Bobaljik 1994 In the case of anaphoric same, idx is housed in an adjunct (DegP) and is likewise not a suitable host for lowering. The correct environment for D-to-idx Lowering is therefore not met (64), allowing P-to-D lowering to go ahead, resulting in P-D contraction. One way of interpreting this is that the presence of two coreferential indices is redundant and therefore pragmatically dispreferred (see also footnote 21), though I leave the precise discourse conditions for each use to future work.
In summary, a more detailed look at German supports the proposal that definite descriptions with and without same are built from different underlying structures whose morphosyntactic differences are conditioned by the part of the structure in which idx is introduced; this proposed difference is consistent moreover with the ability of same to introduce an as-relative. In the next subsection, I offer a comparison between same and relational adjectives that have been argued to be anaphoric. I show that such terms pattern differently from same with respect to how their anaphoric interpretation comes about, offering further support for the idea that anaphora with same is syntactically encoded, and that same does not pattern with adjectives in this regard. 29 All 5 speakers consulted with preferred contraction in this example.

Same, bridging, and relational terms
I argued above that the lack of P-D contraction with same is explained if idx in such cases is selected by Deg, rather than by D as in simple anaphoric definites. One question that emerges from this claim is how same compares to other relational terms that have likewise been argued to involve an implicit argument (Mitchell 1986;Partee 1989; see also Condoravdi & Gawron 1996, a.o.). For example, relational adjectives such as local are known to have a discourse anaphoric use, as in (67) Heim's (1982) sense, which is to say that they impose particular familiarity conditions on the context in which they are uttered. On this view, the use of local requires some kind of accommodation (see Condoravdi & Gawron 1996: 15), in this case of a new variable that is assigned to a particular location relative to the context, even if that location has not been explicitly introduced by an antecedent.
Importantly, Condoravdi & Gawron (1996) do not argue for a syntactic representation of this variable. Relevant for our purposes is that Condoravdi & Gawron draw in their analysis a connection between relational terms such as local and definite descriptions that may also be accommodated without an explicit antecedent, as in (68): The Porsche lurched to a stop. The engine was smoking. Condoravdi & Gawron 1996: 14 The use of the definite the engine in (68) constitutes a case of bridging (or associative anaphora, Clark 1975;Hawkins 1978). The availability of local in similar contexts (in that no explicit location is introduced as an antecedent in (67a)) leads Condoravdi & Gawron (1996) to conclude that implicit arguments behave like bridged definite descriptions, and not like pronouns, as the latter require an overt antecedent to be used anaphorically.
Importantly, Schwarz (2009) investigates bridging contexts with unique and anaphoric definites in German, and shows that not all bridging contexts are alike. Instead, different types of bridging relations result in different forms of the definite article. In particular, Schwarz shows a distinction between what he calls producer-product bridging and part-whole bridging. In the former, the anaphoric form of the article is used (69), while in the latter, the non-anaphoric form is (70): (69) Producer-product bridging (Schwarz 2009: 51) Das Theaterstück missfiel dem Kritiker so sehr, dass er in seiner Besprechung the play displeased the critic so much, that he in his review kein gutes Haar an dem/#am Autor ließ. no good hair on the/on.the author left 'The play displeased the critic so much that he tore the author to pieces in his review.'

(70)
Part-whole bridging (Schwarz 2009: 52) Der Kühlschrank war so groß, dass der Kürbis problemlos #in dem/am the fridge was so big, that the pumpkin unproblematic in the/in.the Gemüsefach untergebracht warden konnte. vegetable-drawer stored be could 'The fridge was so big that the pumpkin could easily be stowed in the crisper.' Schwarz argues that cases of producer-product bridging are special in that they involve twoplace relational terms such as author, whose meanings necessarily encode an internal argument as in (71), differentiating them from one-place nouns such as crisper:  While Schwarz does not discuss the German data or offer a concrete analysis, he suggests that terms such as local be treated as part-whole relationships (p. 226), interpreted via situational uniqueness (cp. Condoravdi & Gawron's (1996)

accommodation). This suggestion is consistent
with the observation that, with local, the weak form of the article is preferred: (73) Hans ist nach Ulm gezogen und spielt gerne Fußball. Aus diesem Grund hat er Hans is to Ulm moved and plays gladly football for this reason has he sofort beim/#bei dem örtlichen Fußballverein vorbeigeschaut. immediately by.the/by the local football.club stop.by 'Hans moved to Ulm and likes to play football. For this reason, he immediately popped around the local football club.' I submit that while both same and anaphoric adjectives like local involve the weak form of the article, the structural conditions in each case are distinct, that is, contraction results for different reasons. In the case of same, anaphora is structurally encoded, but the locus of idx differs from that in unmodified anaphoric definites in such a way that contraction is blocked (Section 5.1).
In the case of local however, there is no implicit variable in the structure, and the contextdependent relation is achieved via more global means (cf. Martí 2003); P-D contraction applies in this case as the default, as idx is not present in the structure.
Supporting this view, we in fact find evidence for the structural nature of anaphora with same from further investigation of data from bridging. The novel observation here is that same is felicitous in the same contexts in which the strong, anaphoric form of the article is, namely in producer-product bridging (74), but not in part-whole bridging (75): Producer-product bridging with same Peter möchte den neuen Film im Kino sehen, weil ihm letztes Jahr ein Peter would.like the new film in.the theater see, because him last year a anderer vom selben Regisseur so gut gefallen hat. other from.the same director so well pleased has 'Peter would like to see the new film at the cinema, because he liked another one by the same director so much last year.'

(75)
Part-whole bridging with same #Ich finde die Kirche schön, aber die andere Gebäude im selben Dorf sind Peter finds the church nice, but the other buildings in.the same village are baufällig. run-down #'I find the church nice, but the other buildings in the same village are run-down.' The same is true for covarying uses. Schwarz reports that the contrast observed in contraction also holds in cases of covariance (from Schwarz 2009: 63), such that contraction is still dispreferred with producer-product pairs (76a), but preferred with part-whole pairs (76b): Covariance in bridging a. Jeder, der einen Roman gekauft hat, hatte schon einmal eine everyone rel a novel bought has had already once a Kurzgeschichte #vom/von dem Autor gelesen short.story by.the/by the author read 'Everyone that bought a novel had already once read a short story by the author.' b. Jeder Student, der ein Auto parkte, brachte einen Parkschein am/#an dem every student rel a car parked attached a parking.pass on-the/on the Rückspiegel an. rear.view.mirror prt 'Every student that parked a car attached a parking pass to the rearview mirror.' I show with the contrast in (77) that, in cases of covariance, same is similarly licensed only with producer-product -not part-whole -pairs: Covariance in bridging with 'same' a. Jeder, der einen Roman gekauft hat, hatte schon einmal eine everyone rel a novel bought has had already once a Kurzgeschichte vom selben Autor gelesen short.story by.the same author read 'Everyone that bought a novel had already once read a short story by the same author.' b. #Jeder Student, der ein Auto parkte, brachte einen Parkschein am selben every student rel a car parked attached a parking.pass on.the same Rückspiegel an. rear.view.mirror prt #'Every student that parked a car attached a parking pass to the same rearview mirror.' What these data reveal is that same, just like the anaphoric form of the definite article, requires the presence of idx, explaining why it patterns with the strong, anaphoric form. It is not available in part-whole bridging, in which anaphoricity is not the result of extra structure, but accommodation of some kind.
In sum, while the current contention is that anaphora has a structural source in anaphoric definites, the context-dependency of non-anaphoric definites in certain bridging contexts, along with that of adjectival, relational terms such as local, is derived differently, pointing to structural differences between these superficially similar types of expressions. While the full range of behaviors of anaphoric modifiers in P-D contraction environments is not addressed here, it poses an interesting avenue for future work.

