is semantically a proposition. They can take many such things as adjuncts.
There is no language in which the syntactic subject can be a referentially
clause-internally-dependent reflexive (in the true sense of the reflexive).
There is no language in which we can extract a verb out of an embedded clause,
although we can extract all kinds of nonverbs. There is no language in which a
verb root is a full proposition, rather than predicate. (In pro-drop languages
the verb stem might be full proposition, when the “dropped” argument is
_morphologically_ available on the verb. Topic-drop is a different
phenomenon.) There is no language which is not structure-dependent. There is
no language which exhibits hierarchical dependencies of the kind 3124 and 2413
that we saw in (4).

There is a longer list, which might get more technical depending on one’s
favorite linguistic theory, but these will suffice for our purposes as far as
syntax-semantics and sequencing are concerned. The linguist’s claim is that
there has been no such languages, and there will never be even if we could
magically fast-forward or fast-backward the evolution of the language-forming
capacity, hence the need for a linguistic theory to explain the gaps.313131An
analysis of one striking historical example for the gap in (9i) which competes
with modern analyses and reaches the same result is the study of old Hittite
by Bach and Cooper (1978).

Case (vii) has already been touched upon, around discussion of (4). Case (vi)
has been a Chomskyan classic, sometimes considered to be the cornerstone of
his syntactocentrism, for example arguing for structure-dependence of yes/no
question inversion in English.323232Case (iii) is Chomsky too (and Haj Ross),
that is, syntactically argued, but, like others, semantic in nature. They are
the ones I will concentrate on (and leave the rest to an upcoming book)
because they are brought to focus by categorial grammar, which also tries to
explain structure-dependence in (vi) rather than assume it as Chomskyans do
(Bozşahin, 2012). Unsurprisingly, semantics is brought in to the explanation.
More to the point of the current article, they are about sequences humans find
connected and interpretable.

###  9.1 Neither syntax nor semantics suffices for understanding linguistic
structure

The following examples manifest different semantics depending on the verb
used, although the surface syntactic structure (intonation, grouping,
phrasing) is the same for all the verbs listed.  Mary
persuaded/promised/expected/wanted John $[$to study$]$. In ‘persuade’, John
studies; in ‘promise’ Mary does. For ‘expect’ and ‘want’, John is only the
subject of studying and not an argument of these verbs. For example, Mary does
not expect John, or want him. (These are respectively known as object-control,
subject-control/raising-to-object, and exceptional case-marking verbs.)

They are bounded dependencies, where the verb specifies the role of its
argument in the infinitival clause in brackets, if any. In other bounded
dependencies, such as passive, where the governor likewise uniquely identifies
the roles of the particular argument it is interested in, the telicity of the
verb makes a difference although the surface syntactic structure is considered
acceptable across the board but semantically odd in some cases (shown with
$\sharp$): John was persuaded/expected/$\sharp$promised/$\sharp$wanted $[$to
study$]$ (by Mary).

For the same verbs participating in unbounded constructions, such as
relativization, (a–b) below, coordination (c–d), and topicalization (e), where
the dependencies between arguments can cross clausal boundaries indefinitely
without being an argument of any of the intervening verbs, we see the same
surface syntactic structure for all the verbs in question.  I met the man that
$[$Harry thought $[$Jenny claimed $[$Mary
persuaded/promised/expected/wanted to study$]$ $]$ $]$. The man that $[$Harry
thought $[$Jenny claimed $[$Mary
persuaded/promised/expected/wanted to study$]$ $]$ $]$ walks. $[$Mary asked$]$
and $[$Jenny $[$believes Larry
$[$persuaded/promised/expected/wanted$]$ $]$ $]$ John to study. Mary
persuaded/promised/expected/wanted $[$John $[$to attempt $[$to leave$]$ $]$
$]$
and $[$Jenny $[$to try $[$to arrive$]$ $]$ $]$This man, Jenny $[$knows
$[$Mary persuaded/promised/expected/wanted to study$]$ $]$One important
problem then is how we can acquire the semantic distinctions of these verbs if
syntax suffices for semantics, because the surface syntactic structures
engendered by these verbs are uniform in bounded and unbounded constructions,
and presumably, this is the data we are exposed to in acquiring language. One
answer, emanating from Chomsky (1970), is that their internally represented
syntactic structures are different. Another answer, which CCG follows, is that
surface structure _is_ syntactic structure, but their logical command
relations differ, which means such command relations must be represented as
part of the elements, in this case the verbs, because we know that children
can acquire their distinction.333333‘Promise’-class is notoriously difficult
for the child, crosslinguistically. However, they are acquired early (Sherman
and Lust, 1993), but later than other verbs, around the age of four years to
five and a half (Hyams and Orfitelli, 2018). However, both theories agree that
the computational process that drives the surface structure is one and
syntactic,343434Recall once again the famous Chomsky example _colorless green
ideas sleep furiously_ , which is considered grammatical but senseless. The
idea of single computation sets Chomskyan transformationalism and CCG apart
from multi-structural multi-computational proposals in linguistics, such as
HPSG (Pollard and Sag, 1994), LFG (Bresnan and Kaplan, 1982), autolexicon
(Sadock, 1991), and “tiers” approaches (Jackendoff, 2002). The additional
burden on latter theories is to explain how such multiple structures meet if
they are computed independently, and what happens when multi-computations
conflict. A further distinction of all of them from cognitivism in
linguistics, for example, Croft (2001); Fauconnier and Turner (2002);
Langacker (2008); Goldberg (2013), is more agnostic treatment of computation
by the latter. which in the case of CCG implies that semantic representation
in the form of logical command relations is insufficient but necessary to
acquire the meaning distinctions above.353535Recent theorizing in Chomskyan
way of thinking tries to unify language of thought with language (although
Chomsky himself has been equivocal in this respect), by identifying gaps of
ungrammatical but acceptable expressions on one side, and ungrammatical and
unacceptable expressions on the other, suggesting that the difference evinces
for (I)nternal-language as LOT; see Dupre (2020). The I-language$\approx$LOT
hypothesis would face the same burden of explaining how the surface-
syntactically identically behaving expressions can differ in meaning. Both
views would have to assume something unlearned to bootstrap what is learned,
to explain the limited and uniform time window of acquisition without infinite
regress, which is perhaps the main spirit of Fodor (1975), and, in the case of
CCG, what is learned from has no latent computational structure. And let’s not
forget that a deeply rooted anthropocentrism about thinking would follow from
the I-language$\approx$LOT project. If thought is language, not merely
language-like, then animals including closest cousins of ours which lack
linguistic ability would imply that they lack thinking as well. It seems like
good minds such as Hume, who wrote back in 1748 that “the animal infers some
fact beyond what immediately strikes his senses”—and by _infer_ he did not
mean ‘reason’ neither for animals nor humans, deserves a second chance about
sources of thought (Fodor, 2003).

In addition to following the tradition of assuming that surface structure
(which was a theoretical proposal by early Chomsky) is syntactic structure,
which was anticipated by Husserl (1900), CCG further proposes that semantics
is insufficient but necessary to explain language acquisition. The rationale
is the following: No one has been able to show convergence to a competence
grammar without an assumption of a homomorphic conceptual base which is
available directly to all children in a limited time window (Chomsky, 1965;
Lenneberg, 1967; Pinker, 1979; Berwick, 1985; Yang, 2006; Ambridge, Pine and
Lieven, 2014). Semantic bootstrapping as an umbrella term covering this way of
thinking assumes that all human languages can be supported by a conceptual
structure if it is sufficiently homomorphic to world’s syntaxes. What is
acquired is syntax-semantics correspondences of words, and what the child is
assumed to be exposed to is utterance meanings and forms, not the words
themselves in isolation, and under uncertainty. In other words, the child
already knows that forms have meanings, otherwise, if that property is also
learned, then we would have had to have seen much greater variation in
timeline of language acquisition. What the child learns is which forms go with
which meanings. Working with this rationale shows signs of capturing timeline
of child development and known patterns, such as vocabulary spurt, sudden
jumps, fast mapping, and syntactic bootstrapping (as an effect rather than
cause). In this way of exploration the task of the modeler is not to commit to
a specific shape and style of the homomorphic base (logic, psychosemantics,
etc.), but to assume that one exists and supports compositionality of concepts
and thoughts (Ambridge, Pine and Lieven, 2014). Therefore the critical
position that CCG takes is claiming that syntax is learned from semantics at
the level of words eventhough they are not received in isolation; see Abend et
al. (2017). What is variant and what is invariant in this exploration are
therefore critical.

###  9.2 Invariants and variants of combination

The direct connection to sequencing and its semantics in CCG is that bounded
constructions need no more than function application, which also happens to be
the only primitive of the idea of combinators, and unbounded constructions
need no more than composition ($\mathbf{B}$) and substitution ($\mathbf{S}$).
Altogether they amount to Steedman’s (2000) principle of projective dependency
for language, that surface structure in all its aspects is projected from a
lexicalized grammar unchanged, undeleted and unmoved, including avoidance of
predicate abstractions on the fly—therefore all predicates are specified in
the lexicon. Languages differ only in their lexicons.

