New APPS: Art, Politics, Philosophy, Science

Observations on the Leiter vs. Jenkins-Ichikawa affair

By Catarina Dutilh Novaes

Those of you who can’t get yourselves to be offline even during the Xmas break have most likely been following the events involving Brian Leiter (BL), Jonathan Ichikawa (JI) and Carrie Jenkins (CJ), and the lawyers’ letters regarding the legal measures BL says he is prepared to take as a reaction to what he perceives as defamatory statements by (or related to) Ichikawa and Jenkins. As a matter of fact, a blog post of mine back in July seems to have played a small role in the unfolding of these unfortunate developments, and so I deem it appropriate to add a few observations of my own. 

On multiple occasions (and in particular in comments at Facebook posts), Leiter claims to have been directed to Jenkins’ ‘Day One’ pledge by this blog post of mine of July 2^nd 2014, in defense of Carolyn Dicey Jennings. It begins:

Most readers have probably been following the controversy involving Carolyn Dicey Jennings and Brian Leiter concerning the job placement data post where Carolyn Dicey Jennings compares her analysis of the data she has assembled with the PGR Rank. There have been a number of people reacting to what many perceived as Brian Leiter’s excessively personalized attack of Carolyn Dicey Jennings’s analysis, such as in Daily Nous, and this post by UBC’s Carrie Ichikawa Jenkins on guidelines for academic professional conduct (the latter is not an explicit defense of Carolyn Dicey Jennings, but the message is clear enough, I think). [emphasis added]

Leiter claims that this observation is what led him to Jenkins’ post in the first place, which he perceived as a direct attack on him. He also claims that this is what the passage above implies, and continues to repeat that the post “was intended by Jenkins as a criticism of me (as everyone at the time knew, and as one of her friends has now admitted), and thus explains my private response, which she chose to make public.” However, there is nothing explicitly indicating that the post was intended as a criticism of BL beyond the fact that he read it this way and keeps repeating it. 

Conceptual genealogy for analytic philosophy - Part II.3: The historicity of philosophical concepts

By Catarina Dutilh Novaes

This is the fourth and for now final installment of my series of posts on conceptual genealogy. Part I is here; Part II.1 is here; Part II.2 is here; a tentative abstract of 2 years ago, detailing the motivation for the project, is here. 

I now discuss the five main features of the historicist conception of philosophical concepts that motivates and justifies the method of conceptual genealogy for philosophical concepts. In a sense, this is the backbone of the  paper and of the whole project, so I'm particularly interested in feedback from readers now.

-----------------------------------------

We are now in a better position to describe in more detail what I take to be the five main characteristics of the historicist conception of philosophical concepts that I defend here, borrowing elements from Nietzsche’s conception of genealogy and Canguilhem’s concept-centered historical approach. In short, these are (they will each be discussed in turn subsequently):

1. Historical change
2. Superimposition of layers of meaning
3. Contingency
4. Multiple lines of influence
5. Connected to (extra- or intra-philosophical) practices and goals

Directory of Philosophers from Underrepresented Groups in Philosophy

...is online! It merges the different lists hitherto available with specific underrepresented groups within philosophy and for different areas into a single directory. From the description:

The UPDirectory publicizes information about philosophers who are members of traditionally underrepresented groups in philosophy. The purpose of the directory is to provide an easy-to-use resource for anyone who wants to learn more about the work of philosophers who belong to underrepresented groups within the discipline. [...]

For the purposes of the UPDirectory, traditionally underrepresented groups in philosophy include women philosophers, black philosophers, Asian philosophers, Latina/o and Hispanic Philosophers, Indigenous/Native philosophers, LGBTQ philosophers, and philosophers with a disability, among others. [...] Inclusion in the directory is primarily a matter of self-entry.

So, philosophers belonging to one or more of these underrepresented groups: go add yourselves! And everybody else: go check it out! Make sure you use this amazing resource next time you plan a conference, an edited volume etc.

Conceptual genealogy for analytic philosophy - Part II.2: Canguilhem on genealogy of scientific concepts

By Catarina Dutilh Novaes

This is the third installment of my series of posts with different sections of the paper on conceptual genealogy that I am working on. Part I is here; Part II.1 is here; a tentative abstract of 2 years ago, detailing the motivation for the project, is here. 

I now turn to Canguilhem as an author exemplifying the kind of approach I have in mind when I speak of 'conceptual genealogy'. The main difference is that Canguilhem focused on scientific concepts (especially from biology and medicine), whereas I am articulating a methodology for the investigation of philosophical concepts (though of course, often the line between the two groups will be rather blurry). The same caveat of the previous installment on Nietzsche applies: this is a very brief and inevitably superficial discussion of Canguilhem's ideas, on which there is obviously much more to say.

-----------------------------------------

The thesis of the relevance of historical analysis for philosophical theorizing rests crucially on a historicist conception of philosophical concepts, namely that they are not (or do not correspond to) a-historical essences or natural kinds. However, ‘historicism’ can have different meanings (Beiser 2011, Introduction), so let me now spell out in more detail in what sense I defend a historicist conception of philosophical concepts.

