Dr Lavinia Picollo is a lecturer in Philosophy at UCL. Her research focuses on philosophical logic, formal metaphysics, and the philosophy of logic and mathematics.
- How did you come to philosophy and your particular interests?
My parents (especially my mother) were obsessed with having a knowledgeable kid. I would get a book every Sunday. Sometimes they were just tales, some other times they were more ‘scientific’: a book about bird taxonomy, another about dinosaurs, some on astronomy, and so on. Instead of dolls and make-up (which most girls my age used to get) I would get a telescope for my birthday, a chemistry set, or a big model of the human body with the systems of the human body, all detachable. This worked well on me, as I was extremely curious and eager to learn. I was fascinated by each of the areas of knowledge with which I was presented (except physics, which I only came to like a few years ago). I went from wanting to be a palaeontologist, to an archeologist, an architect, and then an astronomer. As I entered my teenage years, I grew a strong interest for literature and mathematics. However, I soon realised I was not interested in learning the details and boring data of any of these areas. I would always focus on more general, meta-questions; one could say ‘’philosophical’ questions, although I didn’t know anything about philosophy by then. I started a degree in mathematics and another one in literature at the same time. In both my professors would nag: “this is not philosophy class!”. So I finally got the message. I changed from literature to philosophy, and I finally felt at home. My questions were no longer frowned upon, found idle, distracting, or besides the point. It was a relief.
I continued to study mathematics. As I moved forward in my degree I discovered the fascinating combination of philosophy and mathematics. I focused almost exclusively on logic and philosophy of mathematics for about ten years. I was obsessed. Luckily the obsession diminished and gave way somehow recently to broader and healthier interests within philosophy that, although related to logic and the philosophy of mathematics, expand into other areas such as metaphysics, philosophy of language, philosophy of science, and epistemology.
- What motivated you to stay in academia? If you encountered (or continue to encounter) obstacles, what supports have you found?
My decision to study philosophy came together with, and was rather a consequence of, my decision to be a philosopher. It soon became clear to me that the only viable option to achieve that goal was to become an academic. So I directed all my efforts towards that. Once I was in, leaving academia never occurred to me.
The only obstacle one could say I encountered was the infamous two-body problem, which, fortunately, has recently been resolved. For a while it threatened the choice between having an academic career and having a family. Sadly, This is a difficult situation I believe many academics find themselves in.
- Have you had any particular role models, mentors, or favourite philosophers?
The relation between philosophy and mathematics was particularly attractive to me as an undergraduate student, as I was also studying mathematics at the time. So I decided to attend a seminar on Orayen’s Paradox, a puzzle that arises from the fact that (i) the semantics for languages with quantifiers is developed within set theory and (ii) set theory is itself formulated in a language with quantifiers. Eduardo Barrio, who would later supervise both my undergraduate and my PhD dissertations and become a mentor to me, was the seminar leader. In the past he had worked mostly on truth from a philosophy of language perspective (with a focus on Davidson) but was changing course towards philosophical logic, philosophy of mathematics, and formal metaphysics. That seminar was a huge turning point for me. Every topic and every issue discussed in class fascinated me.
In the subsequent terms Barrio offered seminars on other topics in the area, including one on second-order logic and plurals, one on formal theories of truth, on Gödel’s Incompleteness, etc. In addition, he organised reading groups and a work-in-progress seminar. I attended absolutely everything. Argentina was doing well back then; we had money to invite philosophers from all over the world. Some of them deeply influenced me, including Agustín Rayo, Gabriel Uzquiano, Oystein Linnebo, Roy Cook, Graham Priest and, perhaps most importantly, Volker Halbach.
Although most of us hadn’t even graduated by then, these (back then young) philosophers were very generous with us enthusiasts. They devoted a lot of time to talking and discussing philosophy with us during their visits to Buenos Aires. Some of them also corresponded with us profusely thereafter.
After his first visit to Buenos Aires, Volker Halbach kindly invited me to spend some time in Oxford and encouraged me to apply for the DPhil there. For personal reasons I didn’t apply, but I did visit. It was a happy coincidence that Volker and I were both working on (reference and) self-reference in formal languages in connection to the semantic paradoxes at the moment. This was mainly due to the Visser-Yablo Paradox boom that took place about a decade ago. We had numerous supervisions that shaped my work enormously. Thereby Volker became, informally, my graduate thesis co-supervisor as well as a mentor.
Finally, among my favourite philosophers whose written work influenced me greatly I should mention Frege, Hilbert, Carnap, Gödel, Tarski, Quine, and Putnam, followed by Boolos, Field, Horwich, Leitgeb, Shapiro, and Wright.
- How have your expectations about what you want to and are able to study in academia changed over time?
At the beginning, Eduardo’s group was more philosophical and less formally inclined, but soon that began to change. The group got more and more interested in formal aspects of logic and, for some time, so did I. In those days my focus was on proving philosophically interesting theorems, providing philosophically motivated formal theories, and publishing in good specialised journals.
This continued to be the case during my first year or so at the Munich Center for Mathematical Philosophy (the MCMP). I moved there for a postdoc after defending my viva in October of 2016, and a year after I took up an assistant professorship. Since my second year at the MCMP my interests started to drift towards more metaphysical issues revolving around deflationary views on properties, propositions, numbers, and modalities, as well as some topics in the philosophy of mathematics, such as neologicism, indeterminacy, and mathematical pluralism. These are the issues that mainly occupy me now.
- Could you tell us more about your favourite developments or moments in your area of work?
I prefer problems to solutions and, above all, tragedies. My favourite is the tragedy concerning Frege’s logicism, triggered by Russell’s Paradox. I also like the efforts made towards resuscitating Frege’s view, especially those by Wright based on inferentialism, entitlement, and presuppositions of epistemic projects.
I should mention as well Tarski’s work on truth, including his indefinability theorem based on the liar paradox and his proposed way of avoiding it, which gave rise to model theory and the whole literature on formal theories of truth.
Another fascinating tragedy is the one set off by the compactness and Löwenheim-Skolem theorems, which brought about two of the most interesting topics in the philosophy of mathematics: Benacerraf’s structuralism and Putnam’s model-theoretic argument.
The ultimate tragedy, for which we owe Gödel, consists in the incompleteness of first-order arithmetic, set theory, and any sufficiently expressive system of the like. This catastrophic result proved by not only (arguably) put Hilbert’s programme to rest but also sparked the mechanism vs anti-mechanism debate, posed a serious epistemic problem for mathematical realism, led to the discovery of (certain) inaccessible cardinals, legitimised self-referential expressions, and much more.
Finally, allow me one last favourite moment, which rather than a tragedy is a revelation. That is when Ramsey realised that we could do without the word ‘true’ if propositional quantification were available in the language.
- How does your experience of working in academia relate to what you are studying/teaching?
My experience of working in academia consists basically in my research and my teaching; plus the organisation and attendance of academic events and some horrible administrative duties. Academia also creeps into other aspects of my life. I’m lucky to have many academic friends, most of whom are philosophers and a non-negligible number of whom work in my topics or areas. My partner is also a philosopher, so discussing philosophy is very much part of my everyday life.
- How do you wish philosophy had been taught differently during your studies? Do you teach your subject any differently than you were taught?
The philosophy degree (and many others) at the University of Buenos Aires is very long; it usually takes five to seven years to complete. It’s possible to take a ‘continental’ path and an ‘analytic’ path. It’s also possible to do a bit of both, as I did. I cannot say much about the continental path, but the analytic one lacks — or at least used to lack — some fundamental subjects, including epistemology and classical metaphysics. I wish those courses had been available when I was a student.
Introduction to logic was taught pretty much as I teach it now. For advanced logic I prefer to work with my own material, which differs considerably from the book that was in use when I was a student: Hunter’s Metalogic: An Introduction to the Metatheory of Standard First Order Logic. In my courses I cover most of the material in the book but, in addition, I introduce some axiomatic set theory and some relevant philosophical readings, including some on Orayen’s paradox, Benacerraf’s structuralist view of mathematics, and Putnam’s model-theoretic argument. For discussion seminars I’ve adopted a slightly different methodology. I also let students present a paper each week, but guiding questions are given in advance and consist a more-or-less rigid script for their presentations.
- How do you recommend students navigate the balance between passing their degree and finding the time and resources to learn beyond their curriculum about liminal or silenced topics?
Time management is a very personal thing, but I would strongly recommend doing some independent readings on topics that are not discussed in the curriculum. If one is interested in a topic that is not covered by any course or not to their satisfaction, a fun and effective option in my experience is to organise a reading group on the topic. Reading philosophy by myself doesn’t work as well for me as when, in addition, I discuss the salient bits of the text with other people interested in the subject.
- How can (or should?) non-Western philosophy be incorporated into teaching at an undergraduate level?
As I understand it, philosophy is grounded in a number of difficult questions, perhaps those that no special science or discipline aims at or is close to answering, even indirectly. These questions can and have changed through time, and can and do also differ across cultures. Philosophical practice consists, roughly, in answering or working towards an answer to those questions in a reasoned manner. Philosophers should be free to choose the questions they would like to work on, but the answers given in the literature they take into account for their research should be chosen by their relevance and interest, regardless of the tradition, culture, or time in which they originated. A well-designed philosophy course would follow the same principle, which would likely result in the incorporation of some non-Western views.
If one wishes to incorporate more non-Western philosophy to general courses, one could focus on questions within the area that come from non-Western traditions to a higher degree. For more specialised modules it’s easier. One could simply choose a topic or class of questions that have received good attention and treatment in non-Western cultures.
In logic, philosophy of mathematics, and formal metaphysics, excellent work is currently being done in several parts of the non-Western world (by non-Westerners), including China, South Korea, and Japan. I should also mention Mexico, Brasil, and Argentina, which are often considered to be non-Western countries despite their history, language, and culture (perhaps because they are poor and, thus, have been exiled from the West, together with many Eastern European countries). The philosophical work that’s being developed in these countries should certainly not be neglected.
- Is there any advice you would like to pass on to all and especially minority undergraduates studying philosophy?
In my view, gender and ethnic differences have little bearing in the capacity one has for studying and doing philosophy. And the biggest obstacle a woman or a member of a minority faces in this respect in philosophy has to do with a low creedence in this fact, either of themselves or of others. What worked for me as one of the very few women pursuing graduate studies in logic and philosophy of mathematics at the time was to open up, be vocal, and make myself known, so that it was clear (perhaps even to myself) that I was just as capable of engaging in philosophical debate as others. But I’m not sure this advice is useful for everybody. Each of us has their own ways of dealing with these issues.
- With 2020 coming to an end, have the events of this year changed the way you relate your studies to everyday life? Is there anything in particular that you have learnt or would like to take from this year?
What I missed the most this year is face-to-face seminars and academic events. I realised I learn a great deal from those interactions with both colleagues and students, and that my productivity is substantially impaired by the lack thereof.
A more positive lesson I take from 2020 is that, while asynchronous teaching is inconvenient in many ways, it’s probably worth keeping, even once (or if) everything goes back to ‘normal’. Having the possibility to re-record a lecture when it doesn’t go exactly according to plan can be a curse for perfectionists but also be a blessing for their students. Unlike face-to-face lectures, pre-recorded sessions allow me to explain fundamental topics in a way that I find satisfactory. As a result, this year my advanced logic students had considerably less difficulties understanding complex issues than some of my previous students.
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