We have seen these functionalities of planned action as application (7.1),
composition (7.3), and substitution (7.3). Linguistic valuation of their input
categories is naturally expected to differ from that of planning, usually
considered to consist minimally of the noun phrase ($\mathit{NP}$), the verb
phrase ($\mathit{VP}$) and the clause ($\mathit{S}$). For plan valuation I
have used $\doteq$ for category assignment. For linguistic categories I use
CCG notation for it, which is :=.

These linguistic categories are not considered universal, since everything
that is specified in the lexicon can be projected.363636This is one major
difference from Chomsky’s universal grammar, where N(oun) and V(erb) are
considered innate, treating them as universals, among others such as adjective
(Baker, 2003). They are seen more of capturing distributional diversity of
categorization across the world’s languages, held together by universal
projection.373737See Bozşahin (2012); Steedman (2020b) for what would be at
stake linguistically if we include rules such as subcomposition (7.3) for
projection and similarly-inspired rules, and for some alternatives. Briefly,
$\mathbf{D}$ would be required to syntactically handle examples such as _the
film’s ending $[$that I$]$ and $[$that you$]$ preferred_ (Steedman, p.c.). So
far, all the syntactic contexts that have been identified requiring
$\mathbf{D}$ involves one closed-class element such as ‘that’ in this example,
for example ‘what’ in _$[$ what you can$]$ and $[$what you won’t$]$ sell_,
therefore alternative analyses in which these elements lexically compose would
be available—they are morphologically bound elements in many languages. The
other candidate extension for projection, christened $\mathbf{L}$ by Steedman
and Bozşahin for language (see Steedman (2020b)), which we used implicitly
without a name in (7.3), concerns the case theory of CCG and does not engender
predicate abstractions during projection. It would be at work in deriving the
fragments in brackets in the following example: _I persuaded $[$Mary to buy$]$
and $[$Harry to sell$]$ the house._ Its connection to $\mathbf{S}$ of (7.3)
cannot be overlooked in relation to intensionality. $\mathbf{L}$ is defined in
one directional variant as follows, cf. $\mathbf{S}$ for the same
directionality (we shall soon see that $<$$\mathbf{L}$ is needed in analyzing
expressions such as above):
$\mathit{(X\kern-1.0pt/\kern-1.0ptY)\kern-1.0pt/\kern-1.0ptZ}$$\colon\kern-1.0ptf$
$\mathit{Y\kern-1.0pt/\kern-1.0ptW}$$\colon\kern-1.0ptg$ $\Rightarrow$
$\mathit{(X\kern-1.0pt/\kern-1.0ptZ)\kern-1.0pt/\kern-1.0ptW}$$\colon\kern-1.0pt\lambda
x\lambda y.fy(gx)$ ($>$$\mathbf{L}$)
$\mathit{(X\kern-1.0pt/\kern-1.0ptY)\kern-1.0pt/\kern-1.0ptZ}$$\colon\kern-1.0ptf$
$\mathit{Y\kern-1.0pt/\kern-1.0ptZ}$$\colon\kern-1.0ptg$ $\Rightarrow$
$\mathit{X\kern-1.0pt/\kern-1.0ptZ}$$\colon\kern-1.0pt\lambda x.fx(gx)$
($>$$\mathbf{S}$) The common pattern is that $\mathbf{S}$ and $\mathbf{L}$’s
main functors are necessarily two-argument functions, unlike $\mathbf{B}$. One
of these arguments is more liberal in $\mathbf{L}$, allowing limited
intercalation, such as
$\mathit{(A\kern-1.0pt/\kern-1.0ptB)\kern-1.0pt/\kern-1.0ptC~{}B\kern-1.0pt/\kern-1.0ptD~{}D~{}C}$,
but not
$\mathit{(A\kern-1.0pt/\kern-1.0ptB)\kern-1.0pt/\kern-1.0ptC~{}B~{}C}$, adding
more to the repertoire of semantically connectable sequences. This is
different than the freely order-inverting $\mathbf{C}$, which does the
intercalation that we just rejected, which is a function of type $\lambda
f\lambda g\lambda a\Rightarrow fag$. It is known to overgenerate in language;
see Bozşahin (2012) for extensive discussion.

Going back to (1), repeated below, we can see complex categorization at work
in (9.2) in controlling semantic nondecomposability and syntactic
decomposability. [exno=1] Zhāngsān shēng qì le// Zhangsan generate air asp//
‘Zhangsan got angry.’// Zhāngsān shēng le hǎodà de qì// Zhangsan generate asp
huge nom air// ‘Zhangsan got very angry.’ (lit. ‘Zhangsan generated huge
air.’)// Zhāngsān shēng wán qì le// Zhangsan generate finish air asp//
‘Zhangsan stop being angry.’ (lit. ‘Zhangsan finished generating air.’)//

shēng :=
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0pt\mathit{NP}_{\mathrm{\scriptstyle\mbox{\scriptsize
q\\`{\i}}}}}$ $\colon\kern-1.0pt\lambda x\lambda
y.\mathit{angry}^{\prime}_{\circ x}y$ shēng :=
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP}$$\colon\kern-1.0pt\lambda
x\lambda y.\mathit{generate}^{\prime}xy$ where ‘$\circ$’ as the subscript of a
predicate means that what follows it is an event modality of the predicate
rather than an argument of the predicate itself, from Bozşahin (2023). The
correspondence is kept strictly compositional by avoiding vacuous abstractions
for example on
‘$\kern-1.0pt/\kern-1.0pt$$\mathit{NP}$${}_{\mathrm{\scriptstyle\mbox{\scriptsize
q\\`{\i}}}}$’, also avoiding the need for implicature when it is not
necessary.383838In Bozşahin (2023), a category such as
$\mathit{NP}$${}_{\mathrm{\scriptstyle\mbox{\scriptsize q\\`{\i}}}}$ is called
a head-dependent type, which differs from an ordinary $\mathit{NP}$ type by
being all about reference to the head-form _qì_. Such types, and even more
specific types such as singletons—references to a token rather than token type
as in ‘bucket’ of kick the bucket, need no auxiliary projection apparatus
(Bozşahin, 2023).

Although decomposable meanings of ‘generate’ and ‘air’ are available in freer
syntax of (1b–c), the reference of the events is to becoming angry in all
cases, which is not obtained as implicature, that is, by post interpretation.
It is the verbal subcategorization which fixes this reference; cf. freer
reference of the verb for ‘generate’ in (b) where cooccurrence with phrases
involving _qì_ is not expected. In such categorization and subcategorization
we can avoid the polysemy fallacy pointed out earlier (footnote 4) by
principally deciding categorization based on categorial choice of reference,
as done by main predicate constants in (9.2). Needless to say, lexical
semantics has to play a role in it as well.393939One more process is needed to
make categories such as (9.2a–b) contrastive, that is, relatively exclusive,
to do justice to lexical semantics work that is needed to carve them out.
Default reasoning (Reiter, 2001) is designed to handle inferences of this
kind.

I am not suggesting that CCG’s current way of theorizing and complex
categorization are complete or minimal in their apparatus. I am arguing that a
mathematical understanding of the sources of empirical assumptions goes a long
way in appreciating and assessing any linguistic theory. Linguistics is not
mathematics, but mathematical understanding of linguistic structure may reveal
the structure of the invariant so that the variants (the linguistic data and
its typology) can be better understood.

For CCG in particular, we can have a better understanding of what is at stake
regarding choice of combinational universals (i.e. its necessary apparatus to
deal with all constructions) and projection (sufficiently minimal apparatus
for them), by having a closer look at $\mathbf{L}$ and $\mathbf{S}$,
respectively.

Combinator $\mathbf{L}$ of footnote 37 has two applications deferred, one to
receive $\mathit{\kern-1.0pt/\kern-1.0ptZ}$, and the other to receive
$\mathit{\kern-1.0pt/\kern-1.0ptW}$. Its combined result carries over these
types without reduction. Its result combines with $\mathit{W}$ first, which
does not necessarily follow from the deferred applications. In that sense, its
combination would not be necessarily functional; it could be conceived as
combining first with $\mathit{Z}$.

