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)
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.
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?”
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.
[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…)
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.
It’s Friday evening, so I’m just in time for another BMoF. The reason for the ‘delay’ is that I just came back from Munich, and the notorious paucity of German youtube did not allow for a timely BMoF. But it was also in Munich that I finally got to meet Steven French, who besides being an accomplished philosopher of science and the editor of a ‘small, provincial journal’ (his words), is a big fan of Brazilian music. (He lived in Brazil for some time in the 1980s.) I asked Steven what his request would be for today’s BMoF, and his answer was: ‘Faroeste Caboclo’ (1987). It is an interesting choice: an extremely long song, with even longer lyrics (not a single line gets repeated), by a band that was hugely popular in my youth, Legião Urbana. (I posted a few songs by them a few years ago.) After the tragic death of leader Renato Russo (a victim of AIDS) in 1996, the band ceased to exist, but their music remains immensely popular among successions of younger generations.
‘Faroeste Caboclo’ tells the story of João de Santo Cristo, a criminal who ends up dying as a hero. The story is so elaborate that a whole movie was recently made based on the song. Below I am posting a video of the song illustrated with scenes from the movie, so that gives listeners who do not understand Portuguese at least an idea of what the whole thing is about. So all in all, a terrific suggestion by Steven, who I hope will like the video I'm posting below.
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). UPDATE: supportive post also at the Feminist Philosophers.
It goes without saying (but I’ll say it anyway) that we, NewAPPS bloggers, fully support Carolyn’s right to post her important analyses of job placement data, and deplore the tone and words adopted by Brian Leiter to voice his objections to her methodology. (This is not the first time that episodes of this kind involving Brian Leiter and junior, untenured colleagues occur; I for one deem such episodes to be inadmissible.)
Most readers will have had at least some exposure to John Searle’s interview by Tim Crane, which was published earlier this week. It was then hotly debated in the philosophical blogosphere at large (in particular at the Leiter Reports). Together with Peter Unger’s interview published roughly around the same time, it seems that the ‘old guard’ is on a Quixotesque crusade to chastise the younger crowd for the allegedly misguided, sorrow state of current philosophy. Now, I do think there is some truth to be found in what Searle says about the role of formal modeling in the philosophy of language, but his objections do not seem to apply at least to a growing body of research in formal semantics/philosophy of language. Moreover, it is not clear whether his own preferred methodology (judging from his seminal work on speech acts etc.) in fact does justice to what he himself views as the primary goal of philosophical analyses of language.
Here are the crucial passages from the interview (all excerpts from the passage posted by Leiter), the main bits in bold:
Well, what has happened in the subject I started out with, the philosophy of language, is that, roughly speaking, formal modeling has replaced insight. My own conception is that the formal modeling by itself does not give us any insight into the function of language.
Any account of the philosophy of language ought to stick as closely as possible to the psychology of actual human speakers and hearers. And that doesn’t happen now. What happens now is that many philosophers aim to build a formal model where they can map a puzzling element of language onto the formal model, and people think that gives you an insight. …
Last week I had a post up celebrating Chico Buarque’s birthday, and among other things I mentioned his relationship with young singer Thaís Gulin (I’m not sure if they are still together or not, but that’s not the point obviously). But it would be utterly unfair to portray her only as ‘Chico Buarque’s girlfriend’, and so to dispel this image of Gulin, here is one of her own songs, ‘Cinema big butts’. It is the strange mix of her own ‘Cinema americano’ interjected with her cover of the 1990s ‘trash-classic’ ‘Baby got back’. The result is at the very least surprising and refreshing. It is the kind of song that provokes reactions of either love or hate, but in any case no indifference; to me, it is strange and compelling at the same time. So, ‘shake that healthy butt!’
Some time ago, I wrote a blog post defending the idea that a particular family of non-monotonic logics, called preferential logics, offered the resources to explain a number of empirical findings about human reasoning, as experimentally established. (To be clear: I am here adopting a purely descriptive perspective and leaving thorny normative questions aside. Naturally, formal models of rationality also typically include normative claims about human cognition.)