Conceptual genealogy for analytic philosophy - Part II.1: Nietzschean Genealogy

By Catarina Dutilh Novaes

This is the second installment of my series of posts with different sections of the paper on conceptual genealogy that I am working on. Part I is here; a tentative abstract of 2 years ago, detailing the motivation for the project, is here. 

I now present some of the basics of Nietzschean genealogy which will then be central for my general project. The goal here is thus not to offer a thorough account of Nietzsche's thought on the matter, obviously (a lifelong project!), but it should still be an accurate presentation of some aspects of it. If that is not the case, please do let me know! (I rely mostly on Geuss' and Leiter's interpretations.) Feedback in general is more than welcome.

---------------------------------------

The mundane, commonsensical sense of genealogy is typically related to the idea of vindication, i.e. of validation of one’s authority through the narrative of one’s origins. This is particularly conspicuous in historical disputes for political power within the traditional monarchic model: a contestant has a claim to the throne if she can prove to be a descendent of the right people, namely previous monarchical power-holders. In such cases, a genealogy is what Geuss (1994, 274) describes as ‘tracing a pedigree’, a practice as old as (Western?) civilization itself. The key idea is the idea of transmission of value: a person with noble ancestry inherits this status from her ancestors.

Conceptual genealogy for analytic philosophy - Part I: Analytic philosophy and the a-historical conception of philosophy

By Catarina Dutilh Novaes

As some readers may recall (see this blog post with a tentative abstract -- almost 2 years ago!), I am working on a paper on the methodology of conceptual genealogy, which is the methodology that has thus far informed much of my work on the history and philosophy of logic. Since many people have expressed interest in this project, in the next couple of days I will post the sections of the paper that I've already written. Feedback is most welcome!

Today I post Part I, on the traditionally a-historical conception of philosophy of analytic philosophers. Tomorrow I will post Part II.1, on Nietzschean genealogy; on Thursday and Friday I will post Part II.2, on the historicity of philosophical concepts, in two installments.

-----------------------------------------

Wiliams (2002) and Craig (2007) fittingly draw a distinction between genealogies that seek to expose the reprehensible origins of something and thereby decrease its value, and genealogies that seek to glorify their objects by exposing their ‘noble’ origins. The former are described as ‘subversive’, ‘shameful’ or ‘debunking’, while the latter may be dubbed ‘vindicatory’. (I will have much more to say on this distinction later on.) Nietzsche’s famous genealogical analysis of morality is the archetypal subversive genealogy, and has given rise to a formidable tradition of deconstruction of concepts, values, views, beliefs etc. by the exposure of their pudenda origo, their shameful origins. As described by Srinivasan (2011, 1),

Nietzsche’s innovation prompted a huge cultural shift towards subversive genealogical thinking – what might be called the ‘Genealogical Turn’ – including Freudian analysis, 20th-century Marxism, Foucault’s historical epistemology, certain strands of postcolonial and feminist theory, and much of what goes by the label ‘postmodernism’. These ideological programmes operate by purporting to unmask the shameful origins – in violence, sexual repression, gender or racial hegemony and economic and social oppression – of our concepts, beliefs and political structures.

Philosophy, children, curiosity, and wonder

By Catarina Dutilh Novaes

Today is UNESCO’s World Philosophy Day, which is celebrated on the third Thursday of November every year. As it so happens, November 20th is also the United Nations’ Universal Children’s Day (here is a blog post I wrote for the occasion 2 years ago). I am truly delighted that these two days coincide today, as children and philosophy are two of my greatest passions. But the intimate connection between children and philosophy runs much deeper than my particular, individual passions, and so it should be celebrated.* As Wittgenstein famously (but somewhat dismissively) put it: 

Philosophers are often like little children, who first scribble random lines on a piece of paper with their pencils, and now ask an adult "What is that?" (Philosophical Occasions 1912-1951)

My own favorite definition of philosophy is that philosophy is at heart the activity of asking questions about things that appear to be obvious but are not. (True enough, it also involves attempting to provide answers and giving arguments to support one’s preferred answers.) And so it is incumbent on the philosopher to ask for example ‘What is time, actually?’, while everybody else goes about their daily business taking the nature of time for granted. Indeed, philosophy is intimately connected with curiosity and inquisitiveness, and this idea famously goes back all the way to the roots of philosophy as we know it:

In memoriam: Patrick Suppes

By Catarina Dutilh Novaes

As readers will have noticed, since yesterday there has been an outpour of expressions of sorrow for the passing of Patrick Suppes everywhere on the internet. He was without a doubt one of the most influential philosophers of science in the 20th century, and so all the love and appreciation is richly deserved. I do not have anything much to add to what others who knew him better have been saying, but I thought of posting a link to the video podcast of a lecture he delivered at the Munich Center for Mathematical Philosophy some two years ago, titled ‘A neuroscience perspective on the foundations of mathematics’. (Back then I even wrote a blog post about the lecture, just before it took place.)

