The Illogician

Call for Abstracts (issue 2026 ii)

Fri, 10 Apr 2026 12:00:00 +1000

Hey MoL Community!

We’re putting out a call for abstracts for the second issue of the MoL magazine, The Illogician! Whether you’ve got a thought-provoking essay, a compelling opinion piece, a review of something interesting, or a summary of a paper that caught your eye, we want to hear about it. Any logic-related topic is welcome, from deep and serious pieces to comical stories. Just keep your abstract to a maximum of 300 words and submit the following form by April 27th. All Master of Logic, Logic Year, and ILLC PhD students are welcome to submit an abstract. Looking forward to seeing your ideas!

Call for Quotes (issue 2026 i)

Wed, 17 Dec 2025 23:45:00 +1000

Overheard anything memorable during this semester? The Illogician is collecting funny quotes from students and staff for its first issue. Submit by Jan 6th!

Call for Abstracts (issue 2026 i)

Tue, 07 Oct 2025 12:00:00 +1000

Hey MoL Community!

We’re putting out a call for abstracts for the second issue of the MoL magazine, The Illogician! Whether you’ve got a thought-provoking essay, a compelling opinion piece, a review of something interesting, or a summary of a paper that caught your eye, we want to hear about it. Any logic-related topic is welcome, from deep and serious pieces to comical stories. Just keep your abstract to a maximum of 300 words and submit the following form by October 29th. All Master of Logic, Logic Year, and ILLC PhD students are welcome to submit an abstract. Looking forward to seeing your ideas!

Call for a Technical Supervisor

Thu, 04 Sep 2025 10:00:00 +1000

Do bad websites and sloppy typesetting infuriate you? The Illogician is looking for one (or more) tecnhical supervisor(s).

Tasks

work on this website, were the online version of the Illogician is published;
offer technical assistance to our graphic designer during the import of the authors’ drafts into the publishing project.

Tools

Git (version control);
Markdown/Hugo (static website framework);
SSH (secure shell protocol).

As the tools above are relevant for website administrators and coders alike, this call is also open to people with no prior experience, but that would like to learn about them from the current board members.

Board 2025/26

Fri, 01 Aug 2025 15:00:00 +1000

Core Members

Idske (Head of Graphic Design)

Hugo (Editor-in-Chief)

Mariana (Secretary & Treasurer)

Giuliano Gorgone (Technical Supervisor)

Logic & Philosophy

Isabel

Matteo (Celli)

Matteo (Mercuri)

Thiago

Logic & Language

Alex

Giannis

Logic & Computation

Mariana

Emke

David

Giuseppe

Louise

Logic & Mathematics

Hugo

Idske

Josje

Bardo

Call for Quotes (issue 2025 ii)

Fri, 23 May 2025 15:00:00 +1000

Overheard anything memorable during this semester? The Illogician is collecting funny quotes from students and staff for its first issue. Submit by June 27!

Call for Illustrator(s) (issue 2025 ii)

Mon, 12 May 2025 15:00:00 +1000

What You’ll Do

Create illustrations to accompany articles, essays, and creative content regarding logic
Work closely with editors and writers to visualize ideas

What You Get

€15 per illustration
Your work published and credited in print and online
Experience working with an editorial team

How to Apply

Send a short introduction and 2–3 samples of your work (or a link to your portfolio) to Josje.van.der.laan@student.uva.nl .

Deadline

June 20th 2025

Questions?

Reach out to Josje.van.der.laan@student.uva.nl .

Call for Abstracts (issue 2025 ii)

Thu, 24 Apr 2025 16:32:00 +1000

Hey MoL Community!

We’re putting out a call for abstracts for our upcoming brand new MoL magazine, The Illogician! Whether you’ve got a thought-provoking essay, a compelling opinion piece, a review of something interesting, or a summary of a paper that caught your eye, we want to hear about it. Any logic-related topic is welcome, from deep and serious pieces to comical stories. Just keep your abstract to a maximum of 300 words and submit the following form by May 16th. All Master of Logic, Logic Year, and ILLC PhD students are welcome to submit an abstract. Looking forward to seeing your ideas!