In particular, I claimed that preferential logics could explain what is known as the modus ponens-modus tollens asymmetry, i.e. the fact that in experiments, participants will readily reason following the modus ponens principle, but tend to ‘fail’ quite miserably with modus tollens reasoning – even though these are equivalent according to classical as well as many non-classical logics. I also defended (e.g. at a number of talks, including one at the Munich Center for Mathematical Philosophy which is immortalized in video here and here) that preferential logics could be applied to another well-known, robust psychological phenomenon, namely what is known as belief bias. Belief bias is the tendency that human reasoners seem to have to let the believability of a conclusion guide both their evaluation and production of arguments, rather than the validity of the argument as such.
Well, I am now officially taking most of it back (and mostly thanks to working on these issues with my student Herman Veluwenkamp).
The great Chico Buarque joined the club of the ‘over-70’ yesterday (recall Caetano Veloso joining the club last year). Now, while one may speak of a constant stream of talented musicians in Brazilian music, we still haven’t come across anything like the brilliant generation of singers/composers emerging in the later 1960s, including Caetano Veloso, Gilberto Gil, Milton Nascimento and of course, Chico Buarque. They are now all in their early 70s, and alive and kicking. Chico Buarque in particular released an acclaimed new album in 2011 (Chico), and a DVD surveying his whole musical career in 2012. He also continues to pursue a celebrated literary career; in particular, his 2009 novel Spilt Milk has been translated into a number of languages (I very much enjoyed the novel myself).
To celebrate Chico’s birthday, here is ‘Essa pequena’ from his 2011 album (about his relationship with singer Thais Gulin – here is the two of them in the duo ‘Se eu soubesse’), and a classic, ‘O que será’ (1976), a duo with Milton Nascimento. So here’s to many more productive years for him, from which we all benefit…
Thanks to fellow Brazilian logician Valeria de Paiva, I cam across this amazing video, ‘City of Samba’, created by the multimedia artists Jarbas Agnelli and Keith Loutit. The city of samba is, of course, Rio de Janeiro, a city that is perennially beautiful no matter how you look at it; but through the tilt shift lenses of the artists, it becomes frankly supernatural. The music is also specially composed by Jarbas Agnelli, using non-percussion instruments to recreate the magical drumming of a samba school. (Here is a video where he explains the creative process.)
Many of you may by now be a bit fed-up with the World Cup-induced Brazil frenzy, but I assure you that this video will blow your mind even if you are suffering from Brazil-fatigue.
Anyone who spends a modicum of time on the internet will have been exposed to the recent hashtag battle opposing #NotAllMen and #YesAllWomen, so I don’t need to rehearse the details here. What I think is significant is that there may well be a sense in which both camps are right: it may well be the case that the proportion of men engaging in the more extreme forms of sexism and violence against women – the limit cases being sexual assault and rape – is relatively small, while the proportion of women being victims of these assaults is very high. There is no contradiction between the two.
Indeed, a 2002 study mentioned in this recent Slate article (which Eric W also linked to in a recent post – btw, it’s Eric’s post that got me thinking about this issue) on the sexual histories of college men found that ‘only’ 6% of those interviewed had attempted or successfully raped someone. But the catch is that there was an average of 6 rape attempts per perpetrator. So the math is simple: in a population of 100 college men and 100 college women, if 6 men are rapists but each engage in rape attempts 6 times during their college years, then it is perfectly possible that 36 of the 100 women, so more than a third of them, will have been the victims of successful or attempted rapes. (Naturally, there may also be cases of men sexually assaulting other men, but it seems that, in the college population in particular (as opposed to the prison population, or among younger male victims), the wide majority of cases is of male perpetrator and female victim.)
