Welcome

I’m a PhD student at Utrecht University trying to figure out the meaning of language, and the meaning of life in my spare time. You can find out more about my research project and other interests under the ‘Research’ tab above. This page also contains a list of papers and publications.

Apart from this, I blog about things that interest/move/amuse/anger me – including but not limited to social justice, food, art, feminism, religion and my latest unfinished sewing projects.

Teaching:

  • Inleiding Taalkunde 2014/2015 (with Rick Nouwen and Michael Moortgat)

Past teaching:

  • Semantiek 2013/2014 (with Alexis Dimitriadis, Assaf Toledo & Yoad Winter) – course website
  • Inleiding Taalkunde 2012/2013 (with Marieke Schouwstra & many others) – course website
  • Foundations of Semantics and Pragmatics 2012/2013 (with Yoad Winter and Assaf Toledo) – course website
  • Semantiek 2012/2013 (with Yoad Winter and Assaf Toledo) – course website
  • Inleiding Taalkunde 2011/2012 (with Rick Nouwen)
  • Semantiek 2011/2012 (with Yoad Winter)
  • Inleiding Taalkunde 2010/2011 (with Anna Chernilovskaya and Yoad Winter)

Other:
I’m a co-organiser of LUSH (Leiden Utrecht Semantics Happenings), a series of monthly talks in semantics and pragmatics alternating between Utrecht and Leiden. Visit the website here.

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Friday, March 13th: defense & workshop

No matter how superstitious you might be, this programme surely contains enough reasons to get out of bed this Friday the 13th anyway!

Workshop on the occasion of Hanna’s defense

Date & time: March 13th, 2015, 9:00-12:30
Location: Kromme Nieuwegracht 80, room 1.06 (Ravesteijnzaal)

Programme:

9:00-9:15 coffee/tea
9:15-9:30 opening (Yoad Winter)
9:30-10:10 Thomas Ede Zimmermann (Johann Wolfgang Goethe University Frankfurt am Main): Fregean varieties of compositionality
10:10-10:50 Bart Geurts (Radboud University Nijmegen): Pragmatics and processing
10:50-11:10 coffee/tea
11:10-11:50 Jakub Dotlacil (Groningen University): Processing pluralities: syntax and the lexicon
11:50 -12:30 Hanna de Vries (Utrecht University): Animacy and semantic number: three case studies

Abstracts:

– Thomas Ede Zimmermann: Fregean Varieties of Compositionality
According to the Principle of Compositionality, the meanings of complex expressions can be systematically derived from the meanings of their immediate parts. For more than a century, varieties of this principle have played a central role in logic and semantic theory. I will take a look at the role of compositionality within Frege-Carnap semantics.  More specifically, I will compare 3 different ways of spelling out the principle: Intensional Compositionality, according to which intensions are derived by combining intensions; Fregean Compositionality, according to which, depending on the environment, extensions are derived by combining extensions; and Baroque Intensionality, according to which in certain environments indirect intensions need to be invoked.

– Bart Geurts: Pragmatics and processing
One of the standard objections against the Gricean approach to pragmatics is that it makes communication impossibly hard from a psychological point of view, causing e.g. Wilson (2000) to object that “it is hard to imagine even adults going through such lengthy chains of inference in the attribution of speaker meanings.” However, Grice’s “lengthy chains of inference” were never meant to be understood as hypotheses about ordinary mental states and processes, and the merits and demerits of Gricean pragmatics are not contingent on a mentalistic construal of intentions and other attitudes.
The purpose of Gricean reasoning is to make explicit why the hearer is entitled to draw certain inferences from what the speaker says. This raises the question of how pragmatics, thus construed, relates to the theory of processing. To answer this question, I adopt the general framework proposed by Marr (1982) for describing information-processing systems in general. In Marr’s terminology, Gricean pragmatics seeks to provide a “computational” account of communication, analysing speakers’ and hearers’ behaviour in terms of their propositional attitudes and communicative goals on the assumption that, by and large, speakers try to be cooperative.
Whereas a computational theory describes a system from the outside, so to speak, a processing theory deals in internal processes, states, and representations. Computational and processing theories constrain but don’t determine one another: in general, there will be many different ways a computational theory can be implemented at the processing level. But although a computational theory and its processing implementation may look very different, there are reasons to suppose that, in the case of Gricean pragmatics, there are important correspondences between the two levels. While the evidence that is currently available doesn’t support any substantive hypotheses (be they Gricean or not) about the dynamics of pragmatic processing, it does allow us to say with some confidence that interlocutors routinely model each other’s propositional attitudes: beliefs, desires, intentions, and so on. In recent years, it has become fashionable to deny this, but I argue that there is solid evidence for this claim, which is in line with the key tenets of Gricean pragmatics.