As much as it is sad to see dear, talented people passing away, I think it is comforting to note that Suppes lived his life to the fullest until the very end, for example by flying across the ocean to give a lecture on a new, exciting topic at age 90. The vitality he displays in the lecture is truly impressive, and a lovely reminder of his decisive contributions to philosophy and the sciences.

In memoriam: Alexander Grothendieck

By Catarina Dutilh Novaes

Alexander Grothendieck, who is viewed by many as the greatest mathematician of the 20^th century, has passed away yesterday after years of living in total reclusion. (To be honest, I did not even know he was still alive!) He was a key figure in the development of the modern theory of algebraic geometry, among others, but to philosophers and logicians he is perhaps best known as one of the major forces behind the establishment of category theory as a new foundational framework for mathematics. 

So far, I’ve only seen obituaries in French (Libération and Le Monde), as Grothendieck (of German origin) lived almost all of his life in France (I expect that soon obituaries in English will be available too). His life story is almost as remarkable as his mathematical achievements: his father died in Auschwitz in 1942, while he was sent to a concentration camp in France with his mother. In all of his adult life, he was as passionate about pacifism as he was about mathematics (and perhaps even more), and continuously engaged in a number of activist initiatives like lecturing on category theory in a forrest of bombed Vietnam to protest against the war. He seems to have basically stopped doing any mathematics in the 1970s, but the influence of his work in the field is bound to remain colossal in many years or even centuries to come.

What does it take to be the official supervisor of your PhD students in the Netherlands?

By Catarina Dutilh Novaes

You have to be a full professor, that’s what it takes. This is an entirely absurd, obsolete system – in particular in view of the fact that many PhD studentships are financed by external funding obtained by researchers who cannot be the official supervisors of these students (and who in practice do all the supervising work). The system is not only unfair; it is also nefarious for the functioning of academia in the Netherlands as a whole. (See a statement (in Dutch) by three philosophers and members of the Young Academy of the Royal Netherlands Academy of Arts and Sciences – Ingrid Robeyns, Arianna Betti and Peter-Paul Verbeek – with nine objections to the current system.)

Reinhard Muskens, a very distinguished logician-linguist-philosopher at the University of Tilburg, has started a petition asking the board of his university to revise this policy and extend the rights to be the official supervisor of a PhD thesis to non-full professors. Muskens himself has attracted very large amounts of external funding in his long and fruitful career as a researcher, has de facto supervised a number of PhD students, but still does not have what is referred to as ‘promotion rights’ around here. 

Street harassment caught on camera

By Catarina Dutilh Novaes

Related to my post on the invisibility of sexual harassment earlier this week, here’s a video that has been making the rounds on the Internet, and rightly so: a woman walks on the streets of NYC, and a hidden camera captures the unsolicited comments and aggressive attempts at making contact by numerous men she runs into. Now, that’s a good way to make (street) harassment more visible!

 

What is the (recent) history of the term ‘intuitions’ in philosophy?

By Catarina Dutilh Novaes

As reported a few weeks ago, I’ve been working on a paper with my student Leon Geerdink (for a volume on the history of early analytic philosophy being edited by Chris Pincock and Sandra Lapointe) where we elaborate on a hypothesis that I first presented in a blog post more than 3 years ago: that the history of analytic philosophy can to a large extent be understood as the often uneasy interplay between Russellianism and Mooreanism, in particular with respect to their respective stances on the role of common sense for philosophical inquiry. In the first part of the paper, we present an (admittedly superficial and selective) overview of some recent debates on the role of intuitions and common sense in philosophical methodology; in the second part we discuss Moore and Russell specifically; and in the third part we discuss what we take to be another prominent instantiation of the opposition between Russellianism and Mooreanism: the debate between Carnap and Strawson on the notion of explication.

The paper is now almost ready (and we’d be happy to share the draft if anyone is interested), but one puzzle remains: when and how did the term ‘intuitions’ begin to be used in the philosophical literature in its current sense(s)? (As argued by C.S.I Jenkins, the term seems to be used in different senses in the current debates.) As established by Leon, Russell and Moore do not use the term ‘intuitions’ in any of these senses (and in particular, not in the sense of common sense and folk beliefs); instead, they use the term in the technical, largely Kantian, sense of immediate knowledge. We have not found occurrences of the term in the Carnap/Strawson debate either.

Does anyone know the answer to this pressing question? The SEP entry on intuitions is silent on the history of the terminology, and I haven’t found any discussions of this issue in the recent papers I’ve been reading for this project (maybe I’m missing something?). Not much hinges on this matter for the purposes of my paper with Leon, but it did make us curious. Perhaps our knowledgeable readers know the answer? We hope so!