In less than a week from now, the opening match of the World Cup will take place, between Brazil and Croatia. Inevitably, the World Cup exposes spectators to a variety of national anthems from around the world – many of which we’d be just as well not having to listen to. To be honest, the Brazilian national anthem is not particularly beautiful, especially as the lyrics contain the usual dose of chauvinism; but in an instrumental version, here with the virtuoso mandolin player Hamilton de Holanda, it actually sounds surprisingly good.
Continuing the football-themed series I started last week, today I’m posting ‘Fio Maravilha’ by Jorge Ben(Jor). In January 1972, the iconic team Flamengo was playing a friendly game against the Portuguese team Benfica in the Maracanã, and Jorge Ben, a fanatic Flamengo supporter, was among the spectators. Less than 15 minutes before the end of the game, the score was a frustrating 0 x 0, and so the spectators started to demand that João Batista de Sales, a much beloved player who was benched for that match, be let in the game. Coach Mário Zagallo finally decided to comply, and Sales was brought in as a substitute. In no time he scored an astonishing goal, sadly not immortalized on video. The goal is however immortalized in the song ‘Fio Maravilha’, which was the nickname given to Sales after this match; it was an angel’s goal, according to Jorge Ben. The song became very popular and won a national song festival in 1972, in the voice of singer Maria Alcina.
Jorge Ben recorded 'Fio Maravilha' a number of times: I'm posting here 'Fio Maravilha' on its own, and also a hugely popular medley of this song with two other Jorge Ben classics: 'Taj Mahal' and 'País Tropical'. (And let me say for the 1000th time that Jorge Ben is an effing genius.)
Last year weannounced the launch of Ergo, an Open Access Journal of Philosophy. Today is the grand day of the publication of Ergo’s very first issue, with four amazing papers. To commemorate this occasion, the Ergo editors asked four distinguished philosophers each to comment on one of the four papers by means of blog posts. These are:
Julia Jorati (OSU) on a paper in early modern by Paul Lodge (Oxford), at The Mod Squad.
I’ve written a fewposts in the recent past questioning the whole idea of anonymous peer-review as a reliable guide to quality – in philosophy as well as elsewhere. In other disciplines, there have been numerous recent cases of ‘false positives’, i.e. papers which made it through the peer-review process but then were discovered to be fundamentally flawed after they were published (leading to a very large number of retractions).
The issue with false positives is well known, but as I’ve suggested in some of my previous posts, the issue of false negatives is equally serious, or perhaps even more serious, and yet it tends to be under-appreciated. A recent piece by JP de Ruiter, a psycholinguist at the University of Bielefeld, articulates very nicely why it is serious, and why it remains essentially invisible.
The two main goals of a review system are to minimize both the number of bad studies that are accepted for publication and the number of good studies that are rejected for publication. Borrowing terminology of signal detection theory, let’s call these false positives and false negatives respectively.
It is often implicitly assumed that minimizing the number of false positives is the primary goal of APR. However, signal detection theory tells us that reducing the number of false positives inevitably leads to an increase in the rate of false negatives. I want to draw attention here to the fact that the cost of false negatives is both invisible and potentially very high. It is invisible, obviously, because we never get to see the good work that was rejected for the wrong reasons. And the cost is high, because it removes not only good papers from our scientific discourse, but also entire scientists. […] The inherent conservatism in APR means that people with new, original approaches to old problems run the risk of being shut out, humiliated, and consequently chased away from academia. In the short term, this is to the advantage of the established scientists who do not like their work to be challenged. In the long run, this is obviously very damaging for science. This is especially true of the many journals that will only accept papers that receive unanimously positive reviews. These journals are not facilitating scientific progress, because work with even the faintest hint of controversy is almost automatically rejected.
With all this in mind, it is somewhat surprising that APR also fails to keep out many obviously bad papers.
Another sad loss this week: psychologist Sandra Bem, a pioneer in the empirical study of gender roles, passed away on Tuesday, May 20th. Here is the most complete obituary I could find so far, which details nicely her scientific contributions and the practical impact they had in gender policies. For example, it was largely based on her scientific work that the infamous practice of segregating classified job listings under "Male Help Wanted" and "Female Help Wanted" columns was finally abandoned, after a 1973 decision of the US Supreme Court ruling against the practice. (The case was against a particular press, but within a year all other newspapers in the country changed how their classified ads were listed.)