Moreover, syntactic case functions of some residuated complement clauses would
remain open problems without the harmonic backward $\mathbf{L}$, which is the
backward variant of $\mathbf{L}$:
$\mathit{Y\kern-0.3pt\backslash\kern-0.2ptW}$$\colon\kern-1.0ptg$
$\mathit{(X\kern-0.3pt\backslash\kern-0.2ptY)\kern-1.0pt/\kern-1.0ptZ}$$\colon\kern-1.0ptf$$\Rightarrow$$\mathit{(X\kern-1.0pt/\kern-1.0ptZ)\kern-0.3pt\backslash\kern-0.2ptW}$$\colon\kern-1.0pt\lambda
x\lambda y.fy(gx)$ ($<$$\mathbf{L}$)

It is harmonic because the argument which is composed over ($\mathit{W}$) and
the function composed over ($\mathit{Y}$) have the same directionality. Two
examples from verb-medial languages English and Mandarin Chinese are (only
_persuade_ ’s category is shown for brevity):  I persuaded((S\NP)/VP)/NP
$[$Mary to buy$]$ and $[$Harry to sell$]$ the book Nà-běn wǒ hùi shùifú
$[$Zhāngsān qù mǎi$]$ érqiě Lǐsì qù mài de shū// That-Measure I will persuade
Z to buy and L to sell rel book// ‘the books which I will persuade Zhangsan to
buy and Lisi to sell’// For example, (a) in the following analysis shows that
$\mathbf{L}$ must be at work in assembling _Mary to buy_ of (9.2a) locally so
that all verbs and residual complements can take their arguments with correct
cases (of who does what to whom in _persuade_ and _buy_ , as shown in
(b)):404040I follow the CCG convention of displaying a tree with leaves on top
and root at the bottom. A line is drawn to show span of local combination, for
example _Mary_ combines with _to buy_ in (9.2a) using backward harmonic
variant of $\mathbf{L}$. Tree display is flattened to save space. $[$Mary to
buy $]$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-0.3pt\backslash\kern-0.2pt(((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP)}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP))\kern-1.0pt/\kern-1.0ptVP}$
$\mathit{VP\kern-1.0pt/\kern-1.0ptNP}$ $\colon\kern-1.0pt\lambda
p.p\,\mathit{mary}^{\prime}$ $\colon\kern-1.0pt\lambda p\lambda q.qp$
$\colon\kern-1.0pt\lambda x_{1}\lambda x_{2}.\mathit{buy}^{\prime}x_{1}x_{2}$
$>\kern-2.0pt\mathbf{B}$
$\mathit{\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP))\kern-1.0pt/\kern-1.0ptNP}}$
$\mathit{\colon\kern-1.0pt\lambda z\lambda q.q(\lambda
x_{2}.\mathit{buy}^{\prime}\,z\,x_{2})}$ $<$$\mathbf{L}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP)\kern-0.3pt\backslash\kern-0.2pt(((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP)}$
$\mathit{\colon\kern-1.0pt\lambda p\lambda x\lambda
x_{2}.p\,\mathit{mary}^{\prime}(\mathit{buy}^{\prime}x\,x_{2})}$

persuaded | Mary to buy
---|---
| $<$$\mathbf{L}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP}$ | $\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP)\kern-0.3pt\backslash\kern-0.2pt(((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP)}$
$\colon\kern-1.0pt\lambda x\lambda p\lambda y.\mathit{persuade}^{\prime}(px)xy$ | $\colon\kern-1.0pt\lambda p\lambda x\lambda x_{2}.p\,\mathit{mary}^{\prime}(\mathit{buy}^{\prime}x\,x_{2})$
$<$
$\mathit{\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP}}$
$\mathit{\colon\kern-1.0pt\lambda x\lambda
y.\mathit{persuade}^{\prime}(\mathit{buy}^{\prime}x\,\mathit{mary}^{\prime})\mathit{mary}^{\prime}\,y}$

No other CCG projective combinator can combine (a) while maintaining case
functions true to their argument-takers, the verbs.

The appeal of $\mathbf{L}$ is that it is known that constructions interact to
interleave their argument taking. If we assume following Steedman (1996) that
some English PPs must be arguments _because_ they can cause a verb to suspend
coordination and complementation much like node raising, as in (a), then
analyses such as (b) are naturally offered by $\mathbf{L}$ for any such
interaction.  I folded the rug over, and the curtains under, the painting.
Steedman 1996:41
folded the rug over
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptPP\kern-1.0pt/\kern-1.0ptNP}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptPP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptPP\kern-1.0pt/\kern-1.0ptNP)}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptPP))\kern-1.0pt/\kern-1.0ptNP}$
$\colon\kern-1.0pt\lambda x\lambda y\lambda z.\mathit{fold}^{\prime}yxz$
$\colon\kern-1.0pt\lambda p.p\,\mathit{rug}^{\prime}$
$\colon\kern-1.0pt\lambda p\lambda q.q(\mathit{over}^{\prime}p)$
$<$$\mathbf{L}$
$\mathit{\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptPP\kern-1.0pt/\kern-1.0ptNP)}}$
$\mathit{\colon\kern-1.0pt\lambda f\lambda
g.f\,\mathit{rug}^{\prime}(\mathit{over}^{\prime}g)}$

The phenomenon is crosslinguistically and cross-constructionally available.
The following Turkish “split genitive” (interleaving of _man’s house_ and
_me_) is not entirely intonation-neutral in my Turkish, therefore we can think
of an analysis without $\mathbf{L}$; but, for those who see no difference from
the unsplit genitive, $\mathbf{L}$ could provide an analysis:414141This
distinction is important. If $\mathbf{L}$ is a freely-projecting combinator,
it cannot add such semantics. Adam-ın ben-i ev-i etkiledi. man-gen.3sg I-acc
house-poss.3s impressed $\mathit{NP\kern-1.0pt/\kern-1.0ptNP}$
$\mathit{NP}$acc
$\mathit{(S\kern-1.0pt/\kern-1.0pt(S\kern-0.3pt\backslash\kern-0.2ptNP))\kern-0.3pt\backslash\kern-0.2pt(NP\kern-1.0pt/\kern-1.0ptNP)}$
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle
acc}}}$ $\colon\kern-1.0pt\lambda
x.\mathit{poss}^{\prime}\,x\,\mathit{man}^{\prime}$ $\colon\kern-1.0ptme$
$\colon\kern-1.0pt\lambda q\lambda p.p(q\,\mathit{house}^{\prime})$
$\colon\kern-1.0pt\lambda x\lambda y.\mathit{impress}^{\prime}xy$
$>$$\mathbf{L}$×
$\mathit{\mathit{S\kern-0.3pt\backslash\kern-0.2pt(NP\kern-1.0pt/\kern-1.0ptNP)\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle
acc}}}}$ $\mathit{\colon\kern-1.0pt\lambda x\lambda
y.\mathit{impress}^{\prime}x(y\,\mathit{house}^{\prime})}$ $<$
$\mathit{\mathit{S\kern-0.3pt\backslash\kern-0.2pt(NP\kern-1.0pt/\kern-1.0ptNP)}}$
$\mathit{\colon\kern-1.0pt\lambda
y.\mathit{impress}^{\prime}\mathit{me}^{\prime}(y\,\mathit{house}^{\prime})}$
$<$
$\mathit{\mathit{S}\colon\kern-1.0pt\mathit{impress}^{\prime}\mathit{me}^{\prime}(\mathit{poss}^{\prime}\,\mathit{house}^{\prime}\mathit{man}^{\prime})}$
‘The man’s house impressed me.’ ‘It was the man’s house that impressed me.’

The split is not construction-specific in Turkish. In the following example,
_we surrounded_ intercalates _Hasan believe_ :  Hasan’ın biz-i kuşattı(-k) san
-dığı üniversite H-3s we-acc surrounded-1p believe rel.3s univ.
$\mathit{\mathit{S}_{\mathrm{\scriptstyle
3s}}\kern-1.0pt/\kern-1.0pt\mathit{IV}_{\mathrm{\scriptstyle 3s}}}$
$\mathit{IV\kern-1.0pt/\kern-1.0pt(IV\kern-1.0pt/\kern-1.0pt\mathit{NP}_{\mathrm{\scriptstyle
acc}})}$
$\mathit{VP\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle
acc}}}$
$\mathit{(IV\kern-0.3pt\backslash\kern-0.2ptVP)\kern-1.0pt/\kern-1.0pt\mathit{NP}_{\mathrm{\scriptstyle
acc}}}$
$\mathit{(NP\kern-1.0pt/\kern-1.0ptNP)\kern-0.3pt\backslash\kern-0.2pt(\mathit{S}_{\mathrm{\scriptstyle
3s}}\kern-2.0pt\mid\kern-2.0pt\mathit{NP}_{\mathrm{\scriptstyle}})}$
$<$$\mathbf{L}$
$\mathit{\mathit{(IV\kern-1.0pt/\kern-1.0pt\mathit{NP}_{\mathrm{\scriptstyle
acc}})\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle
acc}}}}$ $>\kern-2.0pt\mathbf{B}_{\times}$
$\mathit{\mathit{IV\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle
acc}}}}$ $>\kern-2.0pt\mathbf{B}_{\times}$
$\mathit{\mathit{\mathit{S}_{\mathrm{\scriptstyle
3s}}\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle acc}}}}$
$<$ $\mathit{\mathit{NP\kern-1.0pt/\kern-1.0ptNP}}$ ‘the university which
Hasan believes we surrounded’ Unlike the split genitive, there is no
grammatical variant where _bizi_ would not intercalate: *_Bizi Hasan’ın
kuşattı(-k) san-dığı üniversite_. This has been an open problem in Turkish
linguistics; see for example Kornfilt (1988, 2007); Moore (1998).