 

The invisibility of sexual harassment

By Catarina Dutilh Novaes

A few years ago, I was going through airport security at Schiphol for a short European flight (to Munich, if I remember correctly), with hand-luggage only. As I was struggling with some lower back pain at the time, I was bringing an electric massager with me; sure enough, when my trolley went through the x-ray, the massager caught the guard’s attention. He made me open the trolley, and asked: ‘what is this?’ I said: ‘it’s an electric massager’. His reply (salacious voice): ‘oh, but isn’t it better if someone else does the massaging on you?’ (Wink, wink…) I am usually rather short-tempered, and normally would have made quite a fuss about it, but I didn’t want to risk missing my flight so I simply moved on.

Now, this is only one of many similar episodes I and every single woman in the world have experienced in our lives – nothing very extraordinary about it. But when I told my friendly, well-meaning male friends about this episode, they just couldn’t believe their ears: yes, there it was, a male airport security guard making entirely inappropriate remarks to a female traveler.

This episode illustrates a well-known phenomenon: the invisibility of harassment to those who do not experience it (and similarly for racism, ableism etc.). The ‘nicer’ guys who do not engage in overt harassment often think it is so inconceivable that anyone could be so grotesque that they fail to see it when it happens near them (and in fact, it often does not even happen near them; I doubt that the security guard would have made his remark had I been accompanied by a male travel companion). This tends to lead to an under-appreciation of the problem among these well-meaning men. Moreover, the men who do engage in such behavior often think there’s nothing wrong with it (‘hey, it’s just a joke!’), and so also fail to appreciate the gravity of the problem. 

The upside down world paradox

By Catarina Dutilh Novaes

(Cross-posted at M-Phi)

As most kids (I suspect), my daughters sometimes play ‘upside down world’, especially when I ask them something to which they should say ‘yes’, but instead they say ‘no’ and immediately regret it: ‘Upside down world!’ The upside down world game basically functions as a truth-value flipping operator: if you say yes, you mean no, and if you say no, you mean yes.

My younger daughter recently came across the upside down world paradox: if someone asks you ‘are you playing upside down world?’, all kinds of weird things happen to each of the answers you may give. If you are not playing upside down world, you will say no; but if you are playing upside down world you will also say no. So the ‘no’ answer underdetermines its truth-value, a bit like the no-no paradox. Now for the ‘yes’ answer: if you are playing upside down world and say ‘yes’, then that means ‘no’, and so you are not playing the game after all if you are speaking truthfully. But then your ‘yes’ was a genuine yes in the first place, and so you are playing the game and said yes, which takes us back to the beginning. (In other words, 'no' is the only coherent answer, but it still doesn't say anything about whether you are actually playing the game or not.)

 

Transferability as the epistemic value of deliberation

By Catarina Dutilh Novaes

Today my research group in Groningen (with the illustrious online participation of Tony Booth, beaming in from the UK) held a seminar session where we discussed Fabienne Peter’s 2013 paper ‘The procedural epistemic value of deliberation’. It is a very interesting paper, which defends the view that deliberation has not only epistemic value (as opposed to ‘merely’ ethical, practical value), but also that it has procedural epistemic value (as the title suggests), as opposed to ‘merely’ instrumental value. I'll argue here that I agree with the thesis, but not for the reasons offered by Peter in her paper.

The paper begins with the following observation:

An important question one can ask about collective deliberation is whether it increases or decreases the accuracy of the beliefs of the participants. But this instrumental approach, which only looks at the outcome of deliberation, does not exhaustively account for the epistemic value that deliberation might have. (Peters 2013, 1253) 

One way to spell out this idea is the following: suppose there were two knowledge-producing procedures with the exact same accuracy, i.e. which would produce the same amount of true beliefs and avoid the same amount of false beliefs. Moreover, procedure D involves deliberation, while procedure O relies entirely on an oracle, for example. If we can show that procedure D is superior to procedure O on purely epistemic grounds, then we can establish that deliberation has procedural epistemic value, rather than merely instrumental epistemic value (i.e. increase accuracy).

The PGR board letter, and a different perspective

Many of you will have seen the following Facebook update posted by both David Chalmers and Jason Stanley (it’s astonishing how events in the philosophy profession unfold over at Facebook!):

Over the past day or so, 24 members of the advisory board of the Philosophical Gourmet Report have signed a letter saying that they value the extraordinary service that Leiter has provided with the PGR, and that they now urge him to turn over the PGR to new management. The letter (drafted by David Chalmers, Jonathan Schaffer, Susanna Siegel, and Jason Stanley) has been delivered to Brian Leiter, who received it with good grace. We are in the process of collecting more signatures, and will soon make the letter public.

At this point, this is pretty much the best outcome anyone could hope for, in my opinion. It is now a matter of waiting to see how the situation will further unfold, but should Leiter agree to step down, a PGR led by a number of people from the current board seems like a very promising solution. Brian Weatherson weights in with some ideas/suggestions, and mentions in particular Leiter’s treatment of Linda Martín Alcoff a few years ago, which seems not to have been on the radar enough in recent discussions. (Every time I thought of the possibility of BL throwing some legalese at me on account of my post suggesting he step down from the PGR, I reassured myself that he had said similar things before about others, but with a different tone altogether.) 