There are many other aspects of Sandra Bem’s life and work worth mentioning, but let me focus on two of them. As an undergraduate in 1965, she met Daryl Bem, then a young assistant professor, and a romantic relationship between them began. (Yes, there are successful stories too, apparently…) Initially, she did not want to get married, as this course of events seemed to preclude the professional path she had in mind for herself. But Daryl was not deterred, and so together they agreed on an arrangement that would allow her to flourish professionally, and which would basically consist in what is now known as equally shared parenting – an ideal that many couples aspire to, but which remains a challenge to implement (speaking from personal experience!). The ‘experiment’ was largely successful, and Sandra narrates all the ups and downs of raising two children (a boy and a girl) on this model in her 1998 book An Unconventional Family. (I’ve been meaning to read the book for years, and now may well be the time to stop procrastinating.)
In a few weeks, the football World Cup will start in Brazil, so in the coming weeks I will be posting a few football-themed songs. Don’t worry: I will not be posting the monstrosity that is the official theme song (with Pitbull & co. -- I refuse to put the link up). I will focus instead on some classics about football in Brazilian music.
Some may recall that the World Cup in Brazil has been surrounded by controversy, especially with the truly astonishing amount of money that seems to have gone into the construction of the stadiums. But like it or not, it will happen, so we may as well get ready for it.
Let me start with ‘É uma partida de futebol’ (1996) by the pop/ska band Skank (I’ve posted about them before). Both the song and the video nicely convey the fanatic, euphoric approach to football among fans in Brazil, with lots of footage from actual matches and the supporters; so quite a treat for football fans!
Last week I was ‘touring’ in Scotland, first in St. Andrews for a workshop on medieval logic and metaphysics, and then in Edinburgh for a workshop on philosophical methodologies, organized by the Edinburgh Women in Philosophy Group. In the latter, I presented a paper entitled ‘Virtuous adversariality as a model for philosophical inquiry’, which grew out of a number of blog posts on the topic I’ve been writing in the recent past (here, here and here). Quoting from the abstract:
In my talk, I will develop a model for philosophical inquiry that I call 'virtuous adversariality', which is meant to be a response to critics from both sides [those who criticize and those who endorse adversariality in philosophy]. Its key feature is the idea that a certain form of adversariality, more specifically disagreement and debate, is indeed at the heart of philosophy, but that philosophical inquiry also has a strong cooperative, virtuous component which regulates and constrains the adversarial component. The main inspiration for this model comes from ancient Greek dialectic.
And so I gave my talk, and somewhat against the spirit of it, everybody in the audience seemed to agree with pretty much everything I had said – where are these opponents when you need them? But one person, Amia Srinivasan (Oxford), raised what is perhaps the most serious objection to any adversarial mode of inquiry, virtuous or not: it may well minimize our endorsement of false beliefs, but it does so at the risk of also minimizing our endorsement of true beliefs.
Some years ago, at the end of an evening that probably involved more alcoholic beverages than it should have, I found myself as a member of a small party of four, composed of two colleagues (and incidentally, good friends) and one PhD student (all three male). As the conversation progressed, I ended up saying things that were somewhat sexually explicit (as some readers may recall, I don’t shy away from talking about matters pertaining to sexuality – see a recent lecture of mine on the science of female orgasm). To be clear, what I said could not have been construed as ‘flirtatious’ in any way, but the next day I came to deeply regret the whole episode. My reasoning was as follows: had I been a male individual, and had the student in question been a female individual, what I said would have been undoubtedly inappropriate, by my own lights. (Similar considerations could be offered concerning interactions with colleagues, but I was particularly concerned with the asymmetry between me and the student).