Board 2024/25

Sat, 01 Mar 2025 15:00:00 +1000

Core Members

Thiago (Editor-in-Chief)

Josje (Graphic Design)

Stefano (Technical Supervisor)

Logic & Philosophy

Matteo (Celli)

Matteo (Mercuri)

Logic & Language

Thomas

Giannis

Logic & Computation

David

Giuseppe

Louise

Logic & Mathematics

Josje

Bardo

2025 ii: Editorial Note

Mon, 01 Jan 0001 00:00:00 +0000

The beauty of the ILLC, and what makes it such a special place, is the diversity of thought. Students and professors from so many different backgrounds and intellectual interests, sharing ideas and passions, all drawn by a single common interest: logic, whatever that means. To celebrate this kaleidoscope of perspectives, we the students of the MoL decided it was about time for us to have the means to share with the MoL community what we are the most enthusiastic about.

2025 ii: Hints and Solutions to Cryptic Clues

Mon, 01 Jan 0001 00:00:00 +0000

Erratum

In the third cryptic clue, “cardinal” should read “radical”.

Hints and solutions

You may now contact David Kühnemann for hints and solutions to the cryptic clues.

A conceptual history of BHK negation

Mon, 01 Jan 0001 00:00:00 +0000

Introduction

It is somewhat an item of common sense that sentences of natural language may at times be false rather than true. Yet, despite the obviousness of this observation, the role played by falsity in the context of modern logic is at best very modest. Indeed, the received view on the matter, dating back to Frege ((Frege 1919),(Frege 1979) "Logik"), defends that falsity is a psychological notion, but not a logical one, because all instances of false propositions can be circumvented by treating them as instances of true propositions prefixed with a negation operator. In this article, we argue that falsity holds his spot as a substantial logical notion in the context of intuitionistic logic. We do so by first by presenting the role of false proposition in Franz Brentano’s reform of traditional logic, which stands in strong opposition to the received view. We then move to the $BHK$ semantics for intuitionistic logic (christened after Brouwer, Heyting, and Kolmogorov). This, we argue, inherits some fundamental traits of Brentano’s treatment of false propositions, and thus constitutes a witness for a system where the notion of falsity is conceptually prior to the one of negation.

Compactness and Completeness in Contemporary Romantic Interaction

Mon, 01 Jan 0001 00:00:00 +0000

Introduction

Attempts to formalize human preference, belief, and intention have given rise to robust epistemic and dynamic-logical frameworks. However, one domain remains resistant to logical analysis: romantic interaction.

This paper introduces Affective Predicate Logic (APL), a first-order modal framework designed to capture inferential patterns arising in digital romantic communication, specifically through participant observation of the Hinge dating platform between October 2024 and October 2025. While individual affective exchanges appear logically consistent, their aggregation leads to systematic model-theoretic failure. In particular, we demonstrate violations of completeness and compactness under classical semantics. Empirical data drawn from the case study shows persistent undecidability of propositions such as $\mathtt{TheyLikeMe}(a)$¹ and semantic collapse following interpretive divergence over “jazz.”

Construct Colimits in a Topos Using Elementary Methods

Mon, 01 Jan 0001 00:00:00 +0000

An elementary topos is a category with finite limits, exponentials, and a subobject classifier $t:1\rightarrow\Omega$. We do not know from the definition that a topos has colimits. Surely we have theorems¹ ensuring that a topos at least has finite colimits, but this is far from intuitive. We might ask for a more straightforward construction of certain colimits in a topos; we want more explicit expressions using limits, exponentials, and the subobject classifier. Thanks to online posts by Todd Trimble², we have an intuitive way of constructing the initial object and coproducts. In the following, we focus on the construction of the initial object as a representative example of a colimit in a topos.