However, there is another aspect of Brian Leiter’s behavior that seems worth noting. I’ve been contacted by a graduate student at Chicago offering the following testimony:

This is not about the PGR

UPDATE : The post has been slightly edited, for reasons I can clarify if people get in touch with me directly.

======================

In his response to the ‘Statement of concern’ made public yesterday by Sally Haslanger and David Velleman, Brian Leiter is now presenting the issue as a ‘crusade’ against the PGR by long-term critics of the PGR. In light of this suggestion, a few clarifications seem in order.

There may be many reasons why something like the PGR is good for the profession; but I can think of no good reason why it should run by someone like Brian Leiter (despite the fact that he is the originator of the PGR). He systematically resorts to aggressive, offensive and intimidating behavior against those who dare express views different from his own, both in public and in private correspondence, often targeting junior colleagues and others who can't 'compete' with his power and influence. We are talking about a pattern here, not isolated events. Now, it is partly through the PGR that Brian Leiter has become such a powerful figure in the profession, and he has arguably been misusing his position of power and influence to target colleagues who he disagrees with on a number of issues.

The question is then whether (given these frequent displays of disrespectful behavior) he is suited to run an initiative that has become so influential as the PGR. A related question is whether he is not misusing the power and influence he has acquired through the PGR and his blog to impose his views and positions by resorting to intimidation and other silencing maneuvers. More generally, I (and others) feel it is important to send the signal that his aggressive behavior is simply unacceptable; it conveys a very disturbing message, if one of the most powerful members of the profession goes around insulting people with no consequences for himself. And why are there no consequences? Arguably, because most people are too scared of him to speak up, especially as they fear PGR-related repercussions.

So no, this is not primarily about the PGR; it's about what many of us perceive as Leiter's inappropriate behavior on a large number of occasions. As many others, I am in principle not opposed to the continuation of the PGR (as a service to graduate students, for example, or as an instrument for hiring negotiations with the university administrators), but *not* in its current structure, i.e. as a one-man-show run by someone prone to intemperate reactions. This is why I voted ‘No’ at the poll currently being held on the question: “Should we proceed with the 2014 PGR?” My own position is that the PGR should be thoroughly reformed, in particular put under new leadership (preferably, a group of people rather than a single person), if it is to be continued. In sum, I have no objections to a reformed 2015 PGR. 

This being said, Leiter has been running the PGR diligently for years (even if one can quibble with the reputation-based methodology used), and for this he should be thanked (at least by those who think that the PGR has had an overall positive effect on the profession, and there seem to be many such people). It should also be recognized that he has acted admirably on a number of occasions when issues in the profession arose, and perhaps it is also worth noting that none of what I am saying here pertains to his scholarly work, which is (or so I am told) of the highest quality.

Inappropriate correspondence -- to say the least!

Many readers will have seen this already, but it needs to be widely shared and viewed: David Velleman and Sally Haslanger have been collecting instances of Brian Leiter threatening people with legal action, among other kinds of intimidating tactics, in private correspondence. Here are some examples. (My understanding is that there are more such examples, which may eventually be posted as well.) These are people he disagrees with on a number of issues, but the level of aggressiveness in his responses is astonishing, shocking, and unacceptable in a professional context (or any context, for that matter).

(This is why my comment to his recent post on having been threatened with legal action only once in his blogging career was: the question is not how many times he was threatened with legal action; the question is how many times *he* threatened others with legal action. Answer: many times, from the looks of it.)

The emails speak for themselves; no further comment is required. At the very least, I think this calls for those involved with the PGR in various capacities (board members, evaluators) to reassess their involvement.

UPDATE (09/24): there is now a statement in support of Carrie Ichikawa Jenkins signed by her colleagues at UBC and many colleagues elsewhere (myself included).

Review of T. Parsons' Articulating Medieval Logic

By Catarina Dutilh Novaes

(Cross-posted at M-Phi)

I was asked to write a review of Terry Parsons' Articulating Medieval Logic for the Australasian Journal of Philosophy. This is what I've come up with so far. Comments welcome!

===================================

 Scholars working on (Latin) medieval logic can be viewed as populating a spectrum. At one extremity are those who adopt a purely historical and textual approach to the material: they are the ones who produce the invaluable modern editions of important texts, without which the field would to a great extent simply not exist; they also typically seek to place the doctrines presented in the texts in a broader historical context. At the other extremity are those who study the medieval theories first and foremost from the point of view of modern philosophical and logical concerns; various techniques of formalization are then employed to ‘translate’ the medieval theories into something more intelligible to the modern non-historian philosopher. Between the two extremes one encounters a variety of positions. (Notice that one and the same scholar can at times wear the historian’s hat, and at other times the systematic philosopher’s hat.) For those adopting one of the many intermediary positions, life can be hard at times: when trying to combine the two paradigms, these scholars sometimes end up displeasing everyone (speaking from personal experience).