This episode led me to formulate and since then apply a principle of parity to regulate my behavior in professional situations: not to say or do anything that would be construed or viewed as problematic, had I been a man dealing with (especially more junior) women, be they colleagues, students etc. Until then, I would on occasion make remarks during class (e.g. ‘here, size does matter’ when talking about some issue pertaining to model-theory) which seemed to me to be ok (and in a sense, even a ‘political statement’ in some way), but which would not have been appropriate if uttered by a man. I do not make such remarks in class anymore.
A few weeks ago, the Rainforest Alliance, an NGO whose aim is to "conserve biodiversity and ensure sustainable livelihoods", released a promotional song, ‘I’m alive’, recorded in the Tijuca Forest in Rio de Janeiro, celebrating the wonders of Brazilian rainforests. Some of my favorite Brazilian musicians (Caetano Veloso, Lenine, Criolo) were involved, and the song is inspired by Caetano’s ‘Nine out of Ten’, from his classic 1972 album ‘Transa’. There is a sense in which it is yet another slightly embarrassing attempt by musicians to get involved in a ‘good fight’, but the result is musically not bad at all actually, hence me posting it here at BMoF. But I’m also posting the original ‘Nine out of Ten’ by Caetano Veloso, which, as my friend Jeroen would put it, has a lot more ‘balls’ than this newer version….
Yesterday the great singer Jair Rodrigues passed away at age 75; he was healthy and musically active until the end of his life (performing an average of 15 concerts per month), and died of an acute, violent heart attack. He is one of the lesser-known but very talented singers to have emerged in the 1960s, known for his samba interpretations, but in fact very versatile as a singer. In the 1960s, he hosted a very popular weekly show on TV with Elis Regina, in which many memorable duets with both were recorded.
I’m posting here the song that Jair Rodrigues is perhaps best known for, the classic ‘Deixa isso pra lá’ (1964) (a surprisingly modern proto-rap), and one of his medley duos with Elis Regina – this one with lots of Bossa Nova classics. He will be missed.
Hitler does not like Gödel's theorem one bit. Perhaps surprisingly, he displays a sophisticated understanding of the implications and presuppositions of the theorem. (In other words, there's some very solid philosophy of logic in the background -- I think I could teach a whole course only on the material presupposed here.)
(Courtesy of Diego Tajer, talented young logician from Buenos Aires, giving continuation to the best Monty Python tradition!)
This week I am posting ‘Palco’, a 1981 song by Gilberto Gil. The other day I was reminded of this song and then showed it to my daughters; they now love it, especially the part at the beginning that goes ‘my soul smells like talcum power, like a baby’s buttocks’ (‘minha alma cheira a talco, como bumbum de bebê'). It’s a great song, even if betrays its 1980s-ness in the instrumental overproduction. But it’s upbeat and lively, so perfect to put ya’ll in the mood for the weekend.
I’m in San Diego at the moment for the Pacific APA. Naturally, California rhymes with sea and sun, and in the absence of a California-themed Brazilian song worth posting (of course, there’s this silly one by Lulu Santos), I had to think of the classic ‘Wave’, composed by Tom Jobim and perhaps best known in the João Gilberto version. But I’m also posting it in the original instrumental version, by Jobim himself, and a live version with Jobim and Herbie Hancock. In other words, plenty of choice for picky ears...
BMoF's guest of this week is Luciana Souza, a Brazilian singer who is surprisingly little known in Brazil, having been based in the US for many years now. (Indeed, I discovered her recently thanks to the recommendation of a BMoF reader.) And yet, she has been receiving wide recognition for her work, including a number of Grammy nominations. One of the remarkable features of her career is that she continues to record classics from Brazilian music, while also making quite a splash in the more ‘traditional’ jazz scene. I’m quite impressed with how versatile Luciana is proving to be, being such an accomplished interpreter both of American standards and Brazilian classics.