Engineering Sexual Orientation

Mon, 01 Jan 0001 00:00:00 +0000

Perhaps Lady Gaga was right - sexual orientation is not our choice: baby, we were born this way. This conception has, after all, done much for the mainstream acceptance of certain queer identities. But if we really were simply born this way, then ought we only to accept non-cis-heterosexual identities simply because those who identify as such, so to speak, just cannot help it? This seems undesirable, as it leaves open the possibility that there might be something inherently blameworthy about them; such a static conception of sexual orientation moreover does not seem to reflect the lived experiences of many individuals (Diamond 2022, 83, 93).

Guidelines

Mon, 01 Jan 0001 00:00:00 +0000

Authors

The process

After submitting your abstract, the editors will review it within a week of the submission deadline. If your abstract is accepted, at least one editor will be assigned to assist you, who will contact you as soon as possible. They will send you a few comments on their first thoughts about your abstract, and some editorial considerations on how to turn it into an article. Upon completion of your first draft, the editorial board will review it, and the editor(s) assigned to you will send their feedback.

Ingredients and Logic - Is putting pineapple on pizza rational?

Mon, 01 Jan 0001 00:00:00 +0000

A MoL dinner

After a week of intense study, four MoL students - $E$, $M$, $S$, and $J$ - met at a renowned Amsterdam pizzeria. The restaurant offered a special deal:

Any group of students ordering pizza from the menu (excluding pineapple) would get 10% off and free dessert.

The chef, $B$, considered pineapple to be the worst topping and explained that it is a very bad combination in terms of flavors, and also does not correspond to traditional standards. So, he deliberately excluded it from the deal in order to convince people not to order it. The menu is divided in two sections Traditional and Non-Traditional. Apart from the Pineapple Pizza, all the other ones in the menu are valid for the deal, therefore the students can choose freely. Furthermore, we notice that the number of Traditional and Non-Traditional pizzas is the same, excluding the pineapple one.

Interview with Prof. Catarina Dutilh Novaes

Mon, 01 Jan 0001 00:00:00 +0000

For the first The Illogician MoL alumni interview series, meet Prof. Catarina Dutilh Novaes (VU). Catarina is a philosopher who moves effortlessly from medieval manuscripts to modern logic, asking big questions about reasoning, dialogue, and what it really means to argue well. Hope you enjoy this wonderful conversation with this illustrious MoL alumnus. Let us know who do you want us to interview next!

Question 1

You were part of the very first cohort of the ILLC’s Master of Logic. The program is famous for its interdisciplinary character. Also you recently received the Lakatos Award, which is traditionally awarded to philosophers of science, so it is a big statement to the interdisciplinary nature of your work and your general approach to philosophy. Were you already drawn to this kind of interdisciplinarity before arriving, or was it something that emerged and developed through the ILLC environment itself?

Logic Dating Profiles

Mon, 01 Jan 0001 00:00:00 +0000

Intuitionistic type

I take things constructively

Topos type

Looking for someone who accepts my internal logic

Euclidean Frame type

All my exes know each other

Reflexive Frame type

I am very self-aware

The Injective type

I promise I will never confuse you with someone else

Disconnected Space type

I don’t open up easily

Logical rhetoric makes illogical debates

Mon, 01 Jan 0001 00:00:00 +0000

Debates as logic

When defining a logical system, amongst other things, we define axioms and inference rules. From the application of the latter to the first, we aim to prove validity of statements in that logical framework, the holy grail of that process, the true goal of that ultimate quest, being the sanctified tautology, a statement true in itself (although bound by the system, but not dependent on any other), a stable result, unquestionable. The parallel between this structure and that of an argument, taken in the sense of a discussion, could not be clearer: speakers argue for certain ideas (their axioms) to be considered, and, through applications of inference rules to that newly found common ground, both aim for the tautology, a statement the other cannot refuse, a conclusion going their way. And, of course, the meat, the heart, of the debate truly is the vivid game of “attacking” and “defending” one’s axioms that ensues, done through evocation of counterexamples, meta-proofs of contradiction, so on and so forth. But why is it then that so many debaters focus on the inference rules instead?

