I. SEMANTICS, PRAGMATICS AND PHILOSOPHICAL LOGIC

P. Schlenker's initial interests concerned some foundational issues in semantics, pragmatics and philosophical logic.  

Context dependency and intensional semantics

His first works pertained to context dependency and intensional constructions.

Context shift: P. Schlenker initiated a formal investigation of context dependency across languages. While in English most indexical expressions depend on the context of the actual speech act (e.g. John thinks that I am an idiot attributes to John a thought about the actual speaker rather than about John), this is not always so in other languages: some indexicals are evaluated with respect to a 'shifted' context in attitude reports (and the equivalent of John thinks that I am a hero can attribute to John a thought about himself). The philosopher David Kaplan had argued that operators that shift the context of evaluation of indexicals should not exist, and for this reason he called them 'monsters'. Linguistic teratology has now found quite a few monsters across languages. P. Schlenker has also extended his research on context shift to the analysis of Free Indirect Discourse in literature, and of Role Shift in sign language.

'Ontological Symmetry': P. Schlenker further developed analyses that treat individual-, time- and world-denoting expressions in a symmetric fashion, with the idea that the abstract semantic vocabulary of language is neutral among these domains. This led to an analysis of if-clauses as definite descriptions of possible worlds, and also to more recent work on uses of pointing in sign language to realize individual, temporal and modal anaphora alike. 

Formal pragmatics 

A perennial question of studies of meaning concerns the division of labor between semantics and pragmatic reasoning; this has led to vibrant debates between theories that (semantically) encode certain inferences in lexical entries, and ones that posit general (and often pragmatic) algorithms that seek to derive them on independent grounds. P. Schlenker's research has been firmly in the second camp, while trying to do justice to important results derived by the first.

Presuppositions: His primary contribution in this area has been to revisit debates about the nature of presupposition computation (or 'projection'). In the 1980's, a 'dynamic turn' took place in semantics, motivated by data from presupposition projection and anaphora resolution. It led to a renewed conception of meaning, seen not as (just) a specification of truth conditions, but as an instruction to update a belief state. While original insights in this direction (due to Stalnaker) were pragmatic in nature,  the more general and rigorous frameworks adopted later (following Heim) encoded these instructions in the lexical entries of operators. The result was both effective and disappointing, as it failed to derive presupposition projection from more basic considerations. P. Schlenker has developed a purely pragmatic alternative to the dynamic analysis (called the Transparency Theory), which derives some of the same results in a more principled fashion, and makes some new predictions, some of which were tested with experimental means. He has also used related ideas to reconstruct the basic concept of dynamic semantics, that of a 'local context', in a pragmatic (post-semantic) fashion. These attempts may have helped re-ignite theoretical debates about presupposition projection.

Expressives and supplements: Influential work by C. Potts suggested that some expressions, such as expressives (e.g. slurs) and supplements (= the meanings of appositive relative clauses) make, for lexical reasons, contributions to a new and separate dimension of meaning. P. Schlenker explored alternative accounts in which such 'bidimensional' analyses are unnecessary: expressives and supplements are analyzed instead within extensions of presupposition theory (combined, in the case of supplements, with a more powerful syntax than is customary).

Presupposition maximization: In some cases, one is required to mark the strongest presupposition that is licensed (e.g. one needs to say the sun rather than a sun). This principle was taken as primitive in several accounts; P. Schlenker tentatively explored an alternative in which presuppositions can sometimes produce information (by way of 'informative presuppositions') and lead, for this reason, to a pragmatic reasoning that yields presupposition maximization.

Anaphora

Constraints on anaphora resolution have played a central role in syntax and semantics, due to odd intra-sentential constraints  known as 'Binding Theory', and also to the existence of binding-like behavior across sentences in discourse.