– Jakub Dotlacil: Processing pluralities: syntax and the lexicon (joint work with Adrian Brasoveanu)
Sentences with pluralities can receive at least two interpretations. For example, John and Bill lifted one box could be true if the boys lifted one box jointly (collective reading), or if the boys individually lifted a box, i.e., there were two lifting events and two boxes might have been lifted in total (distributive reading). Frazier et al. (1999) showed in an eye-tracking experiment that the processor prefers the collective interpretation. This finding was confirmed in Kaup et al. (2002) and Boylan et al. (2011). In semantics, two types of distributivity/collectivity are standardly distinguished: lexical and phrasal. This distinction has not entered the picture in previous psycholinguistic studies. I will discuss a processing experiment (self-paced reading study) that is the first one to take the difference into account. The results show that distributivity itself is not problematic for the processor, only the phrasal distributivity is. What this entails for the theories of processing and distributivity will be discussed in the talk.

– Hanna de Vries: Animacy and semantic number: three case studies
In this talk, I suggest that the relation between animacy and morphosyntactic plurality that exists in many languages (cf. Corbett 2000) reflects a deeper and possibly universal relation between animacy and the formal semantics of NPs. Using three different tests for diagnosing the semantic number of an NP and applying them to Dutch and Afrikaans, we will show that whether an NP is interpreted as semantically singular or semantically plural depends on the degree of animacy of its referent. I will try to prepare this talk with a general audience in mind, so non-semanticists will be able to learn something about the contents of my dissertation as well!

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The semantics of group nouns, part 2: British English

…in which I try to convince you that I was actually wrong in convincing you that groups are atomic. Yeah, sorry about that.

When I first conceived the idea of writing about my research in a way understandable to non-semanticists, I imagined I’d write an attractive new update every two months or so, sharing all my interesting recent ideas in fascinating ways and making everyone who read it wish they had my job. Then reality happened, in which very few of my interesting ideas still make sense after a month or so, and I’m usually too lazy to write blog posts about them anyway (I already wrote a book about them, which was exhausting enough as it is).

But with said book as good as finished, and some extra time for frivolities on the side due to several well-timed weeks of maternity leave (which I have mostly been spending on the couch, tied down by little Roanne’s completely unpredictable feeding and crying schedules), I can finally give you the promised update on British English. Enjoy!

In Part 1 of this post, I pointed out that the two sentences in (1) and (2) have different meanings in spite of appearing very similar:

  1. The linguists are walking or cycling.
  2. The group (of linguists) is walking or cycling.

Imagine a situation in which half of the linguists are walking while the other half are cycling. Most speakers of English would say that sentence (1) is true in this situation, but sentence (2) is false: sentence (2) is only true if either all the linguists in the group are walking, or they are all cycling. I explained this by claiming that the group of linguists refers to an atomic entity, which means that the formal semantics cannot access the ‘parts’ of the group when calculating a meaning for (2); as a consequence, anything that the sentence says about the group of linguists must be true of the entire group. In (1), on the other hand, the plural the linguists refers to a set of entities. A set has parts that are accessible to our formal interpretation mechanisms, which means that it can be ‘taken apart’ by a semantic mechanism known as quantification in order to say something about the individual members of the set – namely, that each of them is walking or cycling.

So, the contrast between (1) and (2) confirms that plurals like the linguists and groups like the group of linguists refer to a different kind of semantic object, despite being intuitively quite similar in meaning. But does it really? One might point out that the grammatical number of the subject is not the only variable distinguishing (1) from (2): another difference is the fact that the predicate is plural in (1), but singular in (2). Could it be possible that it is this distinction, rather than the plural/group contrast, that is actually responsible for the meaning difference?

This may seem like a question that is impossible to answer, because English usually requires the subject and the verb to agree in grammatical number, which makes it hard to look at the role of subject number and predicate number separately. Fortunately, there is an exception to this: in British English, singular human group NPs like the group of linguists are allowed to appear with a plural predicate, as in (3):

  1. The group of linguists are walking or cycling.

And sure enough, once you replace the singular verb with a plural verb in this way, the sentence becomes identical in meaning to the one in (1) (I checked this with a whole bunch of British English speakers). In other words, if the verb is singular, the group subject is treated as a single atomic entity, but if the verb is plural, that same subject is treated as if it were a ‘real’ plural, referring to a set of entities.

So, what does a noun phrase like the group of linguists (or the team, the class, the choir, my family, etc) refer to? When the same expression can have different interpretations depending on the formal context (I am not talking about words with different meanings – for example, the word nail as used by either a carpenter or a manicurist, which are essentially just two different words that happen to sound the same – but about the same word playing different ‘mathematical roles’ in the derivation of the meaning of the sentence as a whole. In part 1 of this post, for example, I mentioned the fact that the adjective huge can be applied to a person (as in “John is huge”), but it can also combine with a noun like idiot to form the meaning ‘someone with a huge degree of idiocy’. It’s clearly the same word, but with different semantic functions depending on the words that surround it.), semanticists like to treat one of these meanings as ‘basic’, and the other(s) as ‘derived’. If we follow this line of thinking, we could either say that the atomic interpretation of group NPs is basic and the set interpretation is derived (in other words, group NPs refer to atomic entities by default unless something in the context actively turns them into set-referring expressions), or, conversely, that the set interpretation is basic and the atomic interpretation derived. Concretely:

  1. Possibility 1: a group NP refers to an atomic entity, but if it appears with a plural verb, this atom is ‘broken up’ into a set of entities.
  2. Possibility 2: a group NP refers to a set of entities, but if it appears with a singular verb, this set is ‘fused’ into an atom.

In my dissertation, I take the second approach, because I think it is much prettier (my supervisor won’t allow me to use those words in my academic writing, but fortunately this is my personal blog where I’m completely free to rank formal theories according to their prettiness). One reason for this is that the story above does not apply to all collective expressions in British English, but only to those that refer to human (or at least animate) groups. Inanimate collectives like the stack of plates or the list cannot appear with a plural predicate and only ever receive an atomic interpretation. Possibility 2 provides us with an easy way to implement this difference: we simply treat inanimates like stack or list on a par with ordinary entity-referring nouns like cat or table – in other words, by treating them as a different kind of set-theoretical object than animate set-referring nouns like family or team. Because our semantic toolbox, under Possibility 2, lacks the ability to break up atomic entities, stack and list and cat can only refer to atoms and are not expected to trigger plural agreement. On the other hand, Possibility 1 offers us no simple way to distinguish inanimate from animate collectives, since they all refer to the same kind of set-theoretical object (an atomic entity). In order to guarantee formally that the latter can occur with a plural predicate and be interpreted as a set while the former cannot, we would have to build an entire new formal layer on top of our set-theoretical system, where animacy is somehow formally coded in such a way that it determines which atoms can be broken up into sets and which cannot. This is not impossible, of course, but it would require a lot of extra work that is not needed if we adopt Possibility 2.

So we end up with a formal theory according to which animate group NPs (like my family) are analysed as sets, while inanimate group NPs (like the stack of plates) are analysed as atoms. Of course, now we want to know why animacy seems to correlate so neatly with an NP’s ability to refer to a set and to occur with a plural VP. If all goes according to plan, I will address this question in the third and final research update!

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LUSH / Amsterdam Colloquium

Below you will find (1) the slides for my recent LUSH talk in Leiden, and (2) slides and extended abstract for my presentation at last month’s Amsterdam Colloquium. (I decided, probably unwisely, to keep my AmCol presentation sober and professional, instead of recycling some of the much more entertaining illustrated slides I created for my colleagues a while before.)

kate and william

William’s terminology is a bit sloppy – he means to say either “group nouns range over sets” or “group NPs denote sets”.

– “Number in morphosyntax and semantics: the case of British English group nouns”. Leiden Utrecht Semantics Happenings (LUSH), Leiden University, November 20, 2013. [slides]  

– “Distributivity and agreement: new evidence for groups as sets”. Amsterdam Colloquium, University of Amsterdam, December 18-20, 2013. [slides] [pre-proceedings]

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I want a more fair and sustainable academia.

For as long as I can remember, I’ve been weirdly fixated on what I’d consider my inevitable future career as An Academic. Somehow, I had picked up on the notion of doctorates, and decided I wanted one – preferably doing something involving animals and Amazon expeditions and the occasional shiny laboratory, but the specific field wasn’t the most important thing, The Title was. I imagined it would turn me into someone who was Officially Brilliant, someone who could then go on to spend a lifetime thinking for a living, a prospect that greatly appealed to me.

My other childhood ambition was to save the world. This was not, in theory, incompatible with my scientific dreams – at least not until my third year at university, when I decided to drop my major in psychology and cultural anthropology and become a linguist. Gone was every opportunity to spend my professional future saving the earth or fixing humankind. I’ve seen my future, and it involves lots of lambdas and semilattices.

Those of you who know me personally know that this has been kind of a struggle for me. I still want to save the world. I want it to be fair and sustainable and full of people whose human rights are being respected. And I kind of want to contribute more to that world than just my puny habits of buying fairtrade coffee and going to conferences by train rather than plane.

Lately, I’ve been wondering whether I, together with anyone who reads this and is interested, could somehow start with academia – after all, this is our world and it’s full of people routinely flying halfway across the world to deliver a single talk, conferences providing unlimited water in plastic bottles & no recycling bins, and huge piles of handouts being printed that no one even looks at. It’s also full of huge egos and people with burnouts and gender biases and commercial publishers with ridiculous profit margins. It’s inspired articles like this and resignation letters like this and scandals like this.

But I don’t really know what to do, let alone how to do it. An online platform where everyone can share their tips and ideas of making academia a better place? Practical guidelines on how to make your conference more sustainable? A kind of pledge for the young and unspoiled to sign in which they promise to stay nice, humble, open-minded servants of Scientific Truth? :)

One thing I do know is that there’s strength in numbers – because some of these fair and sustainable choices involve deliberately not going along with the way things currently are, which might well hurt your career in small but unaffordable ways (these are hard times, and every publication and conference appearance counts). If I decide to take at most one intercontinental trip a year, or only submit articles to less widely known Open Access journals, or become that annoying person who brings up gender imbalances, child care and fair trade coffee at every workshop I organise, fewer people will hear about my work (and like me as a person). But if there’s enough of us, and we manage to turn this stuff into the norm for a new generation of academics, then maybe we can make the world a better place without having to sacrifice our career.

So – do you self-identify as an academic (in any field) and does this post resonate with you? Please let me know and we might think about this stuff together, because I can’t do this on my own. And if you have any other ideas or comments, I’d love to hear them!

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Mijn mening over Zwarte Piet is niet zo belangrijk

Als je het per se wil weten: ik denk dat Zwarte Piet, hoe onhandig we hem ook proberen te ontdoen van alle sporen van het Nederlandse slavernijverleden, te onlosmakelijk verbonden is aan zijn wortels als racistische karikatuur om ooit iets anders te kunnen zijn dan dat. En ook: ik ben dol op Zwarte Piet. Sinterklaas zonder Piet, dat kan gewoon niet – dat voel ik gewoon in mijn blanke, Hollandse onderbuik.

Maar dat maakt allemaal niet zoveel uit, want mijn mening over Zwarte Piet is helemaal niet zo belangrijk. Er is maar één bevolkingsgroep die kan beoordelen of Zwarte Piet racistisch en kwetsend is, en dat is de groep die er al dan niet door gekwetst wordt. En daar hoor ik niet bij, dus wordt het tijd om mijn mond te houden en te luisteren naar de mensen die er wél verstand van hebben.

Iets waarvan ik wel met tamelijk veel zekerheid durf te zeggen dat het racistisch is: dit hele debat, of althans de manier waarop het gevoerd wordt door de pro-Pieten-kant. Je zou er zo een bingospelletje van kunnen maken (dankjewel, Google). “Jullie interpretatie van Piet is verkeerd/ongeldig/getuigt van een gebrek aan historisch besef”? Check. “Stel je niet aan, azijnpissers”? Check. “Ik ken ook Surinamers die zich niet gekwetst voelen door Zwarte Piet”? Check. “De slavernij is eeuwen geleden, get over it“? Check. “Jullie zijn de racisten, met jullie gefocus op de huidskleur van Piet”? Check. Ik kan nog wel even doorgaan.

Een bekentenis: ik was net zo. Ik heb louter positieve ervaringen met Zwarte Piet, want ik hou nu eenmaal van snoep en cadeautjes en gedichten en heb het geluk in een maatschappij te leven waarin mijn huidskleur op geen enkele manier een issue is. Het is helemaal niet zo raar dat ik daarom lang geloofd heb dat iedereen dus blij zou moeten worden van Zwarte Piet, of dat huidskleur in het algemeen op geen enkele manier een issue is in Nederland. Elke blijk van het tegendeel vatte ik welhaast persoonlijk op, als een gemene poging om mij mijn blije geluksbubbel te ontnemen. Geen wonder dat ik daar een beetje geïrriteerd en defensief van werd. Geen wonder ook dat een groot deel van Nederland daar een beetje geïrriteerd en defensief van wordt.

Alleen: blijven hangen in die geïrriteerde, defensieve fase is niet zo volwassen. Volwassen is het om te beseffen dat je niet het middelpunt van het universum bent, dat jouw perspectief niet het enige is, en dat andere mensen ervaringen kunnen hebben die volledig anders zijn dan die van jou en tóch niet minder waar of geldig zijn. Pas als we de ander verwelkomen als gelijkwaardige gesprekspartner en zijn emoties en ervaringen niet bij voorbaat van tafel vegen omdat ze anders zijn dan die van ons, dan pas kunnen we het gesprek op een constructieve manier aangaan.

In de Volkskrant van afgelopen zaterdag schrijft Robert Vuijsje hoe hij zijn Surinaamse vrouw en een klasgenootje van vroeger eens vroeg hoe ze als kind eigenlijk het Sinterklaasfeest hadden ervaren. Zijn vrouw vond het feest “ongemakkelijk, pijnlijk en verwarrend”. De vriend, destijds de enige zwarte leerling in een verder volledig blanke klas, had elk jaar weer dezelfde eenzaamheid gevoeld.

Dat is problematisch. Ongeacht wie er ‘gelijk’ heeft en ongeacht je perspectief op de historische ontwikkeling van Zwarte Piet: elk jaar weer zit een hele groep kinderen zich dus verward en eenzaam te voelen tussen hun zich van geen kwaad bewuste blanke leeftijdsgenootjes. Wie dat a priori niet interessant vindt, wie zijn eigen recht om zich van geen kwaad bewust te zijn belangrijker vindt dan de gevoelens van anderen, wie überhaupt weigert te luisteren naar de gevoelens van anderen en ze bij voorbaat wegwimpelt als irrelevante aanstelleritis, wie agressief en belerend reageert op de pijn van een medemens, die mag gewoon niet beweren dat het met de rassenverhoudingen in Nederland wel snor zit.

Maar toch. Ik ben dol op Zwarte Piet, en zo’n legertje bontgeschminkte Kleurenpieten is toch een beetje een surrogaat. Dacht ik. Ik heb even wat plaatjes gegoogled en werd er eigenlijk best vrolijk van. Wat mij betreft voeren we ze in. Maar zelfs als we besluiten dat niet te doen en Piet ‘gewoon’ zwart te laten – laat dat dan tenminste een collectief besluit zijn, waarbij iedereen gehoord en serieus genomen wordt. Laat er alsjeblieft niemand eenzaam, verward en gekwetst in een hoek hoeven te zitten terwijl de rest pepernoten vreet en zich op de borst klopt dat ze in deze Belangrijke Principekwestie gelukkig geen Duimbreed Geweken zijn.

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De geesteswetenschapper als ontmaskeraar van machtsmythes

hunzijnnogdommerDit artikel verschijnt binnenkort in Radix, waar het zal prijken tussen modaal-epistemische argumenten voor het bestaan van God, discussies over intelligent design en artikelen met ‘Dooyeweerd’ in de titel. Helaas zonder Dooyeweerd, maar mét Walter Wink en Richard Beck en zelfs een zuinig hoofdknikje naar Foucault want daar vroeg de redacteur naar en ik wou natuurlijk niet toegeven dat ik eigenlijk niet zoveel begrijp van de beste man, die ik bovendien structureel verwar met Barthes, Baudrillard en Derrida. Maar ik dwaal af:

Abstract: Onze hele samenleving is doortrokken van subtiele machtsverhoudingen. Of het nu gaat om sociale klasse, leeftijd, etnische achtergrond, sekse, opleidingsniveau, woonplaats of taalgebruik, de mensheid weet zichzelf altijd weer op te delen in groepen met veel en groepen met weinig status. In dit artikel wordt dit geïllustreerd aan de hand van een relatief onderbelicht fenomeen: de hardnekkige maar taalkundig onzinnige notie van ‘goede’ en ‘foute’ grammatica. Vervolgens komt aan bod wat theologen als Walter Wink te zeggen hebben over macht, status en privilege; in navolging van deze theologen betoog ik dat het ontmaskeren van machtsverhoudingen en de mythes die eraan ten grondslag liggen één van de belangrijkste aspecten is van de missie van Jezus, en daarmee ook van de navolging. Tot slot wordt duidelijk dat christelijke geesteswetenschappers hier een belangrijke rol in kunnen spelen: zij hebben zowel de wetenschappelijke middelen om machtsmythes te kunnen identificeren, als de theologische middelen om ze te ontmaskeren.