Interim summary
The treatment of same as an equative head unifies several seemingly unrelated characteristics.
Specifically, the present account unifies the selectional alternation between an implicit argument and an as-relative with the selectional requirements of other equative heads, simultaneously offering a solution to the initially puzzling data from German contraction. Evidence from relational terms offers further support that anaphora with same is encoded in the structure of the DP, though in a different way from anaphoric definites without same. Shifting gears, I turn next to the constituents that compete for the same syntactic slot as idx: as-relatives selected by same.

As-relativization
This section offers an analysis of the structure and interpretation of as-relatives selected by same, and situates them within the larger family of equative and relative constructions. To this end, I propose a matching account (Lees 1960;1961;Chomsky 1965;Carlson 1977b;Sauerland 1998;Salzmann 2006) of as-relatives that involves Ā-movement of an argument before deletion under identity with a matrix antecedent, similar to comparative deletion.

Overview of as-relatives
As-relatives have received considerably less attention (Carlson 1977b;Stowell 1987 b. Kind equative (Carlson 1977b: 380) Such women [ as-rc as we met yesterday ] are a credit to society.

c. Same equative
The woman saw the same cardinal [ as-rc as her father did ].
Previous works largely propose a semantics of as-relatives similar to that of other relative clauses. For example, Rett (2013) argues that degree equatives are property-denoting, and that as performs the function of a wh-operator. More specifically, Rett builds on Stowell (1987) and argues that the gap in the as-relative is simply a variable that remains unbound. In her analysis, the role of as is to serve as an unselective binder, binding this free variable and thereby turning the as-relative into a property-denoting expression (see also Potts 2002;Lee-Goldman 2012).
While I treat as-relatives as a type of relative clause, any analysis of as-relatives without Ā-movement faces a major challenge: A lack of movement would predict a lack of island sensitivity. However, as-relatives introduced by same are in fact subject to a variety of island effects (Ross 1967 Moving forward, my analysis therefore reflects Ā-movement (Chomsky 1977) of the relativized argument (as in Landman 2006;Matushansky 2010b;Charnavel 2015).
Another relevant question concerns the category of as. Some authors treat as as a preposition (e.g., Emonds 1985;Potts 2002;Rett 2013), while others treat it as a realization of C (e.g., Matushansky 2010b;Lee-Goldman 2012;Charnavel 2015). Going forward, as is represented as C, but nothing crucial hinges on this assumption. 31

The nature of the gap
One immediate question concerning as-relatives is the nature of the gap. For instance, Landman (2006) argues that the gap in such-as (kind) equatives consists not in a definite variable as in restrictive relatives, but rather in a noun phrase which she terms a k-like NP. Evidence for this is the fact that the as-relative can contain an existential there-construction: 31 See Potts 2002 andRett 2013 for arguments against treating as as C.
(80) Such women [ as-rc as there were ____ at the party ] came to the show.
Landman therefore takes the gap to be a 'k-like NP' rather than a definite variable, as definites are barred from participating in such constructions according to the Definiteness Restriction in (81) (Milsark 1974): (81) *There be x, when x is an individual variable.
As Landman points out, such-as relatives differ from restrictive relatives in this regard, whose gaps may not be definite arguments (Carlson 1977b;Heim 1987): (82) *Women [ rc that there were ____ at the party ] came to the show.
Importantly, existential there-constructions are likewise not licensed in as-relatives embedded by same, as shown in (83), which pattern with restrictive relatives in this regard: (83) *I saw the same women [ as-rc as there were ____ at the party last night ].
Note that Landman's proposal differs also from treatments of degree equatives involving gradable adjectives, which largely assume that the gap contains a deleted adjective in addition to a degree variable, as seen in (84)  In many analyses of degree equatives, the embedded adjective is deleted after moving to Spec, CP (Bresnan 1973), as described in the following formulation by (Kennedy 2002b: 556) (see also Kennedy 1999 andMerchant 2000): [Comparative deletion] involves overt movement of the compared constituent to the specifier of a clausal complement of than/as, plus deletion under identity with the head of the comparative.
In comparatives, an adjective must be present in the embedded clause for semantic reasons: The degree morphemes more/-er and as impose an ordering on two sets of degrees, and a gradable adjective is required to specify the scale in both sets.
Generally speaking, evidence for comparative deletion in the domain of degree expressions comes from the existence of comparative sub-deletion (Bresnan 1973;, in which some (but not the entire) constituent is missing from the surface presentation of the complement of an equative or comparative. We observe this sub-deletion in degree equatives as well (Bresnan 1975;Kennedy & Merchant 2000): (85) By actually refuting his own early self, Wittgenstein was as unusual as Frege was ____ noble when confronting -not to say applauding -Russell's objections. Times Literary Supplement, 6.26.1998, apud Kennedy & Merchant 2000 Comparative sub-deletion is licensed when the two adjectives denote different properties (e.g., unusual and noble in (85)). Importantly, in the case of as-relatives embedded by same, sub-deletion is also not (generally) available, as in (86): 32 (86) *I saw the same woman [ as-rc as you saw the ____ man ].
As the two objects being equated are necessarily the same individual, the general contrastive conditions licensing sub-deletion are not met; the man that was seen in (86) can never be identical to the woman that was seen. These facts lead to the conclusion that same is not covertly present in the gap in the way that a gradable adjective is in degree equatives or comparatives -following on this analysis from the fact that it is not an adjective, but itself a degree head, and that individuals are being equated, rather than maximal degrees. Again here, as-relatives embedded by same pattern with restrictive relatives in this regard.