Binding Theory: Why can one say, with coreference, His mother adores John, but not: He adores John's mother? This and related constraints gave rise to a set of highly interesting but somewhat arbitrary rules, known as Binding Theory, in the 1970's. P. Schlenker explored a non-standard logical system in which several of these rules follow from one main constraint, which is that objects may not be represented redundantly in a kind of formal 'memory register'. He later explored a more pragmatic strategy to derive a smaller but related set of data.

Dynamic anaphora: Anaphora resolution in discourse provided (together with presuppositions) one of the main motivations for the 'dynamic turn' in the semantics of the 1980's. The key issue was that in a discourse such as [A Frenchman]_i will win the Tour de France. He_i will be famous., the pronoun he is dependent on a quantifier (namely a Frenchman) without being in its  scope (= c-command domain), i.e. without being in the right syntactic domain to make the dependency possible according to standard theories. Dynamic semantics posited new interpretive rules that allow for the desired formal connection: he and a Frenchman may be coindexed and thus semantically dependent. Alternative accounts rejected this radical step, arguing instead that the pronoun should be seen as a description in disguise (akin to the Frenchman, or the Frenchman who won the Tour de France). Here P. Schlenker sided with dynamic semantics because of an investigation of new data: he argued that in sign languages, indices are realized overtly as positions in signing space, and display precisely the pattern of coindexation predicted by dynamic theories. He recently suggested that a related argument can be made on the basis of some pointing gestures in spoken language. 

Philosophical logic

P. Schlenker's research has also been concerned with potential limits of formal semantics due to the existence of semantic paradoxes. 

Eliminating self-reference: To help diagnose their origin, he first generalized results by Yablo to show that, under certain conditions, every semantic result obtained with self-reference (including paradoxes) can be emulated without it. 

Super Liars: He then explored a semantics for paradoxes on which trivalent solutions (which posit that paradoxes are neither true nor false) are inexorably led to posit an infinite hierarchy of truth values. Whenever one assigns a non-classical truth value v to  paradoxical Liar sentence of the form This very sentence has some other value than true among {true, false, …}, one can define a Super Liar sentence as: This very sentence has some other value than true among {true, false, …, v}  – and this value can't be v, on pain of contradiction (since if the Super Liar has value v, what it asserts is in fact true). This leads to an infinite hierarchy of truth values (Roy Cook has independently explored a similar general direction, with different technical constructions).  

Anselm: Finally, P. Schlenker has explored cases in which the existence of subtle and indirect means of self-reference in language leads people's reasoning astray; this has yielded one possible reconstruction of Anselm's proof of God's existence (if the reconstruction is correct, the argument isn't).

II. SUPER SEMANTICS

How far should semantics extend? In recent work, P. Schlenker's research has made two general points: (i) there are rich meaning phenomena beyond the traditional objects of study of formal semantics; (ii) they too can greatly benefit from formal methods. Some of these objects, such as sign languages, are (by now) standard objects of study in linguistics. Others, such as gestures, were not traditionally studied with formal methods. Still others, such as animal communication systems and music, are entirely new additions to linguistics in general and semantics in particular. The program of a 'Super Semantics' seeks both to cast new light on meaning phenomena that have been understudied, and also to come to a richer typology of semantic operations than is currently available. Importantly, the various empirical domains under study have very different formal properties, and thus they call for diverse formal tools as well in their analysis.

Sign language semantics

While it has long been known in linguistics that sign languages have full-fledged (and very interesting) grammars that should constrain theories of linguistic universals, it is only recently that their semantics started being investigated in formal detail. P. Schlenker took part in  this movement with fieldwork on French and American Sign Language (LSF and ASL), developing new methods to elicit precise and replicable acceptability and inferential judgments from native consultants. On a theoretical level, he explored two directions.

'Logical Visibility': First, he investigated cases in which sign language might provide new evidence on abstract structures that were posited on indirect grounds for spoken languages. The fact that logical indices can arguably be realized overtly (as positions in space) is a case in point; the observation that context shift can be overtly realized by shifting one's body is another one. In such cases, sign language makes visible some key elements of the logical grammar of language, and for this reason it brings new light to important theoretical questions.

Iconicity: While sign language has the same general grammatical and logical means as spoken language, it also has far richer iconic resources. For instance, the ASL  verb GROW may be realized more broadly to refer to a larger growth process, and more quickly for a faster growth; similarly, one may point upwards to refer to a very tall individual (but if he is hanging upside down, one will then point downwards). This observation raises some new questions: how does iconicity interact with logical semantics in sign language? and shouldn't one start with sign languages if one wishes to see the full (iconic-rich) extent of universal semantics? These questions led to the development of a formal semantics with iconicity for sign languages; from this broader perspective, spoken languages appear in some respects as 'iconically-challenged' versions of sign languages.

Gesture semantics

Does spoken language have comparable iconic means as sign language? Within the spoken word, these are of course limited: one may iconically modulate a word such as long by making it longer to evoke a long duration (as in: The talk was loooong). But  outside of a few effects of this type, and of onomatopoeias, the iconic potential of the vocal medium is rather limited. By contrast, gestures have a rich iconic potential, and thus a focal point of comparative studies has been whether iconic modulations of signs might play the same role as co-speech gestures in spoken language. Simultaneously, formal semanticists have found that the interaction between gestures and logical operators is in itself interesting and challenging because it is a rich source of new data and problems.

Co-speech gesture projection: The first key finding, due to Cornelia Ebert, was that co-speech gestures do not normally make at-issue contributions. She herself argued that co-speech gestures make the same kind of contribution ('supplements') as appositive relative clauses. Based on the distribution and inferential properties of co-speech gestures, P. Schlenker argued instead that they trigger (weak) presuppositions, albeit non-standard ones, which he called 'cosuppositions': a sentence such as John didn't LIFT help his daughter, where a lifting gesture co-occurs with help, triggers the conditionalized presupposition that if John had helped his daughter, lifting would have been involved. The predictions of the 'cosuppositional' theory of co-speech gestures have been investigated in collaboration with psycholinguists. This theory contributes to the development of a formal semantics/pragmatics for gestures.

Pro- and post-speech gestures: While most research has been devoted to co-speech gestures, great interest lies as well in gestures that follow the expressions they modify (as in: John helped his daughter - LIFT, with a lifting gesture following the sentence), and in gestures that fully replace a spoken word (as in: His daughter, John will LIFT, where LIFT is a gesture that replaces a verb). In recent work, P. Schlenker has argued that post-speech gestures make the same kind of contribution as appositive relative clauses (this was precisely what C. Ebert claimed, but about co-speech gestures, hence an interesting new debate). And he has further proposed that nearly the full typology of inferences in language can be replicated with pro- and post-speech gestures. For instance, a gesture for a helicopter taking off will trigger the presupposition that the helicopter was initially on the ground.  These findings provide a new empirical domain for formal semantics/pragmatics; they also suggest new theoretical directions. It is particularly striking that the relevant inferences can be triggered by gestures that one has never seen before. Arguably, then, these are cases of 'zero-shot learning', and they are suggestive of powerful algorithms that make it possible to divide the informational content of a new gesture among various components of the inferential typology. Gestures might help uncover the precise nature of these algorithms.

Typology of iconic enrichments: Unlike co-speech (and post-speech) gestures, iconic modulations of spoken words (as in loooong) and signs (as in GROW, discussed above) can be at-issue. This yields an answer to the comparative question we started out with: in the end, co-speech gestures will  not yield the same semantic effects as iconic modulations in sign language, because their semantic status is not the same. In fact, many iconic modulations in sign language (e.g. those of the verb GROW) should be compared to iconic modulations of spoken words, as in loooong. But the latter are rare and the former are very common, hence there are significant semantic differences between sign-with-iconicity and speech-with-gestures. This finding has also led to a broader question: can one develop a unified theory of iconic enrichments that cuts across spoken and sign language? Steps in this direction were taken by considering some non-grammatical (disgusted) facial expressions in sign language, and assessing their role as co-sign or post-sign gestures. Initial results suggest that they fit rather well in the typology developed for spoken language. In the end, there appears to be a uniform typology of iconic enrichments that involves co-speech/sign gestures, post-speech/sign gestures, and iconic modulations.