Mathematical Structures in Programming Languages

Mon, 01 Jan 0001 00:00:00 +0000

If you enjoyed the Mathematical Structures in Logic course from last semester, you are going to love Nick’s rebranding for the new year: Mathematical Structures in Programming Languages! Alright, you got me, I haven’t managed to convince Nick yet. Still, don’t you find sticking exclusively to logics kind of limiting? There are so many more formal languages out there. What do their semantics look like? What kind of dualities between those shall emerge? Here, let’s stick to a very simple programming language, Hutton’s razor, defined by the following grammar.

Mathematicians, list your ingredients!

Mon, 01 Jan 0001 00:00:00 +0000

A wise friend of mine once compared being a constructivist to being a vegetarian: even if you are convinced it is the right choice, it is hard to fully commit to it in practice. As a vegetarian and a (developing) constructivist myself, I have come to appreciate just how fitting that comparison is. Both philosophies involve conscious decisions not to use certain things, coming from a deeper commitment to a way of thinking. Just as vegetarians avoid meat, constructivists avoid non-constructive principles like the Law of the Excluded Middle or the Axiom of Choice.¹ Over the years, it has become easier and easier to follow a vegetarian diet and eating meat is (in certain circles) no longer the norm. Perhaps this analogy can be used to our advantage: what we can learn from this development? How could we make it easier to be a constructivist in a world where one often assumes everyone eats “meat” by default?

Merkle Puzzles: How to tell a secret

Mon, 01 Jan 0001 00:00:00 +0000

It is Christmas 1974, in the midst of the cold war, and intelligence officer Alice is trying to reach her asset Bob, who is undercover in Budapest, from her apartment in Amsterdam. She knows Bob has confidential information to share with her, but the two of them suspect their telephone line may be tapped. Indeed, East German counter-intelligence agent Eve is listening in to their conversation. The problem of securely transmitting information over an insecure channel has been studied for thousands of years and could, for many purposes, be considered a solved problem by the 1970s. In particular, ciphers like the one-time pad allowed for unbreakable encryption of communication as long as the two communicating parties agreed on a large enough shared secret, the so-called secret key, ahead of time. Unfortunately for our two protagonists, Bob lost the secret key he had agreed with Alice during his latest undercover operation. Up until this point in history, conventional wisdom was that Alice and Bob were now screwed: That without a secret key shared ahead of time, there was no way for Bob to transmit information such that Alice could decipher it but eavesdropping Eve could not.

Proving Everything While Revealing Nothing: An Introduction to Zero-Knowledge Proofs

Mon, 01 Jan 0001 00:00:00 +0000

Introduction

It’s 2 AM and you’re locked out of your email account. The system asks you to prove your identity by entering your password. You type it in, hit enter, and hope the server isn’t compromised. Even if the connection is encrypted, even if the password is hashed, you’ve just revealed your secret to another computer. If that server gets hacked tomorrow, or if a malicious employee decides to peek at the database, your credential is exposed. For decades, this seemed like an unavoidable tradeoff: to prove you know something, you must reveal it.

Regularity Properties of the Reals and the Axiom of Choice

Mon, 01 Jan 0001 00:00:00 +0000

In this article, we aim to give an introduction to the set theoretic study (Jech 2003) of relation between regularity properties of the reals and the Axiom of Choice. Broadly conceived, regularity properties are desirable properties of set of real that appears in various different fields in mathematics. Among them, we are going to sketch Lebesgue Measurability (LM) and Ramsey Property (RP). Diverse and seemingly unrelated they are, it turns out that they share a surprisingly similar pattern. We are going to show that with Axiom of Choice, we can show the existence of sets that break LM and RP respectively. Moreover, due to a celebrated result of Robert M. Solovay (Solovay 1970), via the method of forcing, we are able to show that the full Axiom of Choice is necessary to break these regularity properties. The negative result was proved by constructing a model where all usual of Zermelo–Fraenkel axioms hold and Axiom of Choice fails, yet ALL sets of reals have LM and RP.