Lees het hele artikel hier (het is de drukproef, dus als je jeuk krijgt van verkeerd afgebroken woorden kun je beter een abonnement op Radix afsluiten, de papieren editie van mij lenen en/of me een mailtje sturen voor de opmaakloze versie)

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Semantic intermezzo 1: ‘every’ and ‘only’

In the previous research-related post, I’ve introduced the idea that natural language determiners (these little words or phrases that you can put in front of a noun, like a, the, every, three, most, all but one, several, infinitely many…) can be analysed as relations between sets. The reason that I love this intuitively simple idea so much is that it basically turns meaning into a kind of puzzle that doesn’t require a lot of background knowledge – just some basic math skills. So, as a kind of intermezzo, let’s look at the interesting case of every and only, whose meanings don’t seem obviously related in actual language, but turn out to be each other’s exact mirror images when you look at the math behind them. Then, next time you’re at a party and the topic of formal semantics comes up (as it is wont to do) you will be able to dazzle everyone with this super-interesting case study in applied set theory!

To make things more easy, let’s introduce some basic formal notation. (No! you might object, formal notation makes things hard! I think this is a sad misconception rooted in the allergy-inducing way that math is generally taught in secondary school (an allergy that took me years to get over, especially since I was used to people telling me that I wasn’t very good at math… but that’s a different story). Don’t worry, though – I will try to paraphrase all the formal stuff in actual English as well. And if you really don’t like math, just skip the bits in green – they are not essential to the story.)

We will use D as a placeholder for determiners, and A and B as placeholders for sets. In this way, we can represent every English sentence according to the template D(A)(B), where A refers to the set corresponding to the subject noun, and refers to the set corresponding to the predicate. For example, we can represent the sentence Every student smiles as:

 every(the set of students)(the set of smilers)

or, for short:

every(student)(smile)

This representation doesn’t yet tell us anything about the meaning of the sentence: in order to know the meaning, we need to know what kind of relation between sets every denotes. So let’s define this relation:

every(A)(B) = 1 iff A is a subset of B
“The sentence Every A Bs is true if and only if every member of the set corresponding to A is also a member of the set corresponding to B

So, Every student smiles is true if every member of the set of students is also a member of the set of smilers. (And you can describe the meaning of any determiner in this way, for example:

less than three(A)(B) = 1 iff |A ∩ B| < 3
“The sentence Less than three As B is true if and only if the number of entities that are a member of both A and B is smaller than 3″

half of the(A)(B) = 1 iff |A ∩ B| = |A – B|
“The sentence Half of the As B is true if and only if there are as many members of A that are also members of B, as there are members of A that are not members of B

This is what I meant when I wrote that this way of looking at determiners turns language meaning into a kind of puzzle.)

Another nice feature of set theory is that it’s very easy to illustrate visually. Like this:

every frog is a prince

“Every frog is a prince”

The rectangle represents the universe (the set of all existing entities), the circles represent various sets of such entities. As you can see, the frogs are a subset of the princes (every entity that’s a member of the set of frogs is also a member of the set of princes), so the sentence Every frog is a prince is true.

Now, on to only. What does the visual representation of Only frogs are princes look like? (Think about this for a second.)

Right. It looks like this:

only frogs are princes

“Only frogs are princes”

In order for the sentence Only frogs are princes to be true, every prince must be a frog: the meaning of the sentence rules out the existence of non-frog princes. (It does not care about the existence of non-prince frogs: only frogs are princes does not mean that all frogs are princes.)

So now you see why I claimed that every and only are each other’s ‘mirror images’ in terms of meaning. Here is another way to represent this idea:

Every A is B ↔ Only Bs are A
“The sentence Every A is B is equivalent in meaning to the sentence Only Bs are A

Which means that, in our official notation:

only(A)(B) = 1 iff B is a subset of A (the reverse of our definition for the meaning of every, above)

Let’s summarise all this. Departing from the idea that the meaning of a determiner can be described as a relation between sets, we looked at the meanings of every and only and discovered that they represent the same relation between sets, only mirrored. And this fun little case study is a real-life example of the way formal semanticists look at language – I could do this stuff all day!

Still hadn’t enough? Read more about the linguistic and set-theoretic properties of only below the cut.

Continue reading

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