Gestural grammar: The recent focus on pro-speech gestures has led to an unexpected finding: gestures make it possible to replicate within spoken language some non-trivial grammatical properties of signs. A case in point pertains to gestural verbs with agreement: Your brother, I will SLAP-a (with a slapping gesture realized slightly towards the side) is grammatically possible because the object is third person; performing the same gesture with a second person object yields deviance (in You, I will SLAP-2, the gesture has to be directed towards the addressee, and cannot be directed to the side). This replicates with pro-speech gestures a distinction between third and second person object agreement verbs in sign language; some more fine-grained properties were shown (in part with experimental means) to be shared between agreement verbs in sign and in  gestures.  But the point is far more general, and extends for instance to gestural pointing to realize anaphora, which shares non-trivial properties of pointing signs. What is particularly remarkable about these data is that non-signers 'know' some sign-like properties of gestures, despite the fact that the relevant pro-speech gestures are extremely uncommon. This knowledge with little or no prior exposure (arguably a kind of 'zero-sot learning') might have relevance for the ways in which deaf people without access to a sign language (homesigners) 'create' communication systems that share some grammatical properties with full-fledged sign languages.

Primate semantics

In a series of collaborative studies with primatologists and psycholinguists, P. Schlenker has attempted to lay the groundwork for a 'primate semantics', which seeks to describe and explain the informational content of the calls of several primate species. A summary of the first study as well as of a broader survey can be found online. These studies make several points. First, the main message is that rich data collected by primatologists are ripe for linguistic analysis, and that methods from contemporary linguistics can illuminate them. From this it doesn't follow that monkey languages and human language share non-trivial properties (although the general methods of formal linguistics can illuminate both).  Second, a key tool of contemporary semantics, that of 'implicatures', plays a key role in the analysis of these communication systems. Third, a by-product of the comparative approach that has been adopted is that aspects of the evolution of monkey calls can probably be reconstructed over millions of years (this was known in the 1970's, but this type of work fell out of fashion and needs to rediscovered and extended). 

Music semantics

While it is almost uncontroversial that music is subject to 'syntactic rules' (although not necessarily related to those we find in language), it is initially very unclear that music has 'meaning' in anything like the usual sense. P. Schlenker has argued that music may trigger rich semantic inferences, and he has sketched a conceptual framework for a music semantics, inspired much more by iconic semantics than by standard logical semantics. The framework ('source-based semantics') is based on the following ideas. First, musical cognition is continuous with normal auditory cognition: in both cases, the semantic content of an auditory percept can be identified with the set of inferences it triggers about its causal sources, analyzed in appropriately abstract ways (e.g. as 'voices' in some Western music). Second,  while some inferences licensed by a musical phrase are based on properties of normal auditory cognition, many others arise from the interaction of the sources with tonal pitch space. Depending on the tonal and non-tonal behavior of the sources, one may infer that they are a background or foreground, animate or inanimate, intentional or not, etc. Finally, these properties make it possible to define an inferential semantics but also a truth-conditional semantics for music: a music piece m is true in a situation s if and only if there is a structure-preserving map between the music and the situation in which it is evaluated. From this it does not follow that music has a precise meaning: in general, it doesn't. But an underspecified semantics is very different from no semantics at all, and the proposed framework has the potential to capture the underspecified and often abstract inferences triggered by musical pieces.

In recent work, new connections were established between music semantics and other areas of Super Semantics. First, Dorit Abusch's idea that visual narratives involve logical variables was extended to music semantics, with particularly important consequences for the music/dance and music/cartoon interaction. Second, it was surmised that musical meanings can enrich films, cartoons and gifs in the same way as co-speech gestures can enrich speech (technically, 'cosuppositions' are generated in these diverse domains).