Rotating Shapes: The long(est) line

Mon, 01 Jan 0001 00:00:00 +0000

“The long line is a topological space somewhat similar to the real line, but in a certain sense ›longer‹.”¹

To understand this statement, we will firstly do a short recap of topology. A lot of statements will just be given, but the reader is encouraged to verify that these hold.

Topology-Basics

A topological space is a tuple $(X,\mathcal{T})$ consisting of a non-empty set $X$ and a topology $\mathcal{T}$ on $X$, i.e. $\mathcal{T}$ is a collection of subsets of $X$, that contains $\emptyset$ and $X$ and is closed under binary intersections and arbitrary unions. We call the elements of $\mathcal T$ the open sets in $X$. When $\mathcal{T}$ is understood, we sometimes refer to the whole space just by $X$. We call a collection $\mathcal{B} \subseteq \mathcal{T}$ a basis for $\mathcal{T}$ if every element of $\mathcal{T}$ is the union of elements in $\mathcal{B}$. In this case, we say that $\mathcal{B}$ generates the topology. Similarly, every set $\mathcal{B} \subseteq \mathcal{P}(X)$, which is closed under intersections and covers $X$ (i.e. $\bigcup\mathcal{B} = X$) forms a basis for some topology. For example, if we have a linearly ordered space $(X,<)$ with at least two elements, then we can define an interval as the set of all elements between two given points. The collection of all intervals forms a basis for the order topology on $X$. This topology will play an important role for the long line.

Rotating Shapes: Two Möbius make a Klein

Mon, 01 Jan 0001 00:00:00 +0000

Most people know that if you take a long piece of paper, twist one end 180 degrees and then glue it to the other one, you get a shape with only one side and edge. Indeed, if you have never seen this, try it out right know! You can place your finger on one side or edge and follow it around until you end up on the “other” one. We call this shape a Möbius strip and would like to study it mathematically. To do so, we must abstract away the physical paper. From this, we will construct a Klein bottle, for which the “inside” and “outside” are also the same.

The Axiom of Bad Choice and its Equivalents

Mon, 01 Jan 0001 00:00:00 +0000

Translator’s note

This paper, unpublished on any known mathematical outlet at the time, dates back to March 1946, and was found in a parcel in the Beth Library, in the ILLC common room, in the Autumn of 2025. Most plausibly, the author unsuccessfully attempted publication multiple times, culminating in a request to E.W. Beth himself. We publish it here, for the first time in almost eighty years, as we believe it is very well worth the attention of the open-minded logicians of the twenty-first century. Below we print what we hope to be the most faithful rendering possible of the original German. Much gratitude is owed to Max Imilian Wehmeier for his help in the translation process.

The Illogicians' Conversation

Mon, 01 Jan 0001 00:00:00 +0000

In this crazy discussion, each speech turn contains a semantically deviant or infelicitous utterance. Can you guess what is causing each oddity?

B: Hi Gottlob! In what way are you doing?
G: Yes! What about you, Bertrand?
B: I’m very happy! Yesterday, I came back from a trip to France or Paris.
B: Most of the master students came with me, that is, all of them. It was their first time in Paris.
G: Really? It surprises me, who has ever been to Paris.
B: After that trip, every student stopped hating Paris. Only one student used to hate Paris.
B: We went to a restaurant. We ate a French ratatouille. Then we went to the Louvre museum. It was delicious!
G: Colorless green ratatouilles always sleep deliciously.
B: Some students took a dessert. They ate democracy.
G: Great! And how was the Louvre? Did you learn that fact about the painting Mona Lisa?: It is Lisa Gherardini that Francesco del Giocondo ordered a painting that portrays.
B: I did! This is such a famous piece. If no student took a selfie in front of this painting, it will probably be published online.
G: Here is a fun fact you might have missed, though. Five of the six Da Vinci paintings exhibited in the Louvre are made of oil on a panel. It is made of chalk on paper. Can you guess which one it is?
B: It is not Mona Lisa and it might be Mona Lisa.
G: The solution is: DA VINCI made Portrait of Isabella d’Este with chalk on paper, not someone else.
B: Oh, I didn’t know that. More people like Da Vinci than I do. Do you like art history?
G: I once read a book about gender equality. By the way, where was your hotel?
B: On earth.
G: Nice! But how much did you not pay for all of this?
B: A lot! The university didn’t give every student any money for the trip.
G: At least, in France you may pay in euros or in pounds. So you didn’t pay change fees. Did you take the time to get informed about French politics?
B: I did! It is false that the king of France is bald. And some ministers look authoritarian.
G: Be careful what you say! Any French student might enter this room. He disagrees with you.
B: Right! I will go back to my office and be as mute as a ringing fire alarm. See you!