As-relatives as matching relatives
Preserving an observed similarity to comparative deletion, I propose that as-relatives selected by same involve a matching analysis along the lines of that argued for restrictive relative clauses by Sauerland (1998; and Hulsey & Sauerland (2006): In (87), the external and internal heads of the relative clause are not derivationally related, but must be identical in order for the lower head to be deleted. Sauerland (2003) draws a comparison between this type of deletion and the type of obligatory deletion observed in comparatives, proposing that relative clauses involve so-called relative deletion of their internal head: 33 32 Subcomparatives seem to work with nouns that denote measurements, as shown in (i): (i) Each individual pixel has the same height as it does ____ width.
The difference observed in deletion effects is likely a result of the fact that these examples do not involve the equation of token individuals, but of types or amounts; see Kennedy 2002a. Same here seems to impose identity between degrees, as suggested by the possible paraphase in (ii): (ii) Each individual pixel has the same degree of height as it does ____ width. 33 In related work, Sauerland (2004) and Hulsey & Sauerland (2006) define this deletion operation in terms of movement deletion, see also Kennedy 2002b. (88) Relative Deletion (Sauerland 2003: 31): In matching relatives, the internal head must not be pronounced. Furthermore, the external head must be the antecedent of the internal head.
A major piece of evidence for the matching analysis comes from the lack of a Condition C violation in relative clauses, as shown in (89) (Munn 1994: 402): The relative of John i [ rc that he i likes ____ i lives far away ].
The lack of a Condition C violation between matrix John and he in (89) can be explained if John need not reconstruct inside the embedded clause, which holds under the matching analysis: In Sauerland's (2003) account, the matching requirement imposed on the internal and external heads can be satisfied if the internal head is itself a pronoun (rather than a proper name), which would not incur a Condition C violation (90a). Contrarily, on a raising analysis of relative clauses (90b) (Brame 1968;Schachter 1973;Vergnaud 1974;Kayne 1994;Bhatt 2002), according to which the internal head undergoes an additional movement out of the relative clause into a matrix position, the possibility of reconstruction is unavoidable. Notably, the lack of Condition C effects is paralleled in as-relatives embedded by same: (91) I hold the same opinion of John i [ as-rc as he i does ____ i ].
Taking these effects as well as the observed similarity with comparative deletion and degree expressions more generally into consideration, I propose a matching analysis of as-relatives introduced by same. 34 The derivation of the as-relative is as follows. First, the internal head noun 'recipe', selected by Op, undergoes Ā-movement to Spec, CP: 34 The alternative to this matching analysis is a raising analysis. One of the key pieces of evidence for the raising analysis (see Bhatt 2002) is the availability of idioms, which require locality for interpretation (Brame 1968). These data are difficult to replicate with same, but where possible, the presence of same appears to give rise to an amount relative (Carlson 1977a;Heim 1987;Grosu & Landman 1998) rather than an individual one (i). In this case, a different interpretation may be needed altogether, along the lines of those proposed for amount relatives (Carlson 1977a;Heim 1987;Grosu & Landman 1998 The composition of the clause embedded by as is then as in (94) following trace conversion and λ-abstraction triggered by movement (Heim & Kratzer 1998) As discussed in Section 4, in order for the embedded clause to compose with same (95) (repeated from (51)), it needs to denote an individual, rather than a property. I therefore propose that the meaning of the as-clause in (94) undergoes the iota type-shift (Partee 1986), on a par with the proposal for definite free relatives by Caponigro (2003; and for degree equatives by Anderson & Morzycki (2015) (cp. Charnavel (2015, and cf. Matushansky (2010a), who makes use of a max-operator instead; her account also differs in several respects, and she is not explicit about adopting either a matching or raising analysis).  (Sauerland 2003), as in (i): The meaning of the embedded clause is now of the correct type to saturate the first argument of same, and composition with the matrix NP proceeds as in (97) The resulting meaning of the matrix DP containing the as-relative is then the unique recipe that is identical to the unique recipe that the speaker used, as in (98)