To recapitulate the discussion of $\mathbf{L}$ for CCG in particular, and for
completeness of mathematics of intercalation in general in the context of
surface configurationality, it is clear that disharmonic varieties of
$\mathbf{L}$ are nonprojective of command relations (Steedman, 2020a).

$\mathbf{L}$ as a combinator would be doubtful in the analytic base of natural
language because not all variants of $\mathbf{L}$ are on the same ground with
respect to Baxter properties. This is in sharp contrast with $\mathbf{B}$ and
$\mathbf{S}$ because both harmonic and disharmonic varieties of $\mathbf{B}$
and $\mathbf{S}$ satisfy Baxter’s condition on universal hierarchies,424242To
see this informally, let us assume that in the terminology of §4, any result
that can locally yield a tree would be considered locally meaningful. We will
use sequence description of §4 in lieu of categories for this; for example,
position 1 will yield the overall result of the entire sequence, that is, it
must be some function $\mathit{1\kern-2.0pt\mid\kern-2.0ptA}$ where
$\mathit{A}$ is likewise positions in the sequence turned into categories and
‘ $\kern-2.0pt\mid\kern-2.0pt$ ’ is some directionality. Because $\mathbf{L}$
abstracts over two arguments we need a wider context to study the impossible
Baxter hierarchies 2413 and 3142. Take 24135 and 53142. 1’s in the these
sequences will be typed as giving the overall result for the tree. All others
must appear as argument categories consistent with the directionality in the
sequence to give rise to a local tree for the entire sequence, following the
enumeration of Stanojević and Steedman (2021) for linguistic examples. The
following combinations show that using disharmonic $\mathbf{L}$ would produce
analyses of illicit 24135 and 53142.  2 4 1 3 5 $\mathit{2}$
$\mathit{4\kern-1.0pt/\kern-1.0pt5}$
$\mathit{(1\kern-0.3pt\backslash\kern-0.2pt4)\kern-1.0pt/\kern-1.0pt3}$
$\mathit{3\kern-0.3pt\backslash\kern-0.2pt2}$ $\mathit{5}$
$>\kern-2.0pt\mathbf{B}_{\times}$
$\mathit{\mathit{(1\kern-0.3pt\backslash\kern-0.2pt4)\kern-0.3pt\backslash\kern-0.2pt2}}$
$<$$\mathbf{L}$×
$\mathit{\mathit{(1\kern-0.3pt\backslash\kern-0.2pt2)\kern-1.0pt/\kern-1.0pt5}}$
$>$ $\mathit{\mathit{1\kern-0.3pt\backslash\kern-0.2pt2}}$ $<$ $\mathit{1}$ 5
3 1 4 2 $\mathit{5}$ $\mathit{3\kern-1.0pt/\kern-1.0pt2}$
$\mathit{(1\kern-1.0pt/\kern-1.0pt4)\kern-0.3pt\backslash\kern-0.2pt3}$
$\mathit{4\kern-0.3pt\backslash\kern-0.2pt5}$ $\mathit{2}$
$<\kern-2.0pt\mathbf{B}_{\times}$
$\mathit{\mathit{(1\kern-1.0pt/\kern-1.0pt4)\kern-1.0pt/\kern-1.0pt2}}$
$>$$\mathbf{L}$×
$\mathit{\mathit{(1\kern-1.0pt/\kern-1.0pt2)\kern-0.3pt\backslash\kern-0.2pt5}}$
$<$ $\mathit{\mathit{1\kern-1.0pt/\kern-1.0pt2}}$ $>$ $\mathit{1}$ which
leaves all the preceding examples in want of analyses.

Turning to combinator $\mathbf{S}$ and to the question of minimality of
projection, we can see that its dependency projection is more than what is
basically required, which is handling one dependency at a time in merging
constituents; recall (9i).

Empirically, the syntactic world that is crosslinguistically carved by
$\mathbf{S}$ shows all the signs of a headed construction, that is, as
something that does not need free projection, in other words, an invariant.

CCG’s $\mathbf{S}$ analyzes parasitic gaps (Ross, 1967; Bresnan, 1977;
Taraldsen, 1979; Chomsky, 1982; Engdahl, 1983), for example _the articles that
I filed _ without reading _ p_, where ‘_p’ is the parasitic gap. It is
considered to be parasitic on the first gap because, without the first gap, we
would get ungrammaticality: *_the articles that I filed them without reading_.
Its categorial syntax-semantics was discovered by Szabolcsi (1983) for the
special case of the category of VP, and identified by Steedman (1987) to be an
instance of $\mathbf{S}$, in this particular case for the backward crossing
variety.

It is a projecting combinator of CCG that handles multiple dependencies in one
step. We need a closer look to see this property:

filed | without | reading
---|---|---
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP}$ | $\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt(S\kern-0.3pt\backslash\kern-0.2ptNP))\kern-1.0pt/\kern-1.0pt\mathit{VP}_{\mathrm{\scriptstyle ing}}}$ | $\mathit{\mathit{VP}_{\mathrm{\scriptstyle ing}}\kern-1.0pt/\kern-1.0ptNP}$
$\colon\kern-1.0pt\lambda x\lambda y.\mathit{file}^{\prime}xy$ |  $\colon\kern-1.0pt\lambda p\lambda q\lambda x.\mathit{wout}^{\prime}(px)(qx)$ |  $\colon\kern-1.0pt\lambda x\lambda y.\mathit{read}^{\prime}xy$
| $>\kern-2.0pt\mathbf{B}$
|
$\mathit{\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt(S\kern-0.3pt\backslash\kern-0.2ptNP))\kern-1.0pt/\kern-1.0ptNP}\colon\kern-1.0pt\lambda
p\lambda q\lambda x.\mathit{wout}^{\prime}(\mathit{read}^{\prime}px)(qx)}$
$<\kern-2.0pt\mathbf{S}_{\times}$
$\mathit{\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP}\colon\kern-1.0pt\lambda
w\lambda
x.\mathit{wout}^{\prime}(\mathit{read}^{\prime}wx)(\mathit{file}^{\prime}wx))}$

Notice that it is not the lexically specified $x$ dependency emanating from
_without_ which $\mathbf{S}$ handles; it is the one within $p$ and $q$ of
_without_ symbolized by $w$ in the bottom row. No other CCG combinator doubly
peeks deep in one step.

This is altogether different than lexically specified multiple dependencies,
for example control verbs. If we think of an object-control verb as having the
following category, the $x$’s in the predicate-argument structure may look
like similarly multiple use; however, this is controlled by an element of
grammar, namely _persuade_ , much like $x$ of _without_ above. persuade :=
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP\kern-1.0pt/\kern-1.0ptNP}$$\colon\kern-1.0pt\lambda
x\lambda p\lambda y.\mathit{persuade}^{\prime}(px)xy$,

In the coordination of multiple clauses with multiple dependencies, the
situation is same as that of _persuade_ : the head of conjunction, not
multiple projection of multiple dependencies, handles the correspondence, for
example for English with the category below when $\mathit{X}$s are residual
($p$ and $q$ being $\lambda x.\cdots x$):434343We are here assuming pointwise
recursion on the semantic types of $\mathit{X}$ at the level of the ground
element, following Gazdar (1980); Partee and Rooth (1983); Steedman (2012).
and :=
$\mathit{(X\kern-0.3pt\backslash\kern-0.2ptX)\kern-1.0pt/\kern-1.0ptX}$$\colon\kern-1.0pt\lambda
p\lambda q.\mathit{and}^{\prime}(p)(q)$

We can see the difference made by lexical elements even in double-control
constructions:  IndonesianMobil mana yang kau=coba $[$ jual $]$// car which
FOC 2sg=Uv.try UV.sell// ‘Which car did you try to sell?’ Arka 2014:(2)//

Assuming we have _coba_ ‘try’ :=
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle
pro}}\kern-1.0pt/\kern-1.0pt(VP\kern-1.0pt/\kern-1.0ptNP)}$$\colon\kern-1.0pt\lambda
p\lambda x\lambda y.\mathit{try}^{\prime}(pyx)x$, with conditions on embedded
subject being matrix pronominal due to preposing (Arka and Manning, 1998),
multiple-control is lexically mediated by the control verb, therefore it is
not a case of handling multiple dependencies in one analytic step. (It is
considered multiple-control because the syntactic correspondents of both $x$
and $y$,
‘$\mathit{\kern-0.3pt\backslash\kern-0.2pt\mathit{NP}_{\mathrm{\scriptstyle
pro}}}$’ and ‘$\mathit{\kern-0.3pt\backslash\kern-0.2ptNP}$’, are realized in
the matrix clause.)444444We are following Kana (1986) in assuming that
Indonesian is basically SVO. In the AV voice _coba_ is realized as _mencoba_ ,
and it is ordinary $\mathit{VP}$ control: [exno=i,numoffset=2em] Aku
mencoba(S\NP)/VP $[$menjual mobil itu$]$.// 1sg AV.try AV.sell car that// ‘I
tried to sell the car.’ Arka 2014:(9a)// In double control, both matrix and
complements verbs are UV-voiced, where ‘car’ in (9.2) is syntactic subject in
the matrix clause and in the complement clause according to Arka. My analysis
of double control is based on his analysis: ‘car which FOC’ would be type-
raised as syntactic subject in an SVO language, that is, as
$\mathit{S\kern-1.0pt/\kern-1.0pt(S\kern-0.3pt\backslash\kern-0.2ptNP)}$. I do
not analyze double control as object-extraction, concurring with Arka. This
subject corresponds—without an additional layer of argument structure—to the
placeholder for the commanded argument of ‘sell’; it is not the actor. In this
sense I believe the pronominal restriction on shared agent argument ‘you’
points to non-actor preposing.