The answers can be found at https://valentin-d-richard.fr/Misc/illogician.pdf

The Logico-Empirical Foundations of Medieval Witchcraft Ascertainment: A Pythonian Analysis

Mon, 01 Jan 0001 00:00:00 +0000

This paper examines the application of proto-scientific methodology in the well-documented medieval inquiry portrayed in Monty Python and the Holy Grail, specifically the “She’s a Witch!” scene. At the core of the tribunal’s reasoning lies the Duck-Weight Equivalence Principle (DWEP), which posits that any individual whose mass precisely matches that of an avian specimen (specifically, Anas platyrhynchos) must, by ancient epistemic law, consist of the same material as ducks. Since ducks float and wood floats, the DWEP formally asserts that such individuals are composed of wood, and hence, by transitive ontological inference, must be witches. This leads directly to the Lemma of Buoyant Malfeasance, though objections persist among anti-floatation theorists who deny the ontological reality of ducks.

The Pineapple Incident - A belief-theoretic and topological analysis

Mon, 01 Jan 0001 00:00:00 +0000

In the famous TV series How I Met Your Mother, Episode 10 of Season 1, the so-called Pineapple Incident presents an epistemologically rich mystery: protagonist Ted Mosby awakens with complete amnesia, a sprained ankle, an unknown woman in his bed, and a mysterious pineapple on his bedside table. This article employs the Multi Layer Belief Model, developed in (Pinto Prieto 2024), to formally analyze this narrative as a case study in belief formation under partial, uncertain, and contradictory evidence.

The Story of Moscow's Methodological Circle

Mon, 01 Jan 0001 00:00:00 +0000

The Moscow Methodological Circle was a philosophical, cultural, and political phenomenon which took part in the rebirth of the study of logic in the USSR, vastly influenced Soviet economy, and still has its place in today’s Russian politics. It originated from the Moscow Logical Circle, which was created in the late 1950s by Aleksandr Zinov’ev, Boris Grušin, Merab Mamardashvili, and Georgij Ščedrovickij, at the Faculty of Philosophy of the University of Moscow. The leader of the group was Zinov’ev, a PhD student at that time, who became a prominent researcher in many-valued logic (see, e.g. (Zinov’ev 1963)).

Too much information? The usefulness of talking redundantly

Mon, 01 Jan 0001 00:00:00 +0000

Suppose you and your favourite MoL-student are procrastinating on your homework assignment (very unrealistic, I know). You decide to play a game – not a very hard one, because your assignment is already difficult enough: one of your laptop screens shows a display containing multiple objects, each of a different shape and colour.

Your task is to think of one of the objects and have your teammate click on it. You are allowed to talk, but you can’t point to the shape or give any other kind of non-verbal hint. Suppose you choose the star in the upper left corner. What do you say to your teammate? Think about it for a minute, before you continue reading.

When if comes after then

Mon, 01 Jan 0001 00:00:00 +0000

Suppose you want to tell someone that you believe that the first edition of The Illogician will be a success, provided that the articles in it are well written. You could convey this message in the usual way, by uttering a sentence such as (1).

(1) If the articles are well written, The Illogician will be a success.

However, it would not be strange to instead say (or hear) exactly the same sentence, but in a different order: