Similatives are Manners, comparatives are Quantities (except when they aren’t)

3.1 Similatives are manners

According to Hengeveld and Mackenzie (2008), Manner expressions can occur as modifiers of two layers: the Lexical Property (6) and the Configurational Property (7). Such modifiers are explicitly distinguished from modifiers expressing Instrument (8), Means (9) and Circumstance (10). Note that, in these and all following examples, only those layers of analysis which are strictly relevant to the phenomena under discussion are explicitly represented. Also note the placeholder “1” preceding the Individual variable “x”, which represents the number operator Singular, and the use of dashes to indicate that further internal layers have been omitted for simplicity (e.g., in (6), the Lexical Property corresponding to the lexeme slow within the head of the Manner expression (m_i)):

• (6) John walked slowly.

•   (f^c_i: [(f_j: walk (f_j): (m_i:–slow–(m_i)) (f_j)) (1x_i)_A] (f^c_i))

• (7) John angrily left the room.

•   (f^c_i: [(f_j: leave (f_j)) (1x_i)_A (1l_i:–room–(l_i))_U] (f^c_i): (m_i:–angry–(m_i)) (f^c_i))

• (8) John cut the meat with a knife.

•   (f^c_i:–John cut the meat–(f_i^c): (1x_i:–knife–(x_i))_Instr (f^c_i))

• (9) John started the engine by turning the ignition switch.

•   (f^c_i:–John started the engine–(f^c_i): (f^c_j:–turning the ignition switch–(f^c_j))_Means (f^c_i))

•   (Hengeveld and Mackenzie 2008, 208–9, 263)

• (10) The boy entered the room dancing.

•   (f^c_i:–the boy entered the room–(f^c_i): (f_j^c:–dancing–(f_j^c))_Circ (f^c_i))^[2]

The distinction between Manner and the other types of modifiers exemplified in (8)–(10) is not new in itself. Rather fine-grained classifications of the types of adverbials generally encompassed by the umbrella-term “manner” have been proposed, for instance, in generative accounts such as Ernst (2002) and Haumann (2007), as well as in functionally oriented ones such as Luraghi (2003, 2014) and Narrog (2014). What is characteristic of FDG, however, is the recognition of Manner as a layer of semantic organization in its own right, as well as the association of each type of modifier with a nucleus pertaining to a specific layer of underlying semantic structure.

As pointed out by Hengeveld and Mackenzie (2008, 263–4), both Manner modifiers of the type of (6)–(7) and the various types of modifiers exemplified in (8)–(10) can be used to answer the question How? (e.g., How did he walk? – Slowly; How did he cut the meat?  – With a knife; etc.). How questions are therefore not a good test for identifying Manner expressions with certainty. A more effective criterion is “the possibility of paraphrasing the expression with a phrase of the form in a … way. This excludes expressions of Instrument and Means [as well as Circumstance, RG]” (Hengeveld and Mackenzie 2008, 264). Compare

• (11) a) slowly       b) in a slow way

•   c) angrily       d) in an angry way

•   e) with a knife     f) *in a knife way

•   g) by turning the switch h) *in a switch-turning way

•   i) dancing       j) *in a dancing way

•   (adapted from Hengeveld and Mackenzie 2008, 264)

Although Hengeveld and Mackenzie (2008, 264–5) argue that similatives of the type of (1) are in fact comparisons, they also point out that in (1) “the manner of her singing is understood figuratively, through the similative like a nightingale. It is then a small step to reinterpreting like as a literal marker of Manner”. That such reinterpretations are indeed likely is evident when one considers that the preposition like is etymologically related to the adverbializing suffix -ly, which allows an adjectival Lexical Property to occur as the head of a Manner and thus functions as a bona fide Manner marker. And, according to Hengeveld and Mackenzie (2008, 265), the function of like in such fixed expressions as like this, like that is precisely that of marking anaphoric or cataphoric reference to a Manner (e.g., She talks to everyone like that; The argument runs like this: …).

In most of its uses, however, like cannot be regarded as a grammaticalized Manner marker but clearly behaves as a lexical preposition. First, it can undergo a number of derivational processes (e.g., unlike, likewise, likeness, liken: see Keizer 2007 on availability for lexical derivation as a criterion for lexical status). Second, as argued by Portero Muñoz (2016), -like is productively used as a bound root, with no semantic difference with respect to the unbound prepositional use (e.g., affix-like, prison-like). Neither of these properties is shared by the grammaticalized preposition/conjunction as, which is functionally rather similar to like but is not available for derivation or compounding (e.g., *un-as, *as-wise, *as-ness, *as-en; *affix-as, *prison-as).

At first glance, it would also appear as though PPs headed by like do not function as Manner expressions. Like Instrument, Means and Circumstance modifiers, and unlike Manner ones, such phrases cannot be paraphrased as in a…way:

• (12) a) He boxes like a veteran.^[3]

•   b) *in a veteran way

Paraphrase tests, however, should be handled cum grano salis. The problem, in this specific case, is that the paraphrase cannot be applied to like a veteran in the very same way as it is applied to the expressions in (11), i.e., by simply replacing a preposition or affix by the phrase in a…way. This is because if like is not a grammatical element but a lexical preposition, then this preposition should be regarded as a predicate and as such it should be included in the paraphrase, just as the predicate turning is included in (11h). As soon as the test is applied in this way, the result is no longer ungrammatical or unacceptable as a paraphrase of like a veteran:

• (13) a) like a veteran b) in a veteran-like way

It might be objected that the results yielded by the in a…way test are not always straightforward. For instance, a phrasal Manner modifier like with care cannot of course be paraphrased as *in a care way. The reason for this, however, is clearly a syntactic one (the fact that care is a noun and not an adjective) and as such is totally unrelated to the semantics of the construction. As soon as this syntactic hindrance is got rid of by converting the noun into an adjective, just like in (13b), the result of the test is indeed the expected one (He cut the meat in a careful way). The other way round, with non-Manner modifiers morphological modification does not change the result of the paraphrase test (cf. *in a knifeful/knifey/knife-using way), not even when the resulting expression is syntactically well formed as in (11h) or (11j) (cf. also with a hammer ≠ in a hammering way). As a further proof of the reliability of the in a…way test, consider an ambiguous sentence such as He said good morning with a smile. In this case, the PP with a smile might be interpreted either as a Manner (i.e., he said “good morning” while smiling) or as an Instrument or Means (he did not utter the words good morning but just smiled as a form of greeting); however, as soon as the sentence is paraphrased as He said good morning in a smiling way, only the Manner reading remains available.

Further evidence that PPs headed by like are in fact Manners is provided by the fact that such expressions can occur in so-called specificational or identificational predications such as (14) and (15), where the other term is a (headed or headless) Manner clause:

• (14) It’s definitely an informal market. The way it works is like a silent auction.

•   (https://www.huffpost.com/entry/dc-food-swap_n_1900820. Accessed 04-30-2021.)

• (15) CityCoin is a Raffle run by municipalities to augment their income to help fund education, public works, and special projects. How it works is like a decentralized lottery built on-top of Metronome.

•   (https://metronometoken.medium.com/world-crypto-con-2018-and-met-hackathon-wrap-up-52ff3a25fb5c. Accessed 04-30-2021.)

A possible objection, in this case, is that certain non-Manner expressions may pass the specificational sentence test, e.g., Instrument-PPs like with…provider in the best way to do this is with a legitimate email service provider.^[4] However, it does not seem possible for actual Manner expressions to fail the test in question: that is, I cannot think of a Manner expression that cannot enter an identificational predication where the other term is a relative clause headed by the noun way or a headless relative clause introduced by how. In other words, this test for Manner status may give false positives, but it would not seem to ever give false negatives.

There are in sum strong indications that similatives are indeed Manners, as in fact has been argued before (e.g., by Haspelmath and Buchholz 1998, 279–80). That similative constructions are a subtype of Manner expressions is after all also intuitively suggested by the functional similarity between, e.g., He boxes like a veteran and He boxes well. The difference between the modifiers like a veteran and well is that the latter has a lexical head (the adverbial Property well), whereas the former has a configurational head consisting of the predicate like together with its argument:

• (16) He boxes well.

•   (f^c_i: [(f_j: box (f_j): (m_i: (f_k: well (f_k)) (m_i)) (f_j)) (1x_i)_A] (f^c_i))

• (17) He boxes like a veteran.

•   (f^c_i: [(f_j: box (f_j): (m_i: (f^c_k:–like a veteran–(f^c_k)) (m_i)) (f_j)) (1x_i)_A] (f^c_i))

The question, at this point, concerns the internal structure of the Manner modifier like a veteran in (17). As mentioned earlier, the head of this Manner consists of a Configurational Property formed by a lexical preposition and its argument: more specifically, then, the question concerns the nature of this argument. At first glance, the most intuitive answer would seem to be that the argument of like is the semantic unit underlying the NP a veteran, i.e., an Individual. This solution, however, clashes with the semantics of the construction, since what is being likened in (17) is not merely the Individuals he and a veteran but rather the way in which he boxes and the way in which a veteran boxes. In other words, if we try and expand (17) into a more explicit sentence, what we obtain is something along the lines of He boxes in a way that is like the way a veteran boxes. The latter paraphrase reveals two important facts about the structure in (17). First, the argument of like is not the Individual veteran but a second Manner, corresponding to the way a veteran boxes; second, this further Manner must also have a configurational head, corresponding to a veteran boxes. Note finally that, as an argument of the predicate like, this second Manner must bear a distinct semantic function: however, since the semantic role of this argument is not explicitly marked by a dedicated preposition or conjunction, it will be formalized as the general semantic function Reference (on which see Mackenzie 1983, 28, Hengeveld and Mackenzie 2008, 203). By expanding the representation in (17) in the way suggested here, we obtain (18):

• (18) He boxes like a veteran.

•   (f^c_i: [(f_j: box (f_j): (m_i: (f^c_k: [(f_l: like (f_l)) (m_j)_Ref] (f^c_k)) (m_i)) (f_j)) (1x_j)_A] (f^c_i))

•   Where (m_j) = ‘(the way) a veteran (boxes)’

This, in turn, is a simplified version of the full representation in (19) (displayed on several rows for ease of reading):^[5]

• (19) (f^c_i: [(f_j: box (f_j): (m_i: (f^c_k: [(f_l: like (f_l)) (m_j: (f^c_m: [((f_j): (m_j) (f_j)) (1x_i:–veteran–(x_i))_A] (f^c_m)) (m_j))_Ref] (f^c_k))(m_i))(f_j)) (1x_j)_A] (f^c_i))

Note that the internal structure of the configurational head of (m_j) is the same as in a headless relative clause. Interestingly, a structural parallel between similatives and headless relative clauses has also been noted in a formal-semantics study by Anderson and Morzycki (2015, 816), although on very different premises. In FDG terms, the only difference between the embedded Manner (m_j) in (19) and the overall Manner variable in (20) is that, being expressed as a finite clause marked for present tense, the latter must be headed by a whole Episode (since this is precisely the layer to which absolute tense operators apply):

• (20) I admire how you live.

•   (m_i: (pres ep_i: (e_i: (f^c_i: [(f_j: live (f_j): (m_i) (f_j)) (1x_i)_φ] (f^c_i)) (e_i)) (ep_i)) (m_i))

•   (adapted from Hengeveld and Mackenzie 2008, 266)

In the “gapped” structure like a veteran, by contrast, there is no need to assume the head of the embedded Manner expression to contain a full-fledged predication: rather, the head of this Manner will be directly restricted by a Configurational Property, represented in (19) as (f^c _m).

While in (17)–(19) the similative like a veteran modifies a Lexical Property, we saw earlier that Manners can also be used as modifiers of a Configurational Property. Similative modifiers are no exception: accordingly, the lexically headed Manner angrily in (7) can be easily replaced by a similative, in which case this modifier will be built on the same representational frame as like a veteran in (19) but occur in the structural position occupied by angrily in (7):

• (21) John left the room like his brother (that is, angrily).

•   (f^c_i: [(f_j: leave (f_j)) (1x_i)_A (1l_i:–room–(l_i))_U] (f^c_i): (m_i: (f^c_k: [(f_l: like (f_l)) (m_j:–his brother (left the room)–(m_j))_Ref] (f^c_k)) (m_i)) (f^c_i))

Note that, without the final parenthetical disjunct, (21) would more likely be interpreted as Like his brother, John also left the room. This reading corresponds to a different underlying structure, which will be discussed in Section 3.2. Once the clarificational parenthesis is added, however, it becomes clear that like his brother is to be interpreted as a Manner modifier of the Configurational Property, just like angrily in (7).

Precisely because similatives can modify a Configurational Property, nothing prevents such expressions from replacing other types of modifiers of the same layer, even when the latter are not Manner expressions. Compare (8)–(10) with (22)–(24) – where, again, the clarificational Discourse Act between parenthesis brings out the intended interpretation unambiguously:

• (22) John cut the ham like a butcher (that is, with a professional machine).

• (23) John started the engine just like everyone else (that is, by turning the ignition switch).

• (24) The boy entered the room like his brother had left the garden (that is, dancing).^[6]

The last example also illustrates the possibility that the predication embedded within the Manner argument of like may not involve the same predicate and arguments as the main predication. A full analysis of (24) is given in (25) (note the Absolute and Relative Tense operators “past” and “ant(erior)” on the relevant Episodes and State-of-Affairs):

• (25) (past ep_i: (e_i: (f^c_i: [(f_j: enter (f_j)) (1x_i:–boy–(x_i))_A (1l_i:–room–(l_i))_U] (f^c_i): (m_i: (f^c_k: [(f_l: like (f_l)) (m_j: (past ep_j: (ant e_j: (f^c_m: [(f_n: leave (f_n)) (1x_j:–his brother–(x_j))_A (1l_j:–garden–(l_j))_U] (f^c_m): (m_j) (f^c_m)) (e_j)) (ep_j)) (m_j))_Ref] (f^c_k)) (m_i)) (f^c_i)) (e_i)) (ep_i))

Manner expressions, however, cannot modify a State-of-Affairs, Episode or Propositional Content: therefore, a similative clause cannot replace a modifier of any of those layers, e.g., an expression of purpose or spatial location (σ^e) (cf. Anderson and Morzycki 2015, 810), absolute time (σ^ep) or propositional attitude (σ^p):

• (26) He boxes like his father (that is, *for a living/*on the street/*on Saturdays/*probably).

Summing up, the similative constructions considered above behave in all respects like Manners. They can be paraphrased by means of the phrase in a…way, be used as modifiers of a Lexical or Configurational Property (but not of other semantic units) and occur in identificational predications in which they are equated to another Manner expression. As regards their internal structure, these similative modifiers consist of the lexical preposition like and a second Manner, which functions as an argument of the latter.

Before moving on to similative constructions which do not denote Manners, let us briefly consider the case of Manner expressions that are not introduced by a lexical preposition/conjunction but rather by a grammaticalized element such as English as or the Romance descendants of Latin quomodo (Fr. comme, It. come, Pt., Sp. como). The latter can be used as interrogative or relative proforms equivalent to English how and introduce headless Manner clauses occurring as arguments or modifiers. This is illustrated in (27)–(28) for Portuguese (where newly introduced elements of the FDG formalism are the aspectual operator “imperf(ect)” and the zero-quantification operator “ø” on the Individual (x_j), ninguém):

The difference between the two clauses in boldface lies in the role that they occupy in argument structure: in (27), the Manner clause is an argument of the predicate gostar, and in (28), it modifies the predicate escrever. As regards their internal structure, however, the two clauses are identical: unlike the similatives considered earlier, these Manner expressions do not contain a second Manner embedded as an argument of a lexical preposition or conjunction. The reason for this is that Portuguese como is not a lexical predicate but a grammaticalized element which indicates that the clause it introduces expresses a configurationally headed semantic unit of the type Manner. A further, crucial difference from the Manner expressions considered above is that the Manner clauses in (27)–(28) are strictly speaking not similatives. In fact, the correct paraphrase for (28) is not Nobody writes in a way that is like (or “similar to”) the way Fernando Pessoa used to write but rather Nobody writes in the (same) way (as) Fernando Pessoa used to write. The latter paraphrase is consistent with the fact that, unlike in the previous examples, in (28) the (m)-unit that modifies the main predicate is coindexed with that which modifies the predicate of the embedded predication. Exactly the same analysis and paraphrase apply to English Manner modifiers introduced by the grammaticalized preposition and conjunction as (e.g., the translation of (28)).

3.2 When similatives are not Manners

In the previous section, we saw that similative modifiers establish a relation between two (Lexical or Configurational) Properties by indicating that these Properties are modified by two Manners which resemble each other. By contrast, in a property-assigning predication such as He is like a veteran, the Individual he is likened to a veteran directly, without specifying in which respect he can be said to resemble a veteran. This means that, unlike in He boxes like a veteran, the predicate like takes the Individual ‘veteran’, and not a Manner, as its argument. In turn, the Configurational Property (f^c _j) formed by the preposition and its argument does not head a Manner expression, but it is directly predicated of the Individual he:

• (29) He is like a veteran.

•   (f^c_i: [(f^c_j: [(f_k: like (f_k)) (1x_i:–veteran–(x_i))_Ref] (f^c_j)) (1x_j)_U] (f^c_i))

Even in modifier similatives, however, the argument of the relational predicate like is not necessarily a Manner. In utterances of the type of He is a boxer like his father, the speaker does not assert that the Property ‘boxer’ applies in the same manner to both Individuals but simply states that both participate in the same type of situation. In other words, it is the whole nuclear predication ‘he be a boxer’ that is said to resemble the nuclear predication ‘his father be a boxer’. It is thus the latter Configurational Property that occurs as an argument of like. This analysis is represented in (30):

• (30) He is a boxer like his father.

•   (f^c_i: [(f_j: boxer (f_j)) (1x_i)_U] (f^c_i): (f^c_k: [(f_l: like (f_l)) (f^c_m: [(f_j) (1x_j:–his father–(x_j))_U] (f^c_m))_Ref] (f^c_k)) (f^c_i))

As shown in this analysis, the Configurational Property (f^c _k) functions as a modifier of the main Configurational Property (f^c _i), that is, it specifies an additional descriptive property of the main nuclear predication. It may be objected that this specification is not of the restrictive type, i.e., it does not narrow down the set of possible referents for (f^c _i) and therefore has no bearing on the truth value of the utterance. Note, however, that one could reply to (30) by saying That’s not true: his father was not a boxer. At any rate, I have proposed elsewhere that not all representational modifiers are restrictive in nature, arguing that this assumption is a relic of traditional Functional Grammar and should be abandoned in FDG (see Giomi 2020a, where I discuss adnominal modifiers of the type of devastated Peter and a wailing Cassandra). See Keizer (2019) for a different treatment of non-truth-conditional representational modification.

Like Manner similatives, this type of similative modifiers can also contain an embedded Episode. In (31), the like-clause bears past tense and includes a modifier expressing absolute time location (namely, the Time (t_i), ‘in 1992’, which bears the semantic function ‘L(ocation)’); hence, the underlying semantic category must be an Episode and not a Configurational Property:

• (31) Euro 2020: Full Of Premier League Quality, Denmark Can Make History Like They Did In 1992.

•   (https://www.newsnow.co.uk/h/Sport/Football/International/Denmark. Accessed 08-05-2021.)

•   (f^c_i:–Denmark can make history–(f^c_i): (f^c_j: [(f_k: like (f_k)) (past ep_i:–they did–(ep_i): (t_i:–in 1992–(t_i))_L (ep_i))_Ref] (f^c_j)) (f^c_i))

A further type of modification structure in which the expression headed by like does not designate a Manner is exemplified by (32) (where the “m” preceding the Individual (x_i), people, represents a Plurality operator):

• (32) Needless to say, people like Veiseh are of great interest to neuroscientists hoping to understand the way the brain records our lives.

•   (https://www.bbc.com/future/article/20160125-the-blessing-and-curse-of-the-people-who-never-forget. Accessed 05-02-2021.)

•   (m x_i:–people–(x_i): (f^c_i: [(f_j: like (f_j)) (1x_j)_Ref] (f^c_i)) (x_i))_φ

In this context, like Veiseh may be paraphrased as similar to Veiseh or of the type of Veiseh.^[7] The underlying semantic structure of the like-phrase is thus the same as underlies like a veteran in (29); the obvious difference is that in (32), this phrase is not a predicate but a modifier of the Individual to which it relates.

3.3 Interim summary

Similative constructions can be broadly divided into predicative and modifier similatives. The former are constructions of the type of (29), where the Configurational Property formed by an adposition/conjunction and its argument is predicated of another semantic unit (of whatever type). Modifier similatives may in turn be split into two subtypes. In Manner similatives, the whole modifying expression corresponds to a Manner headed by a Configurational Property and, within the latter, a second Manner occurs as an argument of a lexical predicate of the type of English like. The second type of modifier similatives does not express a Manner but a Configurational Property, within which the predicate slot is again occupied by a lexical adposition or conjunction. Depending on whether the modified unit is itself a Configurational Property or a nominally headed semantic unit of whatever other category, such similatives may surface either as (reduced) adverbial subordination structures like (30) and (31) or as Adpositional Phrases like (32) (where the argument-NP obligatorily belongs to the same category as the modified unit).

4.1 Comparatives in FDG: Previous approaches

In Hengeveld and Mackenzie (2008, 455; 2021, 52), comparative modifiers are represented as shown in (33):

• (33) John is much/markedly/noticeably more intelligent than his brother.

•   [(f^c₁: (f₂: ♦_Adj (f₂): (f₃: more_Adv (f₃): (f₄: ♦_Adv (f₄)) (f₃)) (f₂)) (x₁)_Standard)) (f^c₁)) (x₂)_U)]

The representation of the degree word more as a Lexical Property correctly captures the fact that such elements can be modified by adverbs like much, markedly, etc. (since grammatical elements are not usually modifiable, see Keizer 2007, Giomi 2020b, 309–15). Abstracting away from the presence of such secondary modifiers, this leads to the following analysis for the utterance in (33):

• (34) (f^c_i: [(f^c_j: [(f_k: intelligent (f_k): (f_l: more (f_l)) (f_k)) (1x_i:–his brother–(x_i))_Standard] (f^c_j)) (1x_j)_U] (f^c_i))

In my view, the representations in (33) and (34) present a number of problems. One of these is that they suggest that intelligent is only modified by more (not by more than his brother) and that his brother is an argument of the modified Property (f_k), more intelligent (not of more only), bearing the function Standard of Comparison. If this were so, it should be possible to omit more and say *John is intelligent than his brother. That comparative degree words like more are in fact predicates taking the Standard of Comparison as their argument has been suggested by Nagamura (2018a), who proposes the following general frame for English comparisons targeting an adjectival predicate:

• (35) (f^c₁: [(f₂: ♦_Adj (f₂): (f₃: [(f₄: more/less/as (f₄)) (x₁)_Standard] (f₃)) (f₂)) (x₂)_U] (f^c₁))

Nagamura’s analysis is thus that the predicate (f₂) is not modified by more/less/as alone, but by a Configurational Property (f₃) which is formed by the comparative word together with its Standard-of-Comparison argument.

4.2 Comparatives are Quantities

While I agree with the principles underlying Nagamura’s proposal, the general frame in (35) still falls short of solving the second drawback that I believe to be inherent in (33)–(34). Namely, all three representations overlook the fact that comparison is after all one specific type of degree modification, as explicitly argued, among others, by Haspelmath and Buchholz (1998, 279–80). Degree modifiers are analyzed in FDG as “indicating the Quantity of application of their head” (Hengeveld and Mackenzie 2008, 270), i.e., they function as lexical heads of variables of the (q) type:

• (36) highly intelligent

•   (f_i: intelligent (f_i): (q_i: (f_j: high (f_j)) (q_i))_φ (f_i))_φ

•   (Hengeveld and Mackenzie 2008, 270)

The rationale behind this analysis is that degrees and quantities are not fundamentally different in notional terms but both pertain to the overarching domain of quantification. And the same goes for other inherently quantificational notions such as for instance rates or volumes (see Hengeveld and Mackenzie 2008, 270–1). From this point of view, speaking of an amount or set of Individuals, the degree to which a Property applies and the rate at which or extent to which a State-of-Affairs takes place are all different ways of referring to Quantities.

Now, since FDG conceives of degrees of application as a subtype of Quantities, it seems straightforward to conclude that comparatives like more than his brother, which likewise indicate the degree of application of their head, should also be represented as Quantities. This is consistent with the fact that words explicitly referring to Quantities are used as comparative markers in several languages, e.g., Italian Giovanni è piu intelligente di quanto lo sia suo fratello, lit. “Giovanni is more intelligent than how-much his brother is” (see Fleischhauer 2016 for further examples). Note finally that, as they introduce the notion of Quantity as a distinct layer of semantic organization, Hengeveld and Mackenzie (2008, 268) do indeed acknowledge that “Quantities arise from the hypostatization of the results of measurement (whether that be counting, estimation or comparison)” (emphasis added). This hint, however, is not taken up again in their discussion of comparatives.

The failure to capture the functional similarity between comparisons and degrees of application is directly related to a further problem with the analysis in (33)–(34). This concerns the assignment of the function Standard to his brother, which suggests that the two terms of the comparison are precisely the Individuals ‘John’ and ‘John’s brother.’ This, however, is not the real meaning of such constructions: rather, a comparison is established between the degree to which the Lexical Property ‘intelligent’ applies to John and the degree to which the same Property applies to John’s brother. While this point is ignored in current FDG accounts of comparison, it has often been made in the formal-semantics literature. For instance, by applying the formalism used in Kennedy (2006, 692), we obtain the following truth conditions for John is more intelligent than his brother (cf. also Heim 2000):

• (37) max{d | intelligent(j) ≥ d} > max{d′ | intelligent(jb) ≥ d′}

•   where “max” = maximalization operator, “d” = degree, “j” = John, “jb” = John’s brother.

(37) is to be read as The maximal degree to which John is intelligent is greater than the maximal degree to which John’s brother is intelligent. Abstracting away from the issue of maximalization (to which I return in footnote 9 below), this representation correctly captures the fact that the terms of the comparison are not two Individuals but two degrees of application (i.e., two Quantities in FDG terms, as explained earlier). (37) being a strictly logical representation, however, it does not capture the fact that the role of more than his brother in grammatical structure is that of a modifier of the predicate intelligent. Once this all-important grammatical fact is taken into account, a more accurate paraphrase for John is more intelligent than his brother is John is intelligent [to a degree (q _i ) such that (q _i ) is greater than the degree (q _j ) to which John’s brother is intelligent] (where the bracketed part corresponds to the modifier). A satisfactory FDG analysis of comparatives targeting an adjectival predicate must necessarily do justice to the two fundamental aspects of such structures that are reflected in this paraphrase – the modifying function of the comparative and its quantificational semantics. This analysis leads to a representation that exploits the same type of semantic frame as was proposed in (19) for similative modifiers, but differs from the latter in that the modifier corresponds to a Quantity and not to a Manner:

• (38) John is more intelligent than his brother.

•   (f^c_i: [(f_j: intelligent (f_j): (q_i:

•              (f^c_k: [(f_l: more (f_l)) (q_j: (f^c_m: [((f_j): (q_j) (f_j)) (1x_i:–his brother–(x_i))_U]

•                       (f^c_m))

•                    (q_j))_Standard

•              ] (f^c_k))

•            (q_i))

•      (f_j)) (1x_j))_U

•   ] (f^c_i))^[8]

This structural isomorphism in the underlying semantic representation of similative and comparative modifiers ties in in a natural way with the typological and diachronic connections between the two types of constructions (see Section 1). In this regard, it is in line with the findings of formal semanticists like Rett (2008, 2011) and Anderson and Morzycki (2015). At the same time, the explicit assignment of the two expression types to two mutually irreducible representational layers (Manners and Quantities) provides a more economical explanation for their different interpretations than the aforementioned accounts, which postulate different kinds of hidden operators and semantic-type shifts. Such null elements and transformational notions have no right of citizenship in a functional model like FDG (see also Section 4.4) and are anyway rendered otiose by the dissociation between semantic categories and semantic frames.

Returning to the structure in (38), note that the embedded Quantity (q_j) is built on the same frame as underlies a headless relative clause (i.e. how intelligent John’s brother is), just like the embedded Manner in similative modifiers (cf. (19)–(20) above). Unlike in similatives, however, the argument embedded within the overall modifier does not contract the semantically general function Reference but the construction-specific function Standard of Comparison. For languages such as English, this analysis is justified by the fact that this semantic function is indicated explicitly by the dedicated preposition/conjunction than.

Before turning to further types of comparisons, it is worth addressing the well-known fact that a sentence including a comparative modifier of an adjectival predicate does not entail that the predicate in question is true of its argument (see, e.g., Kennedy 2006, 692). For instance, while John is intelligent predicates the Property ‘intelligent’ of the Individual ‘John’, by saying John is more intelligent than his brother one is not necessarily saying that John is intelligent – both he and his brother may be incredibly dull. Since this does not usually happen with most types of modifiers (e.g., by removing slowly from John walks slowly, the Property ‘walk’ is still predicated of John), one may wish to conclude that comparatives are in fact not modifiers at all. Note, however, that the same is not true of comparatives that target other types of unit than an adjectival predicate: for instance, John drinks more than his brother and John drinks more beer than his brother undeniably entail “John drinks” and “John drinks beer”, respectively. Analyzing these, but not the former, as modifiers would seem at the very least contradictory.

An even more compelling argument for analyzing both types of comparatives as modifiers is that, even though (38) does not entail “John is intelligent”, the function of more than his brother is still undisputedly that of specifying the degree to which the Property ‘intelligent’ applies to John – namely, a degree which is greater than the degree to which John’s brother is intelligent. Whether this degree is understood to be greater or equal to zero exclusively depends on the available extralinguistic knowledge concerning the intelligence of John’s brother and is therefore not a matter for the Representational Level of FDG, which is only concerned with formalizing those underlying semantic specifications that have demonstrable consequences for the formal encoding of the utterance (see Section 2). The grammar, in other words, does not care about such entailments and presuppositions, which are merely a matter of world knowledge and not one of linguistic structure.^[9] If one rejects this premise and chooses to follow the line of reasoning illustrated earlier, thus denying (some) comparatives the status of modifiers, then one would be forced to conclude that adjuncts like apparent(ly) or pretended (e.g., an apparently good idea, her pretended concern) should likewise not be analyzed as modifiers – although they are to all intents and purposes encoded as such in morphosyntactic terms – because omitting these elements produces the same type of effect as results from the omission of more than his brother in (38). And the same should go for conditional adjuncts – which by definition turn the truth value of the main proposition to “unknown” – as well as, a fortiori, for all negative polarity and zero-quantificational adjuncts (e.g., I never lie, a by no means agreeable situation). To my mind, there is no purely linguistic reason why all these expressions should not be regarded as modifiers, on a par with the comparative constructions dealt with in this article.

Returning to the semantic structure of comparatives, the same type of analysis proposed for (38) can be assumed for comparisons that do not modify a predicate but an argument or another modifier. Consider (39), where the target of the comparison is the Undergoer (x_j), candies:

• (39) John eats more candies than his brother.

•   (f^c_i: [(f_j: eat (f_j)) (1x_i)_A (m x_j: (f_k: candy (f_k)) (x_j): (q_i: (f^c_l: [(f_m: more (f_m)) (q_j: (f^c_n: [(f_j) (1x_k:–his brother–(x_k))_A (m x_l: (f_k) (x_l): (q_j) (x_l))_U] (f^c_n)) (q_j))_Standard] (f^c_l)) (q_i)) (x_j))_U] (f^c_i))

In (39), it is not only the predicate (f_j), ‘eat’, that occurs both in the matrix predication (f^c _i) and in the Configurational Property which heads the Standard of Comparison (i.e., (f^c _n)); the lexical head of the Undergoer, (f_k), ‘candy’, is also the same in both predications. This argument, however, bears a different index in the main and in the embedded predication (i.e., (x_j) and (x_l), respectively), since it is of course not the case that the two brothers eat the very same candies. Conversely, in (40), both the predicate and the lexical head of the Undergoer are different in the two nuclear predications; in such cases, the head of (q_j) is restricted by a whole Episode:

• (40) John drinks more beers than his brother eats candies.

•   (f^c_i: [(f_j: drink (f_j)) (1x_i)_A (m x_j: (f_k: beer (f_k)) (x_j): (q_i: (f^c _l [(f_m: more (f_m)) (q_j: (pres ep_i: (e_i: (f^c _n [(f_o: eat (f_o)) (1x_k:–his brother–(x_k))_A (m x_l: (f_p: candy (f_p)) (x_l): (q_j) (x_l))_U] (f^c _n)) (e_i)) (ep_i)) (q_j))_Standard] (f^c _l)) (q_i)) (x_j))_U] (f^c _i))

In other cases, the head of the Standard of Comparison has a much simpler structure. Consider, for instance, (41):

• (41) Jon Jones Has More Enemies Than Friends In The UFC.

•   (https://www.thethings.com/jon-jones-has-more-enemies-than-friends-in-the-ufc/. Accessed 05-02-2021.)

•   (f^c _i: [(f_j: have (f_j)) (1x_i)_A (m x_j:–enemy–(x_j): (q_i: (f^c _k: [(f_l: more (f_l)) (q_j: (m x_k:–friend–(x_k)) (q_j))_Standard] (f^c _k)) (q_i)) (x_j))_U] (f^c _i))

In this case, there is no need to assume that the Individual ‘friends’ participates in an embedded predication. The Quantity (q_j) is thus structurally identical to a wh-phrase like how many friends. The same principles are relevant to comparisons that modify the subject-argument or another modifier, as in (42) and (43)–(44), respectively:

• (42) More boys than girls sent flowers to him today.

•   (Osborne 2009, 428)

•   (f^c _i: [(f_j: send (f_j)) (m x_i:–boy–(x_i): (q_i: (f^c _k: [(f_l: more (f_l)) (q_j: (m x_j:–girl–(x_j)) (q_j))_Standard] (f^c _k)) (q_i)) (x_i))_A (m x_k:–flower–(x_k))_U (1x_l)_R] (f^c _i))

• (43) John speaks more loudly than wisely.

•   (f^c _i: [(f_j: speak (f_j): (m_i: (f_k: loud (f_k): (q_i: (f^c _l: [(f_m: more (f_m)) (q_j: (m_j:–wisely–(m_j)) (q_j))_Standard] (f^c _l)) (q_i)) (f_k)) (m_i)) (f_j)) (1x_i)_A] (f^c _i))

• (44) John runs more slowly than he walks.

•   (f^c _i: [(f_j: run (f_j): (m_i: (f_k: slow (f_k): (q_i: (f^c _l: [(f_m: more (f_m)) (q_j: (pres ep_i: (e_i: (f^c _n: [(f_o: walk (f_o): (m_j: ((f_k): (q_j) (f_k)) (m_j)) (f_o)) (1x_i)_A] (f^c _n)) (e_i)) (ep_i)) (q_j))_Standard] (f^c _l)) (q_i)) (f_k)) (m_i)) (f_j)) (1x_i)_A] (f^c _i))

Abstracting away from the semantic contrasts captured by the aforementioned representations, all the comparative modifiers considered earlier are built on the general frame (45):

• (45) (v₁: […] (v₁): (q₁: (f^c₁: [(f₂: more (f₂)) (q₂)_Standard] (f^c₁)) (q₁)) (v₁))_{φ}

The differences between the utterances in (38)–(44) concern the semantic category of the unit modified by the comparative, the structural role that is fulfilled by that variable (argument, predicate or modifier) and the internal structure of the Standard-of-Comparison argument of ‘more.’ But, in any case, both the modifier as a whole and the unit that contracts the function Standard of Comparison are invariably Quantities.

4.3 Equative comparisons

It is fairly obvious that, in all the examples discussed in the previous section, the lexical predicate more could be replaced by less with no change to the representational structure of the utterance. At this point, it should be asked whether the same holds true of equative comparisons marked by as … as.

From a logical or conceptual viewpoint, there would not seem to be any particular reason why this should not be the case. As mentioned in Section 3.1, however, as differs from like in being a grammatical and not a lexical element: it is therefore not available for derivational and compounding processes. The same difference exists between as and the comparative degree words more and less (e.g., lesser, lessen, lessness; (n)evermore, furthermore, anymore, moreover, moreness, moresome). As regards availability for modification, the issue is complicated by the ever-recurring difficulty of assessing whether a modifier co-occurring with a head-dependent structure applies to the whole expression or only to the head (see Keizer 2007, 42). In the specific case of constituents introduced by as, it is worth noting that such constituents can be combined with far fewer types of modifiers than phrases headed by more or less. Another indication that as is indeed a grammatical element is the fact that this word, whether on its own or in such combinations as exactly as, twice as, etc. is much less readily available for the prosodic expression of information-structural distinctions than bare or pre-modified more and less (e.g., John is (much/markedly) MORE intelligent than Peter vs #John is (exactly/twice) AS intelligent as Peter).^[10] The reason why this can be taken as an indicator of grammatical status is that pragmatic operators or functions like Emphasis, Focus and Contrast can only be assigned to elements that constitute a separate variable at the Interpersonal Level. Thus, if as cannot bear such interpersonal specifications, it seems safe to conclude that this word does not constitute a Subact of its own – i.e., it has no ascriptive function, which is a further distinctive property of grammaticalized items, as opposed to lexical ones (Keizer 2007, Giomi 2020b, 288–304). Finally, it can be adduced that, when combined with a Negation operator, more and less trigger the form no (no more/no less Adj than; when the form not is used, the scope of the negator appears to be broader). This is not the case with as (cf. *no as Adj as), suggesting that in the former case Negation applies to the Lexical Property more/less, but in the latter, it has scope over the whole expression as Adj as.

If as is indeed a grammatical element, then it certainly cannot be represented as a Lexical Property taking the Standard of Comparison as its argument. Instead, one may want to analyze equative-comparison modifiers by analogy with Manner modifiers introduced by as or its Romance counterparts (see (28)), that is, as Quantity expressions with no second Quantity embedded within them. This tentative analysis is formalized in (46):

• (46) John is as intelligent as his brother.

•   (f^c _i: [(f_j: intelligent (f_j): (q_i: (f^c _k: [((f_j): (q_i) (f_j)) (1x_i:–his brother–(x_i))_U] (f^c _k)) (q_i)) (1 x_j)_U] (f^c _i))

The problem with this representation is that it does not bring out the comparative meaning that is inherent in expressions of the type of (46). Recall from 3.1 that, in Manner modifiers introduced by as (or Portuguese como), the relation between the Manner of action of the main and the subordinate predication is not one of resemblance but one of identity. Equative comparisons, however, are akin to nonequative ones in making reference to two separate amounts or degrees: hence, (46) can be felicitously paraphrased as John is intelligent to a degree (q _i ) such that (q _i ) is equal to the degree (q _j ) to which John’s brother is intelligent.^[11] For this similarity to be reflected in the underlying semantic representation of (46), a second Quantity (q_j) must again be embedded within the modifying Quantity (q_i). As in the corresponding nonequative comparison, this Quantity (q_j) indicates “the degree to which John’s brother is intelligent” and bears the semantic function Standard of Comparison.

The question, at this point, is which predicate assigns this function to the Quantity (q_j). An important hint for answering this question is provided by the formal isomorphism between equative and nonequative comparatives. Both types of comparison, in fact, surface in the format X Adj Y NP. This is illustrated in (47)–(48):

• (47) more intelligent than his brother

•   where X = more

•      Adj = intelligent

•      Y = than

•      NP = his brother

• (48) as intelligent as his brother

•   where X = as₁

•      Adj = intelligent

•      Y = as₂

•      NP = his brother

As we saw in 4.2, more and than function as a predicate and a marker of the function Standard of Comparison, respectively. If the isomorphism between (47) and (48) is to be taken as a semantically significant one, it follows that the elements occurring in the corresponding slots in (48) should be understood as serving exactly the same functions – i.e., the first as is the predicate and the second as marks the argument of the former as a Standard of Comparison. What we still need to decide is how to represent the first as (the one functioning as a predicate), that is, what type of semantic unit is encoded by this element. To arrive at this decision, let us consider the case of equative comparisons that modify a verbal, rather than an adjectival predicate. This use of equative comparatives is illustrated in (49), where only the comparative modifier (in bold) is represented in the formal analysis:

• (49) John drinks as much as his brother.

•   (q_i: (f^c _i: [(q_i) (q_j: (f^c _j:–his brother (drinks)–(f^c _j)) (q_j))_Standard] (f^c _i)) (q_i))

In (49), as much serves the very same function as more in the examples considered above, that is, it occurs as a predicate that takes as its argument the Quantity (q_j) (i.e., the amount (of alcohol) that John’s brother drinks). Rather than being a lexical predicate, however, as much is grammatically a proform denoting a further semantic unit of the category Quantity (see Section 2). Accordingly, as much is represented in (49) as an absent-headed Quantity (q_i), i.e., a Quantity that lacks lexical content (see Hengeveld and Mackenzie 2008, 269): the distinctive feature of equative comparisons, in this respect, is that this headless Quantity (q_i) is predicated of a second Quantity (q_j) and is co-indexed with the overall Quantity denoted by the whole comparative phrase or clause.

If we now return to (46) and (48) with this analysis in mind, it will be clear that the first instance of as in those structures serves exactly the same function as as much in (49). The fact that as rather than as much must be used in equative comparisons that modify an adjectival predicate is a purely morphosyntactic constraint of the English language, which has no bearing on the semantics of the construction – and in fact is not found in many other languages, where the very same form occurs in all types of equative comparison, regardless of the type of element that the expression serves to modify. It follows that the analysis given earlier for (49) can unproblematically be extended to utterances of the type of (46), where the comparative expression modifies the adjectival predicate intelligent. As regards the internal structure of (q_j), this is of course the same as in the corresponding nonequative comparison (38). By representing this internal structure in its full form, the complete analysis in (50) is obtained; needless to say, the same reasoning applies to (49), whose full representational analysis is given in (51):

• (50) John is as intelligent as his brother.

•   (f^c _i: [(f_j: intelligent (f_j): (q_i: (f^c _k: [(q_i) (q_j: (f^c _l: [((f_j): (q_j) (f_j)) (1x_i:–his brother–(x_i))_U] (f^c _l)) (q_j))_Standard] (f^c _k)) (q_i)) (f_j)) (1x_j)_U] (f^c _i))

• (51) John drinks as much as his brother.

•   (f^c _i: [(f_j: drink (f_j): (q_i: (f^c _k: [(q_i) (q_j: (f^c _l: [((f_j): (q_j) (f_j)) (1x_i:–his brother–(x_i))_A] (f^c _l)) (q_j))_Standard] (f^c _k)) (q_i)) (f_j)) (1x_j)_A] (f^c _i))

Summing up, the underlying frame of equative comparisons used as modifiers is as follows:

• (52) (v₁: […] (v₁): (q₁: (f^c ₁: [(q₁) (q₂)_Standard] (f^c ₁)) (q₁)) (v₁))_{φ}

Compare now (52) with the general frame for nonequative comparison (45), repeated here as (53):

• (53) (v₁: […] (v₁): (q₁: (f^c ₁: [(f₂: more/less (f₂)) (q₂)_Standard] (f^c ₁)) (q₁)) (v₁))_{φ}

As is evident in (52)–(53), we have now arrived at a representation that not only correctly captures the functional and structural similarity of equative and nonequative comparatives but also brings out the crucial differences: the grammatical vs lexical nature of the embedded predicate – a headless Quantity in equative comparatives, a Lexical Property in nonequative ones – and the fact that in equative comparison this predicate is coindexed with the Quantity which underlies the whole expression. The equative meaning of frame (52) results precisely from the absence of a nonequative element like more or less, which triggers the second instance of as to mark the semantic function Standard of Comparison (instead of the non-equative relator than). Also note that (52) does not include mathematical symbols like “ =”, which makes it compatible with different contextually determined readings pointing to exact or non-exact equivalence, as well as with the addition of overt modifiers like exactly, approximately and the like.

Just as (53) for nonequative comparatives, (52) also underlies equative comparatives that modify semantic units other than an adjectival or verbal predicate. (54) and (55) illustrate this general point for comparisons that target a unit used in argument position (triggering the form as many…as because the referent is a countable entity) and a unit that in turn modifies another element:

• (54) John drinks as many beers as his brother eats candies.

•   (f^c _i: [(f_j: drink (f_j)) (1x_i)_A (m x_j:–beer–(x_j): (q_i: (f^c _k: [(q_i) (q_j: (pres ep_i: (e_i: (f^c _l: [(f_m: eat (f_m)) (1x_k:–his brother–(x_k))_A (m x_l:–candy–(x_l): (q_j) (x_l))_U] (f^c _l)) (e_i)) (ep_i)) (q_j))_Standard] (f^c _k)) (q_i)) (x_j))_U] (f^c _i))

• (55) John walks as slowly as his brother.

•   (f^c _i: [(f_j: walk (f_j): (m_i: (f_k: slow (f_k): (q_i: (f^c _l: [(q_i) (q_j: (f^c _m: [((f_j): (m_j: ((f_k): (q_j) (f_k)) (m_j)) (f_j)) (1x_i:–his brother–(x_i))_A] (f^c _m)) (q_j))_Standard] (f^c _l)) (q_i)) (f_k)) (m_i)) (f_j)) (1x_j)_A] (f^c _i))

Once again, it is crucial that the two terms of the comparison, (q_i) and (q_j), be assigned different indexes, so as to show that the relation between the two is one of equivalence and not one of sameness/identity. If the latter had been the case, this could have been signaled explicitly by means of the adjective same (e.g., John drinks the same (amount of beer) as his brother). The difference is admittedly a subtle one, but the formal apparatus of FDG offers the means to capture it in a straightforward and consistent way.

4.4 Synthetic marking of nonequative comparison

For Hengeveld and Mackenzie (2008, 454–5), the same analysis given in 4.1 for more intelligent applies when the suffix -er is used instead of the word more. On this approach, the alternation between English analytic and synthetic comparatives is not a semantically based one but merely depends on the phonological shape of the adjectival predicate.^[12] The choice between more and the suffix -er is therefore regarded as a matter for the Phonological Level, whereas at the Representational Level, the lexical predicate ‘more’ is present in both more intelligent and bigger. In Hengeveld and Mackenzie’s view, this also means that, at the Morphosyntactic Level, John is bigger than his brother “will appear as though it were (the ill-formed) *John is more big than his brother. It is the Phonological Level which, having access to the phonological structure of the Utterance, applies the appropriate form, as a suffix”.

A different account of synthetic comparatives is suggested by Keizer (2015, 239), who analyses the Affix -er as a Comparative operator:

• (56) Bigger

•   (comp f₁: big_A)

Nagamura (2018a) endorses Hengeveld and Mackenzie’s (2008) observation that, in such structures as much/markedly bigger, the adverbs “indicate the degree of difference in exactly the same way as more is modified in [much/markedly more intelligent]”. On these grounds, Nagamura concludes that the analysis in (56) is to be rejected because representing -er as a grammatical operator is incompatible with the possibility of modifying the degree of difference. In a recent work, however, Hengeveld and Mackenzie (2021) have returned to the issue of English comparatives and developed an account which incorporates Keizer’s (2015) analysis of synthetic comparison. The authors compare the two utterances in (57) and (58) and develop the argument reported below:

• (57) John is noticeably more intelligent than his brother.

• (58) John is noticeably bigger than his brother.

[I]n [57] modification of the degree expressed by more is indeed possible, but in [58], with the suffixal expression, it is not. One of the readings of [57] is that the property intelligent holds to a higher extent for John, and that this extent is noticeable. The reading in [58], however, is that John’s being bigger than his brother is noticeable. Thus, in [58], noticeably modifies bigger as a whole, and not just the -er suffix. This is due to the fact that the comparative suffix is triggered by an operator (Comp), a grammatical element that cannot be modified […]. As a result, [57] and [58] have different semantic representations. (Hengeveld and Mackenzie 2021, 52)

Hengeveld and Mackenzie (2021) also point out that their earlier analysis of bigger as being semantically identical to more intelligent “requires a transformation at ML, in that first the [Adverbial Word] more is inserted, which subsequently is changed into the Aff[ix] -er. Such transformations are dispreferred in a functional approach”. Therefore, they propose an alternative solution according to which the choice between the Lexical Property ‘more’ and the Comparative operator -er takes place via a look-ahead process between the Representational and the Phonological Level, whereby the Formulator checks “the phonological properties of the lexeme selected for the [predicate] slot” to select the appropriate representational frame.

A first remark to be made about Hengeveld and Mackenzie’s new proposal is that, on one reading at least, noticeably functions as an evidential adverb of event perception. On that reading, it is indeed the case that in (58) bigger as a whole falls within the scope of the adverb; however, it is not the case that “noticeably modifies bigger”. Rather, the adverb would modify the whole State-of-Affairs, which may create the impression that what is in the scope of noticeably is the expression bigger as such.^[13]

A further counterargument to regarding noticeably as modifying “bigger as a whole” is that, if this reading were possible for (58), then one would expect a similar interpretation to be accessible not only in (57) but also in comparatives targeting verbal, rather than adjectival predicates. In an utterance like John drinks noticeably more than his brother, however, noticeably could hardly be argued to modify the predicate and the comparative element together (i.e., drinks more) but is more naturally understood as only modifying more, or at best the whole phrase more than his brother.

That said, even if one admits that noticeably can indeed be interpreted as modifying the (supposed) property bigger, but not as a narrower-scope modifier that only targets the comparative element, this reasoning cannot be extended to all the types of modifiers that may occur in synthetic comparatives. This is a logical consequence of Hengeveld and Mackenzie’s statement that the reading of (58) is that “John’s being bigger than his brother is noticeable”: in fact, as soon as one turns to such structures as John is much/two times/two inches bigger than his brother, it becomes evident that these expressions cannot be rendered as “*John’s being bigger than his brother is much/two times/two inches” (or any paraphrase thereof, e.g., “*John’s being bigger than his brother is great/triple/by two inches”). With such modifiers, the only reasonable interpretation is that the measure modifier makes the difference in size between the two brothers more precise by quantifying over the comparative element itself (i.e., its scope is narrower than the whole unit bigger),^[14] in the very same way as this happens in much/two times/two inches more Adj than his brother. What this indicates is that a comparative element capable of being modified must necessarily be present in the representational frame underlying synthetic comparatives: were it not so, it would not be possible for a degree or measure modifier to quantify over the difference between the two terms of the comparison. It follows that the semantic trigger for the -er suffix cannot indeed be formalized as a grammatical operator ‘Comp’, as pointed out by Nagamura (2018a). At the same time, as argued by Hengeveld and Mackenzie (2021), it is also not possible to represent this element as a Lexical Property, since a non-transformational model like FDG cannot assume such an element to be inserted at the Representational Level and then suppressed during Morphosyntactic or Phonological Encoding.

Luckily enough, modifiability is not the only criterion of which FDG avails itself to determine the lexical or grammatical nature of linguistic elements. Other important parameters are the (im)possibility of the item participating in morphological processes of derivation and compounding and its (un)availability for the assignment of Focus and Emphasis (see Sections 3.1 and 4.3). As soon as these parameters are brought into the picture, it becomes clear that a bound morpheme like the comparative suffix cannot be regarded as an entirely lexical element (it cannot be emphasized or focalized, nor can it be the input for further processes of derivation or compounding). However, it is not a fully grammatical element either, since as argued earlier it can be modified, at the very least, by expressions of measure or degree. Since Keizer (2007), elements that share properties of both lexical and grammatical items have been classified in FDG as lexical operators: such elements resemble lexical items in being inserted in their phonemic form already at the Interpersonal or the Representational Level, but at the same time are akin to grammatical operators in not heading a separate variable of the level in question (precisely because they are not liable to processes that presuppose the status of an independent variable such as derivation, compounding or the assignment of operators and functions). Thus, by analyzing -er as a lexical operator, it becomes possible to do justice to the mix of lexical and grammatical properties displayed by this element. The other important advantage of this analysis is that it is perfectly compatible with Hengeveld and Mackenzie’s (2021) revised approach to synthetic comparatives, which introduces the notion of look-ahead computation involving the Representational and the Phonological Level, thus eliminating the “dispreferred” transformationalist assumption that underlay the account proposed in Hengeveld and Mackenzie (2008).

As regards the formal representation of synthetic comparatives, if -er is analyzed as a lexical operator it of course becomes impossible to postulate an identical representational frame for analytic and synthetic comparatives (since in the latter, there is no lexical predicate like more to take the second Quantity as its argument). At the same time, the underlying representation of analytic and synthetic comparatives must capture the fact that both constructions are functionally equivalent. This is the same situation as we encountered in 4.3 when comparing the syntax and semantics of equative and nonequative comparatives.^[15] Drawing upon the argument developed in that section, the general representational frame for synthetic comparatives can at this point be formalized as in (59), where the lexical operator -er is inserted as such (and not as an abstract placeholder) in accordance with the notational convention introduced by Keizer (2007):

• (59) (v₁: […] (v₁): (q₁: (f^c ₁: [(-er q₁) (q₂)_Standard] (f^c ₁)) (q₁)) (v₁))_{φ}.

Once again, then, by focusing on the functional commonality between the various types of comparative structures and on the specific properties of the linguistic elements that occur in these constructions, we have arrived at a formal representation in which both the similarities and the differences between the various types of comparatives are adequately reflected.