 

Terence Parsons’ Articulating Medieval Logic occupies one of these intermediate positions, but very close to the second extremity; indeed, it represents the daring attempt to combine the author’s expertise in natural language semantics, linguistics, and modern philosophy with his interest in medieval logical theories (which arose in particular from his decade-long collaboration with Calvin Normore, to whom the book is dedicated). For scholars of Latin medieval logic, the fact that such a distinguished expert in contemporary philosophy and linguistics became interested in these medieval theories only confirms what we’ve known all along: medieval logical theories have intrinsic systematic interest; they are not only curious museum pieces.

 

Despite not being the first to employ modern logical techniques to analyze medieval theories, Parsons' approach is quite unique (one might even say idiosyncratic). It seems fair to say that nobody has ever before attempted to achieve what he wants to achieve with this book. A passage from the book’s Introduction is quite revealing with respect to its goals:

 

What makes a mathematical proof beautiful?

By Catarina Dutilh Novaes

 (Cross-posted at M-Phi)

 

In December, I will be presenting at the Aesthetics in Mathematics conference in Norwich. The title of my talk is Beauty, explanation, and persuasion in mathematical proofs, and to be honest at this point there is not much more to it than the title… However, the idea I will try to develop is that many, perhaps even most, of the features we associate with beauty in mathematical proofs can be subsumed to the ideal of explanatory persuasion, which I take to be the essence of mathematical proofs. 

 

As some readers may recall, in my current research I adopt a dialogical perspective to raise a functionalist question: what is the point of mathematical proofs? Why do we bother formulating mathematical proofs at all? The general hypothesis is that most of the defining criteria for what counts as a mathematical proof – and in particular, a good mathematical proof – can be explained in terms of the (presumed) ultimate function of a mathematical proof, namely that of convincing an interlocutor that the conclusion of the proof is true (given the truth of the premises) by showing why that is the case. (See also this recent edited volume on argumentation in mathematics.) Thus, a proof seeks not only to force the interlocutor to grant the conclusion if she has granted the premises; it seeks also to reveal something about the mathematical concepts involved to the interlocutor so that she also apprehends what makes the conclusion true – its causes, as it were. On this conception of proof, beauty may well play an important role, but this role will be subsumed to the ideal of explanatory persuasion.

Intuitions and common sense in recent debates on philosophical methodology

By Catarina Dutilh Novaes

I am working on a paper now (together with my student Leon Geerdink, for a volume on the history of early analytic philosophy being edited by Chris Pincock and Sandra Lapointe) where I elaborate on a hypothesis first presented at a blog post more than 3 years ago: that the history of analytic philosophy can to a large extent be understood as the often uneasy interplay between Russellianism and Mooreanism, in particular with respect to their respective stances on the role of common sense for philosophical inquiry. In the first part of the paper, we present an (admittedly superficial and selective) overview of some recent debates on the role of intuitions and common sense in philosophical methodology; in the second part we discuss Moore and Russell specifically, and in the third part we discuss what I take to be another prominent instantiation of the opposition between Russellianism and Mooreanism: the debate between Carnap and Strawson on the notion of explication.

I am posting here a draft of the first part, i.e. the overview of recent debates. I would be very interested to hear what readers think of it: is it at least roughly correct, even if certainly partial and incomplete? Are the categories I carved up to make sense of these debates helpful? Can they be improved? Feedback would be most welcome!

UPDATE: I forgot to mention that a paper that has been extremely useful for me to organize my thoughts on this topic is Michael Della Rocca's 'The taming of philosophy', which gets quite extensively discussed in other sections of my paper with Leon. It is an excellent paper. However, there is still a substantive disagreement between Della Rocca and us, namely that we think there is a lot more tension between Russell and Moore on the question of common sense's role for philosophy than Della Rocca recognizes (he describes both Moore and Russell as fans of common sense).

Brazilian music on Fridays: the last one

After more than 3,5 years of weekly Brazilian music posts, I decided to discontinue the weekly regularity. For a number of reasons, it had become increasingly difficult for me to keep up with the rhythm (and NOT due to paucity of good Brazilian music!). I may still occasionally post when I come across or am reminded of something particularly inspiring, but it will be a ‘go with the flow’ thing rather than a weekly column. 

For this last (regular) BMoF, I’m posting Caetano Veloso’s ‘If you hold a stone’, which I had intended to post at the very beginning of BMoF (at the time, BMoT) back in February 2011. After writing the whole text, I came to realize that the song was not available on youtube (beginner’s mistake…); for whatever reason, now it is. So if you are interested, go back and read what I wrote back then, and listen to the best song about being homesick that I know of -- appropriate for a goodbye, I suppose.

Many thanks to readers who regularly (or irregularly!) followed BMoF over the last 3,5 years; it's been great fun for me, and hopefully a bit fun for you too. Most likely, there will still be some Brazilian music here at NewAPPS, only less frequently.

A 'mathematical' approach to the usefulness of blogs

I expect many readers to be following the ongoing debate, prompted by a poll run by Leiter last week, on the (presumed) effects that blogs have had for professional philosophy, both at the level of content and at the level of ‘issues in the profession’. (Roberta Millistein weights in at NewAPPS, and I agree with pretty much everything she says; another summary at Feminist Philosophers.) Now, there is a sense in which I am personally not in a good position to have an opinion on this, simply because I haven’t been around long enough to know what it was like before, and thus to be able to draw an informed conclusion. But I can say that my very process of becoming a professional philosopher (not so much content-wise perhaps, but in terms of deciding on the kind of professional I wanted to be) was considerably influenced by reading in particular the Feminist Philosophers blog. Also, I won’t deny that my career as a whole has tremendously benefited from my blogging activity at NewAPPS and at M-Phi, both in terms of the opportunity to discuss my ideas with a larger number of people than would otherwise have been possible, and (more pragmatically) simply in terms of increased visibility and reputation. 

But obviously, my individual experience (or that of other bloggers) is not what is under discussion presently; rather, the question is whether blogs have been good for the profession as a whole. This, however, is obviously a multi-faceted question; it may for example be read as pertaining to the quality of the scholarship produced, to be measured by some suitably ‘objective’ criterion. (As a matter of fact, I do believe that blogs have been ‘good’ for philosophy in this sense, for reasons outlined here for example.) But it may also pertain to the overall wellbeing of members of the profession, in which case the putative effect blogs will have had could be conceived of in terms of a simple formula: for each member the profession (I is the set of all professional philosophers), estimate the net gain (or loss) in professional wellbeing by comparing their situation before (w_b) and after (w_a) the advent of blogs; add it all up, and divide the total by the number of members considered. 

The happiest kids in the world

Exactly 15 years ago today, I arrived in the Netherlands with a suitcase full of dreams (ok, maybe two), ready to start a new phase of my life, but having no idea I'd end up staying for so long. I still do and always will feel a strong bond with my home country Brazil (as BMoF readers of course know!), but looking back on these years, I realize I feel entirely at home here now. Perhaps the main turning point in my relationship with this country was the birth of my children, who were both born here, and who, for all intents and purposes (sadly, including rooting at the World Cup…), are basically Dutch. After they were born, I started feeling a visceral connection with this place, which I didn’t experience before.

However, it is not only because they happened to be born here and have lived here almost all their lives (except for 20 months living in NYC for my older one) that I feel this connection. More importantly, I simply see them happy and thriving, being given all the conditions they need to develop healthily and joyfully, and I am extremely thankful for that. And it’s not only my kids: the Netherlands is consistently ranked as number one at studies comparing the well-being of children in a number of developed countries. 

Everyone’s next question is then: what’s the secret? How does one raise the happiest kids in the world? Obviously, the Netherlands is a prosperous country, with levels of social equality only to be compared to those in the Scandinavian countries, and that goes a long way of course. To start with, virtually every child here has access to health care, education, nutrition etc. (Which is not to say that everything is perfect! But even for what is not so good, it’s still probably better than in most other places.) However, there are more factors involved, and on the basis of my experience as a parent I would like to outline two of them. 

What’s the big deal with consistency?

(Cross-posted at M-Phi)

It is no news to anyone that the concept of consistency is a hotly debated topic in philosophy of logic and epistemology (as well as elsewhere). Indeed, a number of philosophers throughout history have defended the view that consistency, in particular in the form of the principle of non-contradiction (PNC), is the most fundamental principle governing human rationality – so much so that rational debate about PNC itself wouldn’t even be possible, as famously stated by David Lewis. It is also the presumed privileged status of consistency that seems to motivate the philosophical obsession with paradoxes across time; to be caught entertaining inconsistent beliefs/concepts is really bad, so blocking the emergence of paradoxes is top-priority. Moreover, in classical as well as other logical systems, inconsistency entails triviality, and that of course amounts to complete disaster.

 

Since the advent of dialetheism, and in particular under the powerful assaults of karateka Graham Priest, PNC has been under pressure. Priest is right to point out that there are very few arguments in favor of the principle of non-contradiction in the history of philosophy, and many of them are in fact rather unconvincing. According to him, this holds in particular of Aristotle’s elenctic argument in Metaphysics gamma. (I agree with him that the argument there does not go through, but we disagree on its exact structure. At any rate, it is worth noticing that, unlike David Lewis, Aristotle did think it was possible to debate with the opponent of PNC about PNC itself.) But despite the best efforts of dialetheists, the principle of non-contradiction and consistency are still widely viewed as cornerstones of the very concept of rationality.

 

However, in the spirit of my genealogical approach to philosophical issues, I believe that an important question to be asked is: What’s the big deal with consistency in the first place? What does it do for us? Why do we want consistency so badly to start with? When and why did we start thinking that consistency was a good norm to be had for rational discourse? And this of course takes me back to the Greeks, and in particular the Greeks before Aristotle.

 

Is the human referee becoming expendable in mathematics?

(Cross-posted at M-Phi)

Mathematics has been much in the news recently, especially with the announcement of the latest four Fields medalists (I am particularly pleased to see the first woman, and the first Latin-American, receiving the highest recognition in mathematics). But there was another remarkable recent event in the world of mathematics: Thomas Hales has announced the completion of the formalization of his proof of the Kepler conjecture. The conjecture: “what is the best way to stack a collection of spherical objects, such as a display of oranges for sale? In 1611 Johannes Kepler suggested that a pyramid arrangement was the most efficient, but couldn't prove it.” (New Scientist)

 

The official announcement goes as follows:

We are pleased to announce the completion of the Flyspeck project, which has constructed a formal proof of the Kepler conjecture. The Kepler conjecture asserts that no packing of congruent balls in Euclidean 3-space has density greater than the face-centered cubic packing. It is the oldest problem in discrete geometry. The proof of the Kepler conjecture was first obtained by Ferguson and Hales in 1998. The proof relies on about 300 pages of text and on a large number of computer calculations.

Brazilian music on Fridays: 'Vento no litoral'

As this is the last BMoF before the summer break, I had hoped to post something cheerful (especially since we are leaving for Brazil tomorrow). But after a week of so much tragedy – the horrific situation in Gaza, the MH17 flight shot down in Ukraine – it is hard to think of anything that might be remotely appropriate to post today. There is however a song by recent BMoF guests Legião Urbana, a beautiful song about death, which might be just right: 'Vento no litoral'. Renato Russo wrote it after his long-time boyfriend had died, a victim of AIDS (which would in turn take Russo’s life a few years later). To be sure, the song does not have a political dimension to go with the deaths in Gaza and in Ukraine, but insofar as these are also private deaths (many people are now mourning the loss of their mother, father, son, daughter, lover, friend etc.), the song is spot-on what it means to still be alive after the death of a loved one. “Where are you now, beside here inside of me?”

Against the ‘this is nonsense!’ objection

Carolyn Dicey Jennings has a post up discussing the unfortunate implications of criticizing a person’s views in terms of their presumed (lack of) intelligence. I agree with much of what she says there (though I don’t think the issue is exclusively or even predominantly about criticism of women and members of other disadvantaged groups, even if impacts these groups to a greater extent). I want however to bring up another aspect of Brian Leiter’s criticism of Carolyn’s analysis, namely his use of the adjective ‘nonsense’, and connect it to what seems to be a pervasive but somewhat questionable practice among philosophers.

In fact, I was thinking of such a post even before reading Carolyn’s post. The idea was prompted by a conversation with Chris Menzel over lunch last week in Munich. Chris was telling me about some of his thoughts on Williamson’s Modal Logic as Metaphysics, and how Williamson describes the actualism vs. possibilism debate as ‘confused’, i.e. as something that he cannot make sense of. So technically, Williamson is (here) not accusing specific people of holding nonsensical positions, but according to him this is a nonsensical debate, as it were. (Chris Menzel is working on a paper on this material where he objects to Williamson's diagnosis of the debate.)

The notion of ‘nonsense’ has an interesting philosophical (recent) history, dating back at least to the Tractatus, and then later appropriated by the Vienna Circle. (I’d be interested to hear of earlier systematic uses of the notion of nonsense for philosophical purposes.) So, to be sure, it is in itself a philosophically interesting notion, but I think it becomes problematic when 'this is nonsense!' counts as a legitimate, acceptable move in a philosophical debate.

Brazilian music on Fridays: 'Garota de Berlin'

[Special edition] After the massacre of yesterday, there is little left to do other than reminding oneself of other, more mutually rewarding Brazilian-German encounters. So here is ‘Garota de Berlin’, the song that owes its existence to the brief but intense encounter between German singer Nina Hagen and Brazilian singer Supla. This happened back in 1985, when Hagen went to Brazil to perform in the first edition of the Rock in Rio festival. At the time, Supla, now also a reality TV celebrity of somewhat dubious reputation (and the son of two influential politicians – quite a mix!), led the post-punk band Tokyo, and so the band ended up recording ‘Garota de Berlin’ with Hagen’s participation.

The video-clip below is almost comic in its badness, and the song is not exactly a high point in Brazilian music. (I didn’t say that this particular Brazilian-German encounter would be rewarding for all the parties involved, including listeners.) But it is a funny episode in the history of Brazil-Germany relations, and in any case way less painful than those depressing 6 minutes in yesterday's match -- which are easily the most painful 6 minutes in the history of the Seleção.

(On the bright side, I get another chance today! The joys of carrying two nationalities…)

Bad news for academia in Europe

A Portuguese colleague (who has good reasons to remain anonymous) has brought to our attention some very important and worrisome recent events/developments pertaining to research funding in Portugal and Europe, which are described below. Academics in Europe (and also outside Europe) wil do well to pay close attention to these developments.

UPDATE: Perhaps my original phrasing was ambiguous, so to be clear: I am not the author of the post below, rather it is a guest post by the Portuguese colleague in question.

============================

This post serves as a warning, and a plea for help, to academics around Europe.