As-relatives vs. that-relatives
In this final subsection, I focus on the generalization that, like as-relatives, that-relatives license the presence of same, even though there is no antecedent in such contexts.
(99) Today I used the same pancake recipe [ rc that I used yesterday ].
There are in principle two possible sources for that-relatives with same. The first is that same is simply an optional modifier in relative clauses, and that the relative clause adjoins to the NP in the typical way. In this approach, same selects for idx in the same way it does in anaphora, since no as-relative is present to saturate its first argument: (100) 'that'-relative with 'same' (to be rejected) This approach however faces a problem, given the anaphoric nature of same when it does not select for a relative clause: If same first composes with the idx and then the relative clause, we will arrive at a meaning for the entire DP as in (101), which results in an anaphoric meaning for a DP that is not necessarily anaphoric.
As with as-relatives, the puzzle is again however that same is licensed in relative clauses even when no antecedent is present, and thus anaphoricity should not be built in. 37 The second option, proposed by Matushansky (2010b), is that same selects for that-relatives in the same way it does for as-relatives. I adopt this option here and provide novel empirical evidence in support of it. On the present account, this means that the embedded CP is selected for by Deg, as in (102)  Because the that-relative, like the as-relative, is property denoting, it saturates the first argument of same in exactly the same way that the as-relative does after undergoing an iota type shift. In the present proposal, the meaning of (102) is then as in (103) Note the parallel here to anaphora with and without same. Restrictive relative clauses with and without same appear to be almost identical, differing only in the presence of a modifier, they in 37 In German, contraction is also preferred in relative clauses with same, cp. footnote 11. Notably, restrictive relatives fact arise from different underlying structures; while it may seem that same is simply an optional modifier, its presence is in fact indicative of the presence of a degree structure.
Empirical support for this proposal comes from languages that make use of the same marker in equatives and relative clauses. Spanish is one such language, which uses the invariant relativizer que in both relatives with same (104) and those without (105). 39 (104) Juan leyó el mismo libro [ as-rc que leyó Pedro ].
Juan read the same book that read Pedro 'John read the same book that Pedro read.' (105) Juan leyó el libro [ rc que leyó Pedro ].
Juan read the book that read Pedro 'John read the book that Pedro read.' Importantly, relative clauses with and without same can nevertheless be distinguished based on the deletion they allow. In case same is present, the standard may be phrasal (106). If same is omitted however, the sentence becomes ungrammatical (107). Juan read the book that Pedro Intended: 'John read the book that Pedro [read].' This contrast is not expected if same is simply an adjective that modifies an NP independently from the relative clause. The grammaticality of (106) can be explained however if same is a degree head that selects for the relative clause in such cases. What we observe then in Spanish is optionality of the size of the standard, which is expected: As a result of deletion processes restricted to comparatives and equatives, phrasal standards are allowed in degree clauses, but not in relative clauses, and can be independently accounted for (with either the direct or reduction analyses in the terminology of Lechner 2004;Bhatt & Takahashi 2011, see also Merchant 2009).
In sum, by adopting the structure of relative clauses with same as in (102), we can explain the same obviation of anaphoricity that is observed in as-relatives, as well as the size of deletion effects in a language like Spanish. In cases where same is present, a degree syntax is present rather than a typical modifying restrictive relative clause. 39 The Spanish data come from personal communication with Karlos Arregi. I conclude briefly by comparing the account here to the one proposed by Matushansky (2010a), which my account builds on. A crucial component of Matushansky's analysis is that as-relative formation involves the movement of a null operator -housed in an AP modifying the NP -to Spec CP, to the exclusion of the gapped NP, as shown in (108): The motivation for this aspect of her analysis is to derive what she describes as obligatory Verb Phrase Ellipsis (VPE) as in (109), which is not required in restrictive relatives (110).
(110) VPE in that-relatives Lucius likes the same flowers [ rc that his father likes/does ].
In (108), the movement of the operator to Spec CP to the exclusion of the NP it modifies constitutes a Left Branch violation (Ross 1967;Corver 1990). Matushansky therefore aims to derive the obligatory deletion observed in (109) through Kennedy and Merchant's (2002) notion of salvation by deletion (Lasnik 1995): In order to rescue the violation incurred, all material following the moved operator must be deleted, in line with the proposal that ellipsis may serve as a rescue operation for PF violations. That-relatives then differ from as-relatives in the amount of material that undergoes movement: In relative clauses, the entire gapped DP moves to Spec, CP, rather than just the operator.
Matushansky's analysis however faces an empirical problem: The generalization that as-relatives obligatorily involve Verb Phrase Ellipsis is inaccurate, as attested by native speaker judgments as well as the following naturally-occurring example (111); Matushansky's analysis erroneously predicts obligatory VPE in all as-relatives. 40 (111) But with experience you can play the same game as you played before and you can forget the crowd. 41 In the present proposal, the optional ellipsis found in as-relatives is instead on a par with VPE observed in this type of antecedent-contained deletion (Sag 1976;May 1985;Larson & May 1990;Wold 1995;Merchant 2000;Fox 2002;Kennedy 2002b;Bhatt & Pancheva 2004).
To summarize, I have argued in this section for a matching analysis of as-relatives that closely relates them to that-relatives, differing only in whether the relative clause is an NP modifier, or 40 Charnavel (2015) notes that in French, the as-relative must be at least partially elided. 41 https://www.dailyrecord.co.uk/sport/football/relaxed-rangers-will-have-no-fear-of-old-1003119. selected by Deg inside of a DegP modifier. I have also argued that that-relatives with same arise from the same equative syntax as as-relatives, and have shown that if such relatives follow a degree syntax, we can understand why we observe deletion therein on a par with comparative clauses. Unlike English, Spanish does not differentiate morphologically between as-relatives and that-relatives introduced by same, but still offers clues that that-relatives may have two distinct structural sources. One of these sources is facilitated by an underlying degree syntax, supporting the view that same is not an adjective, but an equative head.

Conclusion
The advent of proposals for structurally-encoded indices in anaphoric expressions has increased our understanding of the structure of the DP, while also raising new and important questions about the relationship between anaphora and modification. This work has contributed to this line of enquiry by demonstrating that the view from same-modification reveals that there are distinct paths to anaphora in definite descriptions, which differ according to the position in which idx is introduced. That this is the case is corroborated by a previously unsolved puzzle from German P-D contraction in anaphora with same.
Further, it has been demonstrated that the ability of same to introduce anaphora boils down to the fact that it is an equative head, a proposal which makes sense of an observed alternation between anaphora and relativization, and which leads to a unified analysis for equative degree heads in terms of their selectional properties. Ultimately, the assimilation of same to an equative head that relates individuals rather than degrees casts light on the close relationship between degrees and individuals in both modification and relativization of various kinds, revealing that the syntax may reflect coherence across even distinct ontological types.