In summary, lexical double-use of a resource is not what $\mathbf{S}$ does.
$\mathbf{S}$ is multiple dependency handling in one step of projection. We
must find languages where this is necessary, not just sufficient.

There is plethora of analyses for parasitic gaps, and further assessment of
multiple dependency projection is needed. Culicover and Postal (2001) is a
comprehensive volume on the subject. $\mathbf{S}$-analysis of the construction
implies that it is not a species of coordination. Williams (1990) however
notes that the parasitic gap of the parasitic gap construction is always
optional (e.g. _the articles that I filed without reading them_), therefore
_before_ in (9.2) can be treated as coordinating or subordinating conjunction
licensing both examples (also, _without_):  Who would you warn _ before
striking _ Williams 1990:265 Who would you warn _ before striking him

Optionality is true in cases where offline judgment tests and online reading
have been used to justify multiple dependency handling in one fell swoop: What
did the attempt to repair _ ultimately damage _/it ? adapted from Phillips
2006:(3c)

Williams also notes that there is a wide range of acceptability in English
parasitic gap environments. Therefore an analytic $\mathbf{S}$ implying
universal access to it seems questionable.

I take Williams’s assessment that, as one goes down the list below, from most
acceptable to least, the structure is less and less coordinate-like, to be an
indicator that it must be a headed construction, not necessarily by true
coordination (see Niinuma (2010) for some reasons for that), but in any case
not part of invariant projection. Who did you meet and dislike Williams
1990:279 What did you file before reading The man who people who meet like Who
would pictures of upset Who did you promise friends of to try to find

For example, Kathol (2001) notes that the parasitic gap construction in German
is lexically headed by a select set of prepositions.454545A sublexical head
for the construction is also a possibility which has been realized. In
Turkish, I cannot think of a parasitic gap configuration without the
involvement of the ablative _-den_ ‘from’ suffix, with or without verbal
negation. It has been noted earlier, for example by Engdahl (1983), that
languages like Turkish can opt out of the construction because of optional
pro-drop. It seems that we must concentrate on consequences of the headedness
of the construction by a closed class of grammatical elements such as affixes
and function words.

In summary, there seems to be good reasons to consider an intercalating
lingustic invariant to be not empirically adequate, and simultaneous multiple
dependency projection to be construction-specific, that is, variant, across
languages.

###  9.3 Mobile logical form and grammar

With a mathematical understanding of the proposed invariants and why some of
them can be considered variant, we can have a closer look at the most
important variant for linguistic action, the verb. Verbal categories
materialize as follows using mobile semantics of §8, for example for
_persuade_ :  persuaded :=
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP}$$\colon\kern-1.0pt\lambda
x\lambda p\lambda y.\mathit{persuade}^{\prime}.\mathbf{0}\,(px)xy$ persuaded
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP}$$\colon\kern-1.0pt\lambda
x\lambda p\lambda y.\mathit{persuade}^{\prime}.\mathbf{0}\,(px)xy$ In (a) we
use the declarative CCG notation, where to the left of ‘:=’ is the surface
form of the verb. We have been displaying such categories like (b) in
analysis.

The mobile asynchrony, or offlineness, is invariably part of all lexical
mobile logical forms as outcome of their semantics, using ‘$\mathbf{0}$’ as a
suffix in all linguistic predication. (Note that $x,p,y$ are placeholders,
respectively corresponding to $\mathit{\kern-1.0pt/\kern-1.0ptNP}$,
$\mathit{\kern-1.0pt/\kern-1.0ptVP}$, and
$\mathit{\kern-0.3pt\backslash\kern-0.2ptNP}$ because of the order of
specification, not semantic constants of _persuade_. As such they cannot
receive ‘$\mathbf{0}$’.)

With this categorization, the bounded constructions in which this verb can
participate, and the unbounded ones, unfold as follows in the course of the
surface-analytic process of single computation:  Mary persuaded John to study
$\mathit{Mary}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP}$
$\mathit{NP}$ $\mathit{VP\kern-1.0pt/\kern-1.0ptIV}$ $\mathit{IV}$
$\colon\kern-1.0pt\mathit{mary}^{\prime}.\mathbf{0}$ $\colon\kern-1.0pt\lambda
x\lambda p\lambda y.\mathit{persuade}^{\prime}.\mathbf{0}\,(px)xy$
$\colon\kern-1.0pt\mathit{john}^{\prime}.\mathbf{0}$ $\colon\kern-1.0pt\lambda
p.p$ $\colon\kern-1.0pt\lambda x.\mathit{study}^{\prime}.\mathbf{0}\,x$ $>$
$\mathit{\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP}\colon\kern-1.0pt\lambda
p\lambda
y.\mathit{persuade}^{\prime}.\mathbf{0}\,(p\,\mathit{john}^{\prime}.\mathbf{0})\mathit{john}^{\prime}.\mathbf{0}\,y}$
$>$ $\mathit{\mathit{VP}\colon\kern-1.0pt\lambda
x.\mathit{study}^{\prime}.\mathbf{0}\,x}$ $>$
$\mathit{\mathit{S\kern-0.3pt\backslash\kern-0.2ptNP}\colon\kern-1.0pt\lambda
y.\mathit{persuade}^{\prime}.\mathbf{0}\,(\mathit{study}^{\prime}.\mathbf{0}\,\mathit{john}^{\prime}.\mathbf{0})\mathit{john}^{\prime}.\mathbf{0}\,y}$
$<$
$\mathit{\mathit{S}\colon\kern-1.0pt\mathit{persuade}^{\prime}.\mathbf{0}\,(\mathit{study}^{\prime}.\mathbf{0}\,\,\mathit{john}^{\prime}.\mathbf{0})\mathit{john}^{\prime}.\mathbf{0}\,\mathit{mary}^{\prime}.\mathbf{0}}$

This man, | Jenny | knows | Mary | persuaded | to | study
---|---|---|---|---|---|---
$\mathit{S\kern-1.0pt/\kern-1.0pt(S\kern-1.0pt/\kern-1.0pt\mathit{NP}_{\mathrm{\scriptstyle+topic}})}$ | $\mathit{NP}$ | $\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptS}$ | $\mathit{NP}$ | $\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP}$ | $\mathit{VP\kern-1.0pt/\kern-1.0ptIV}$ | $\mathit{IV}$
$\colon\kern-1.0pt\lambda p.p$ | $\colon\kern-1.0pt\mathit{jenny}^{\prime}.\mathbf{0}$ | $\colon\kern-1.0pt\lambda p\lambda x.$ | $\colon\kern-1.0pt\mathit{mary}^{\prime}.\mathbf{0}$ | $\colon\kern-1.0pt\lambda x\lambda p\lambda y.$ | $\colon\kern-1.0pt\lambda p.p$ | $\colon\kern-1.0pt\lambda x.$
$(\mathit{def}^{\prime}.\mathbf{0}\,\,\mathit{man}^{\prime}.\mathbf{0}$ |  | $\mathit{know}^{\prime}.\mathbf{0}\,p\,x$ |  | $\mathit{persuade}^{\prime}.\mathbf{0}\,(px)xy$ |  | $\mathit{study}^{\prime}.\mathbf{0}\,x$
$\wedge\,\mathit{topic}^{\prime}.\mathbf{0}\,\,\mathit{man}^{\prime}.\mathbf{0})$ |  |  |  |  | $>$
|  |  |  |  | $\mathit{\mathit{VP}\colon\kern-1.0pt\lambda x.\mathit{study}^{\prime}.\mathbf{0}\,x}$
|  |  |  |  | $<\kern-2.0pt\mathbf{T}$
|  |  |  |  | $\mathit{\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)}}$
|  |  |  |  | $\mathit{\colon\kern-1.0pt\lambda p.p(\lambda x.\mathit{study}^{\prime}.\mathbf{0}\,x)}$
|  |  |  | $<\kern-2.0pt\mathbf{B}_{\times}$
|  |  |  | $\mathit{\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP}}$
|  |  |  | $\mathit{\colon\kern-1.0pt\lambda x\lambda y.\mathit{persuade}^{\prime}.\mathbf{0}(\mathit{study}^{\prime}.\mathbf{0}\,x)xy}$
|  |  | $>\kern-2.0pt\mathbf{T}$ |  |  |
|  |  | $\mathit{\mathit{S\kern-1.0pt/\kern-1.0pt(S\kern-0.3pt\backslash\kern-0.2ptNP)}}$ |  |  |
|  |  | $\mathit{\colon\kern-1.0pt\lambda p.p\,\mathit{mary}^{\prime}.\mathbf{0}}$ |  |  |
|  |  | $>\kern-2.0pt\mathbf{B}$
|  |  | $\mathit{\mathit{S\kern-1.0pt/\kern-1.0ptNP}}$
|  | $\mathit{\colon\kern-1.0pt\lambda x.\mathit{persuade}^{\prime}.\mathbf{0}(\mathit{study}^{\prime}.\mathbf{0}\,x)x\,\mathit{mary}^{\prime}.\mathbf{0}}$
|  | $>\kern-2.0pt\mathbf{B}$
|  | $\mathit{\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptNP}}$
|  | $\mathit{\colon\kern-1.0pt\lambda x\lambda y.\mathit{know}^{\prime}.\mathbf{0}(\mathit{persuade}^{\prime}.\mathbf{0}(\mathit{study}^{\prime}.\mathbf{0}\,x)x\,\mathit{mary}^{\prime}.\mathbf{0})\mathit{y}^{\prime}}$
| $>\kern-2.0pt\mathbf{T}$ |  |  |  |  |
| $\mathit{\mathit{S\kern-1.0pt/\kern-1.0pt(S\kern-0.3pt\backslash\kern-0.2ptNP)}}$ |  |  |  |  |
| $\mathit{\colon\kern-1.0pt\lambda p.p\,\mathit{jenny}^{\prime}.\mathbf{0}}$ |  |  |  |  |
| $>\kern-2.0pt\mathbf{B}$
| $\mathit{\mathit{S\kern-1.0pt/\kern-1.0ptNP}}$
| $\mathit{\colon\kern-1.0pt\lambda
x.\mathit{know}^{\prime}.\mathbf{0}(\mathit{persuade}^{\prime}.\mathbf{0}(\mathit{study}^{\prime}.\mathbf{0}\,x)x\,\mathit{mary}^{\prime}.\mathbf{0})\mathit{jenny}^{\prime}.\mathbf{0}}$
$>$
$\mathit{\mathit{S}\colon\kern-1.0pt\mathit{know}^{\prime}.\mathbf{0}}$
$\mathit{(\mathit{persuade}^{\prime}.\mathbf{0}(\mathit{study}^{\prime}.\mathbf{0}\,(\mathit{def}^{\prime}.\mathbf{0}\,\mathit{man}^{\prime}.\mathbf{0}\,\wedge\,\mathit{topic}^{\prime}.\mathbf{0}\,\mathit{man}^{\prime}.\mathbf{0}))(\mathit{def}^{\prime}.\mathbf{0}\,\mathit{man}^{\prime}.\mathbf{0}\,\wedge\,\mathit{topic}^{\prime}.\mathbf{0}\,\mathit{man}^{\prime}.\mathbf{0})\,\,\mathit{mary}^{\prime}.\mathbf{0})\mathit{jenny}^{\prime}.\mathbf{0}}$

In (a), it is explicit that John is persuaded and he studies. In (b), this is
upheld, for ‘this man’; see (7.2) for the logical command relation and its
notation.

All the semantic differences and surface identity of ‘promise/expect/want’
from ‘persuade’ in similar experiences as above then follows from these verbs
having the same surface recipe (syntactic category) but different semantics,
which we write below without the syntactic category to avoid
repetition:464646As with planning, the directional variants of rules of
combination make a difference in how elements are interpreted. Steedman (2000)
shows that the options for language are principally restricted, to harmonic
and adjacent compositions such as ($>\kern-2.0pt\mathbf{B}$) and
($<\kern-2.0pt\mathbf{B}$), and crossing and adjacent ones such as
($>\kern-2.0pt\mathbf{B}_{\times}$) and ($<\kern-2.0pt\mathbf{B}_{\times}$),
as in (9.3). persuaded := $\lambda x\lambda p\lambda
y.\mathit{persuade}^{\prime}.\mathbf{0}\,(px)xy$ promised := $\lambda x\lambda
p\lambda y.\mathit{promise}^{\prime}.\mathbf{0}\,(py)xy$ expected := $\lambda
x\lambda p\lambda y.\mathit{expect}^{\prime}.\mathbf{0}\,(px)y$ wanted :=
$\lambda x\lambda p\lambda y.\mathit{want}^{\prime}.\mathbf{0}\,(px)y$

It will be noticed that in (9.3b) we make crucial use of another functionality
we have seen before: type-raising (7.3). In the domain of organized action it
corresponds to affordances (Steedman, 2002). The CCG claim is that in language
it corresponds to all arguments of verbs having case, for example nominative
and accusative in Latin, ergative and absolutive in Dyirbal, and mixed or
partial in others depending on verbal categories. Its syntactic category is
language dependent, and its semantics is invariant, as shown in (7.3).

This means that we could write (9.3a) with type-raising too, as below, with
same surface and logical command relations, where all arguments are “cased” by
being type-raised. Now all arguments take their subcategorizers (the verbs) as
argument.  Mary persuaded John to study $\mathit{Mary}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP}$
$\mathit{NP}$ $\mathit{VP\kern-1.0pt/\kern-1.0ptIV}$ $\mathit{IV}$
$\colon\kern-1.0pt\mathit{mary}^{\prime}.\mathbf{0}$ $\colon\kern-1.0pt\lambda
x\lambda p\lambda y.\mathit{persuade}^{\prime}.\mathbf{0}\,(px)xy$
$\colon\kern-1.0pt\mathit{john}^{\prime}.\mathbf{0}$ $\colon\kern-1.0pt\lambda
p.p$ $\colon\kern-1.0pt\lambda x.\mathit{study}^{\prime}.\mathbf{0}\,x$
$<\kern-2.0pt\mathbf{T}$
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP)}$
$\mathit{\colon\kern-1.0pt\lambda p.p\,\,\mathit{john}^{\prime}.\mathbf{0}}$
$<$
$\mathit{\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP}\colon\kern-1.0pt\lambda
p\lambda
y.\mathit{persuade}^{\prime}.\mathbf{0}\,(p\,\mathit{john}^{\prime}.\mathbf{0})\mathit{john}^{\prime}.\mathbf{0}\,y}$
$>$ $\mathit{\mathit{VP}\colon\kern-1.0pt\lambda
x.\mathit{study}^{\prime}.\mathbf{0}\,x}$ $<\kern-2.0pt\mathbf{T}$
$\mathit{(S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-0.3pt\backslash\kern-0.2pt((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)}$
$\mathit{\colon\kern-1.0pt\lambda p.p(\lambda
x.\mathit{study}^{\prime}.\mathbf{0}\,x)}$ $<$
$\mathit{\mathit{S\kern-0.3pt\backslash\kern-0.2ptNP}\colon\kern-1.0pt\lambda
y.\mathit{persuade}^{\prime}.\mathbf{0}\,(\mathit{study}^{\prime}.\mathbf{0}\,\mathit{john}^{\prime}.\mathbf{0})\mathit{john}^{\prime}.\mathbf{0}\,y}$
$>\kern-2.0pt\mathbf{T}$
$\mathit{S\kern-1.0pt/\kern-1.0pt(S\kern-0.3pt\backslash\kern-0.2ptNP)}$
$\mathit{\colon\kern-1.0pt\lambda p.p\,\mathit{mary}^{\prime}.\mathbf{0}}$ $>$
$\mathit{\mathit{S}\colon\kern-1.0pt\mathit{persuade}^{\prime}.\mathbf{0}\,(\mathit{study}^{\prime}.\mathbf{0}\,\,\mathit{john}^{\prime}.\mathbf{0})\mathit{john}^{\prime}.\mathbf{0}\,\,\mathit{mary}^{\prime}.\mathbf{0}}$
It is important to keep in mind that case only targets verb-like lexical
elements, that is, it is a second-order (i.e. structural) function which only
depends on eventful singularities in a lexicon. What makes it an empirical
universal is its invariant relation to such singularities. And it does so for
all arguments, nominal and clausal, as above. Notice that the clausal argument
_to study_ is also cased by being type-raised.

With this in mind, it must be evident that even in language everything can be
treated as a function anyway, including entities and predicates, much like
daily organized activity and affordances, therefore offlineness of language
only comes from the speakers-hearers deliberately letting go of change in
expressing themselves. The asynchrony suffixes that we have added in this
section are reflections of the common understanding that people know the
difference between acting and speaking and hearing about acting. Knowing the
difference does not preclude them from continuing to track change, as full
representation of for example (9.3) in mobile semantics shows below; cf. (7.2)
for organized action.  persuaded :=
$\mathit{((S\kern-0.3pt\backslash\kern-0.2ptNP)\kern-1.0pt/\kern-1.0ptVP)\kern-1.0pt/\kern-1.0ptNP}$
$\colon\kern-1.0pt\lambda x\lambda p\lambda
y.\mathit{persuade}^{\prime}.\mathbf{0}\,(px)xy$ (pre:
$\mathit{not}^{\prime}\mathit{do}^{\prime}(x,p),\mathit{know}^{\prime}(y,x)$
add: $\mathit{attempt}^{\prime}(x,p),\mathit{convince}^{\prime}(y,x)$ del: $-$
).$\mathbf{0}$ Only the linguistic logical form and semantic conditions of the
verbal form are necessarily offlined and consequently asynchronic. Syntax is
the active element when computation is driven by the syntactic category,
revealing the semantics in locked-step. We assume that all linguistic elements
are of this dual-functional character and uniquely representational in nature,
taking part in a single computation of dealing with change, recording and
reporting it.

Affordances and type-raising have implications for what can be offlined
without letting go of tracking change. In the case of langauge, it is the
lexical verb’s projection that must be heeded, otherwise case could not always
be a second-order (i.e. structural) function.

Interesting consequences arise for abstracting over a verb’s action or event,
that is, making it opaque in content. (Recall that it does not seem to be
necessary for language, although generative grammarians might find it useful,
employing its functional equivalent: movement.) It means that $\mathbf{D}$ in
action, which we dubbed ‘subcomposition’ in (7.3), can be a spandrel for
deceit in onlineness, whereas language would use lexical or surface ambiguity
for these functions. This is because it creates predicate abstractions, that
is, nonlexical predicates, as a means of covertness in action without needing
offlineness of language, that is, not having to keep silent about something to
be able to do covert action. We can conceive a common base for language and
planning in the simple mathematics of $\mathbf{A}$, $\mathbf{T}$, and
$\mathbf{B}$, without sacrificing their differences and potential sources of
divergence, for example $\mathbf{S}$, $\mathbf{D}$ and $\mathbf{L}$.

##  10 The proposed synthesis in perspective

Three mainstream approaches to semantics in linguistics are interpretation of
a formal system with model-theoretic truth-conditional semantics (Montague,
1970), interpretation of thematic structure from syntactic structure
(Grimshaw, 1990; Hale and Keyser, 2002; Borer, 2005), and interpretation of
surface structure from conceptual structure (Talmy, 1988; Jackendoff, 1990;
Langacker, 1987), none of which addresses the Frame Problem. The problem is
inherently procedural.

We looked at whether there is something to be gained if we conceive the main
task of semantics as understanding change, both in speaking-signing and
acting, which includes tracking it and coping with it. Tracking requires
internal representation of action, online or offline, and coping requires
reference to past, current and future states and ways to deal with them. The
implication is that all knowledge is procedural and prone to side effects. For
example, understanding a verb means knowing what it changes and what it
doesn’t, same as understanding an action means knowing what it changes and
what it doesn’t. Their categorization is obviously domain-specific, but, their
why and how questions appear to target the same problem.

This way of thinking connects language and everyday planning in circumscribed
ways to add to the debate that language can first piggyback on then coevolve
with some other trait (Coolidge and Wynn, 2005; Deacon, 1997; Tomasello, 1999;
Jackendoff and Pinker, 2005; Reuland, 2010; Steedman, 2002, 2014; Hrdy, 2011;
Ullman, 2004). I adopted a Marrian (1977) strategy and made the proposal
explicit at the algorithmic (middle) level, to try to avoid pitfalls of cross-
level purported dichotomies such as the one in grammar/lexicon, which
supposedly corresponds to procedural/declarative distinction at the substrate
(lowest) level according to Ullman (2004). Another level-3 concern is the
supposed language regions of the substrate or causal role of lateralization in
language modularity, which have been questioned by Deacon (1997). Yet another
one is “desymbolization” of Reuland (2010), which means that Chomskyan “merge”
just works independent of semantics, which, if taken technically at the level
of algorithms, cannot support this level if correspondence theories are right.

My only appeal to Marr’s level-1 has been for the purpose of showing that some
algorithms serve to represent offlineness of language and onlineness of action
faithfully. This is concern for the problems rather than their descriptions,
without a dichotomy at the algorithmic level. For us to assess why expressing
thought with language or with action might differ, for a start we must be able
to show their differential effects in environment control of agents doing
actions versus talking about actions.

To make the proposal explicit for these algorithms, I adopted categorial
grammar without multiple dependency projection, which has come to accommodate
rich vocabulary of semantic interpretation in a Logical Form (LF), diverging
from exclusively syntactic ways of dealing with LF (see Carlson (1983) for
discussion), to the point of answering meaningful questions about an utterance
(Lewis and Steedman, 2013; Steedman, 2019). The LF is the only level of
representation in CCG, not for reasons of linguistic-philosophical parsimony
but for its empirical dividends at level-2 and level-3, by which we can
computationally study how children acquire language (Abend et al., 2017). In
current work I turn the LF into a Mobile Logical Form (MLF) of _fluents_ ,
i.e. dynamically changing predicates for nonmonotonic reasoning, whose
relevance to planning has been known (Lifschitz, 2002; Steedman, 2002). I do
this by incorporating ideas from mobile communication theory ($\pi$-calculus)
of Milner (1993). I make use of it to show that concurrent computation when
coupled with a locally interpretable grammar, by which I mean a grammar in
which all elements are compositional and locally interpretable, does not
require multi-level level-3 architectures or separate level-2 computations to
incorporate parallelism into language and action, at the same time supporting
language for sequential expression of thought (Fodor, 1975).

The central claim is that uniquely human characteristics of language-specific
categorization and its acquisition can be bootstrapped by the ability to go
offline, the ability to let go of pursuing change implicated by speech-sign. I
argued that spatiotemporal semantics must move up to mobile semantics to make
the connection explicit. The implication for time course of evolution of the
substrate is that mobile meanings and online thinking about plans may be the
representational support for offline thinking. To see the support, how mobile
meanings evolve is worth reiterating.

The semantics of $\pi$-calculus that concerned us is the standard reduction
rule of concurrent computation, from (8.2):

($\bar{x}z$$.P$ | $xy$$.Q$) $\Rightarrow$ ($P$ | $Q[z/y]$)
It means that processes $P$ and $Q$, whose timing and duration are not known
to each other because ‘ |’ means ‘concurrent’, meet by $P$ supplying $Q$ with
an input in the channel $x$. ($P$ sends and $Q$ receives in this notation.)
What is supplied, $z$, and what is expected, $y$, are local. Semantics of
language and planning consists solely of such processes in their mobile
logical forms (MLFs).

Mobile semantics’ semantics is crucial in studying offlineability of language
and its connections to planning. All MLF objects of language are considered
terminal processes (and suffixed as such, with the “.$\mathbf{0}$ process”),
whereas no planned action is a terminal process unless deliberately specified
as such (for example, seeking shelter in dancing in the rain example (8.4)),
because the communicator has to continue to adjust to states of affairs in the
world.474747“.$\mathbf{0}$” is a level-2 process, which is part of the
algorithmic system. It is related to the level-1 concern for understanding
letting go and not being able to do so. No claim is made about its physical or
psychological grounding at level-3. One connection is Barsalou’s 1999
“perceptual simulators”, which are modal rather than amodal top-down _and_
bottom-up symbolizations, as befits a level-3 concept. However we note that
the ‘let go’ of change implicated by .$\mathbf{0}$ in language does not depend
on the success of the simulation. It successfully terminates, no matter what
the world makes of it.  I covered some examples of MLFs of planned action and
language to support the idea.

Mobility in the logical form brings to discussion the role of semantics in a
competence grammar, which is a top level concept according to Marr. Here too I
started at the algorithmic (i.e. middle) level to make it explicit that
Putnam’s (1975) distinction of expert knowledge of meaning of words, say
$gold^{\prime}$ for the word _gold_ , and the “collective linguistic body’s”
knowledge of the word, must both be _expressed_ as
${gold}^{\prime}.\mathbf{0}$. This is the socio-linguistic meaning of the word
_gold_ , and it has nothing to do with gold expertise, that is, what
$\mathit{gold}^{\prime}$ means to the bearer of that knowledge. It is social,
or _shared_ psychological spaces in Sapir 1933/1949:17-18 terminology (_not_
psychological states), in the sense of being necessarily exchanged. It is
linguistic in the sense that personal expressions are always terminal
processes. The difference is in the procedural semantics of personal knowledge
reflected in personal meanings of $gold^{\prime}$ for the common folk and the
expert, and that has nothing to do with linguistic competence reflected in
$\mathit{gold}^{\prime}$.$\mathbf{0}$. A representational support to clarify
the distinction is necessary but not sufficient.

We might now appear to be at an impasse in taking an internalist or
externalist position in relation of semantics to syntax. The Twin Earth
argument (Putnam, 1975) pointed out that having the same surface expression
does not mean having the same thought. My proposal for studying this
phenomenon is to be explicit at the middle level about how not to directly
ground linguistic LFs in the world (cf. Partee (1981); Johnson-Laird (1983)),
and leave it at that, and about how that differs in representation of online
action.484848There is a further dimension to the debate on representationalism
in cognitive science, which revolves around the idea of whether
representations are empirically necessary to understand cognition; see for
example Fodor (1981); Beer (2003); Mirolli (2012) for the debate. Attacking
the problem starting at Marr level-2 has the implication that positing some
representations may leverage bridge theories between levels, and they might
allow us to explore connections at the problem level rather than solution
level. Dynamic systems theorists who tend to eschew positing representations
at level-3 can do so mainly because their time series computations at level-3
report their results back to level-2 mechanisms for example in analog
computations, which are themselves representational to carry out the
computation (Bozşahin, 2018). _That_ mechanics has to be representational. A
further implication is that, unlike Marconi’s (1997) multiple inward/outward
competence, called inferential/referential competence, we can work with one
notion of competence, of connecting syntax and semantics and their projection
all the way to surface structure, no more no less. This is analytic
competence, much like we argued for for planning in Section 7 and for language
in Section 9. It differs from Chomsky’s notion of uniqueness of syntactic
competence in having to carry terminal processes of semantics in lock-step
with syntax. This ability is not acquired from performance, although the
knowledge of which meanings go with which forms is.

A grammar and its model can be conceived to be different but causally related
species, Vygotsky-style, even Schopenhauer, and we can maintain the uniqueness
of competence without idealistic interpretations, both for grammars of
languages and plans.

##  11 Discussion

Conceiving semantics as semantics of change, planning as scripted worldview
update in a limited channel of mobility, and language as terminal semantic
processes working under universal syntactic constraints reveals a problem
space, not solution space, for common understanding of language and planning.
This space can therefore be assumed to have already incorporated thoughts,
impressions and expressions about the world.

It allows us to ask the following question: Why do we build these views? It
must have something to do with putting all of it to online and offline use,
for control of environment. We can conceive this control as a closed-loop,
that is, a system which is always responsive in its inputs to what it
produces, but also an open-loop, that is, a system with some internal
preferences for desirable input independent of output, choosing a world to be
in rather than coerced to be in it. In this sense it is genuine control. (e.g.
If in my arm I have muscle soreness and I want to limit responses demanded by
environment so that it can heal, I can put it in braces, in effect causing
internal restructuring to avoid certain external demands, choosing to be in a
certain niche.) Systems theory and computer science can be combined to address
philosophical problems provided we avoid the computer metaphor (Cisek, 1999).
I add that we can avoid all metaphors at level-1 and level-2 and study
metaphors at level-3, which seems to be a real need. Computer science and
control systems theory are there to provide transparent working principles at
level-2 to assess claims.

Computer science’s appeal in exploring human practice is its unique ability to
show transparently that a simple mechanism to understand complex behavior need
not itself become complex as the behavior becomes more complex. (Hiding this
transparency, either deliberately or accidentally, is the political force of
the computer.) Transparency is the key in building confidence in a model in
this way of thinking. The daredevil spirit of the process (e.g. _procedural
epistemology_ of Abelson, Sussman and Sussman (1985)) is admittedly difficult
to come to grips with for this reason. However, white-box modeling with the
computer is the bedrock of computational ideas for understanding complex human
behavior, including language and planning, and perhaps even more.

About another daredevil approach in a seemingly unreachable domain,
consciousness, Daniel Dennett once said that Julian Jaynes attempted “software
archeology” in search of origin of consciousness (Dennett, 1986).

Jaynes (1976) had caused quite a stir in the 1970s, which continues these days
as a love-or-hate affair with Jaynes. He suggested that human consciousness is
a recent event, reported on historical record around second millennium B.C.,
which piggybacked on language, which piggybacked on unconscious planned action
and its admonitoring—in the case of Jaynes by gods, which started as the
mind’s coping with hallucinations caused by change of habitat and historic
upheavals, i.e. loss of god-talk.

Although we are not concerned with consciousness in the article, and what
Jaynes says about its recency is difficult to believe, the way he argued is
what prompted Dennett to call it _software_ archeology. Jaynes appealed to
what Dennett calls a “top-down approach”, meaning building a just-so story and
filling in the details transparently about history of natural and cultural
developments in trying to make sense of it altogether, from its substrate to
problem itself—not just some solution, with a causal link in between. In other
words, he practiced what Marr suggested for complex information processing
problems, apparently without knowing Marr’s work at the time of writing the
1976 book, although by 1978 he knew about the computational models in similar
spirit (Jaynes, 1978), citing Pylyshyn (1978) for “that other method”.

He made up representations, that is, targeted level-2, to address a level-1
problem, which enabled him to look for its archaeology at level-3. That in
turn enabled him to build a historical, genetic and epigenetic account for
that level, unlike one biological event causing “merge” in humans (Bolhuis et
al., 2014) to bring about language (and language only). And something did
happen to basal ganglia, parts of which have the major functions of cortical
synchronization and managing “appropriate sequence of thought” (Brown, 1998),
6 to 7 million years ago, by which the most distinct genetic difference is in
FOXP2 transcriptional factor of chimpanzees on one side, and humans,
neanderthals and denisovans on the other. It does not appear to be the unique
biological event that Bolhuis et al. (2014) identify with “merge”, because
they do not consider it—rightfully I think—to be “the gene for language”. It
seems that having a Marr-plus-anthropological account leaves more operating
room for understanding Nature doing its work in the course of time.

His explanation of consciousness may be questionable (though not dubious, to
Williams (2011) or to present author, among others). The argument in this
article is that his reasoning has been promising for all aspects of cognition.
We can conceive a representational basis to computationally support _know-how_
of planned action of colloquy of agents, and language can be seen as a further
categorial shift where speech-sign acts are semantically terminal processes at
this level, unlike action, which means they are offline. Language can be
understood to project only from a grammar and never create predicate
abstractions on the fly in speech-sign delivery or speech-sign understanding,
meaning it only reports what is being offlined, or receives it. In daily
action, most processes cannot be terminal because we have to live with their
consequences, i.e. their preconditions, add lists, delete lists, and the state
of the world. However, the action may be overt, or it may be some kind of
predicate abstraction, the real intent (and even conditions) of which may be
opaque to participants. This is fertile ground for studying _deceit_ , a
favorite subject of Jaynes, and to lay rudiments of a theory for conjuring
minds, from animals to human.

Fodor (1975, 1981, 2008) had hoped to get the best out of computer science in
cognition by choosing combinatory explosion as the basis of creativity in
language and behavior. Difference in offlineness has not been addressed in
this way of thinking as the primary source of complexity, as cause of rise of
belief systems. This too, I claim, can be deeply computer-friendly to study if
we look at computer science as studying extended practice of the human, as
suggested also by some Turing Award recipients (e.g. Valiant, 2013), not
practice of the extended human. (This is quite different than other proposals
for human in the loop for computers, such as Vardi (2011), which can be summed
up as “computing for humans”. The current proposal is “computing qua
humans”—what kind of control and data structures humans can conceive can be
_programmed_ by humans to the extent of not needing homunculi; see Knuth
(1996) for discussion.)494949“Computing by humans” as a distinct practice I
think would be self-defeating for both views, as if other things in nature
also compute. Judging from pancomputationalism and “nature computes”
enthusiasts, it seems difficult to accept that the computer can be just a
human concoction for thinking; see Bozşahin (2016b) for extensive discussion.

The view I propose suggests representational and computational support for
harboring belief about past and future states and unknown events quite early
on for humans, first for planned action, giving representational value to past
and future, then for language. Its consequences for level-1 in working up to
understanding a cultural belief system and its transmission across generations
of level-3 subjects can be leveraged by the level-2 support in theory, rather
than conflating the two levels, which is the preferred way to talk about human
practice in neuroscience and dynamical approaches to mind. From the current
perspective, one way to cope with change is to be responsive to the
environment. Another way is to construct the environment or niche we choose to
be in so that search for desirable inputs causes internal restructuring. Yet
another is to control change centrally, in a way freezing it, for generations,
as in rituals. All of this does something to change in human practice as we
try to find ways to deal with it.

Mobile semantics, that is, representing, tracking and understanding change to
support a basis for coping with it, from its abstraction to concrete
realization, rather than addressing spatiotemporality of change directly, is a
start for understanding the terms of serial or serializable high-level
cognitive processes. In doing so we cannot afford to alienate once again
syntax from semantics, at least not from this kind of semantics.

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