Indeed, last year she released TWO albums (check here for a promotional video of both): one is the third installment of her Duos series, all of which containing nothing but Brazilian songs; the other is called The Book of Chet, and includes classics of the ‘Chet Baker sings’ repertoire. (Having spent a considerable portion of my youth listening to these Chet Baker recordings, I was particularly pleased to discover the Chet album…) Both albums received Grammy nominations, in different categories (Latin jazz and jazz vocal, respectively).
From Duos III, I’m posting ‘Doralice’, made famous through the João Gilberto classic version, and 'Lamento Sertanejo' (the very same song of last week's BMoF) in a medley with Djavan's beautiful 'Maçã do rosto'; from The Book of Chet I’m posting ‘The thrill is gone’ (my favorite from the album is ‘I get along without you very well’, but sadly I couldn’t find it on youtube). This should be more than enough to convince everyone of Luciana's exceptional talent.
A few weeks ago I had a post on different ways of counting infinities; the main point was that two of the basic principles that hold for counting finite collections cannot be both transferred over to the case of measuring infinite collections. Now, as a matter of fact I am equally (if not more) interested in the question of counting finite collections at the most basic level, both from the point of view of the foundations of mathematics (‘but what are numbers?’) and from the point of view of how numerical cognition emerges in humans. In fact, to me, these two questions are deeply related.
In a lecture I’ve given a couple of times to non-academic, non-philosophical audiences (so-called ‘outreach lectures’) called ‘What are numbers for people who do not count?’, my starting point is the classic Dedekindian question, ‘What are numbers?’ But instead of going metaphysical, I examine people’s actual counting habits (including among cultures that have very few number words). The idea is that Benacerraf’s (1973) challenge of how we can have epistemic access to these elusive entities, numbers, should be addressed in an empirically informed way, including data from developmental psychology and from anthropological studies (among others). There is a sense in which all there is to explain is the socially enforced practice of counting, which then gives rise to basic arithmetic (from there on, to the rest of mathematics). And here again, Wittgenstein was on the right track with the following observation in the Remarks on the Foundations of Mathematics:
This is how our children learn sums; for one makes them put down three beans and then another three beans and then count what is there. If the result at one time were 5, at another 7 (say because, as we should now say, one sometimes got added, and one sometimes vanished of itself), then the first thing we said would be that beans were no good for teaching sums. But if the same thing happened with sticks, fingers, lines and most other things, that would be the end of all sums.
“But shouldn’t we then still have 2 + 2 = 4?” – This sentence would have become unusable. (RFM, § 37)
The episode of this week in the web-series Dominguinhos+ has an unbelievably beautiful version of ‘Lamento Sertanejo’, one of Dominguinhos’ classics (also famous in the Gilberto Gil version). It is an amazing collaboration between singer Mayra Andrade, mandolinist Hamilton de Holanda, and guitarist Yamandu Costa, two of the most talented musicians currently in activity in Brazil. Dominguinhos’ accordion itself is not heard here, but the virtuosity of the two musicians combined with Mayra Andrade’s limpid voice is an absolute killer.
Over the weekend I came across this hoax piece of ‘news’, 'reporting' that a boy who had been raised by orangutans has been recaptured so as to live a ‘normal human life’ again in Malaysia. Despite (or perhaps because!) the phoniness of the ‘article’, it did get me thinking: in such a hypothetical scenario, would capturing such a child and bringing them back to a life with humans be the obvious, right thing to do? On the one hand: isn’t it a form of species chauvinism to think that a human being would undoubtedly be better off in the company of conspecifics? Wasn’t the boy doing just fine among orangutans? (In the hypothetical scenario, that is.) On the other hand: can a human being really thrive and live a fulfilling life exclusively among members of other species (and from a very early age)? This strikes me as an eminently philosophical question, though also partially empirical.
Relatedly, I am currently dealing with another surge of demands for a pet in our household. The current proposal is for rabbits, but I’m resisting this move by pointing out that rabbits belong in the wild, with other rabbits. They wouldn’t be happy living with us, no matter how often my kids will pat and caress them, as they promise. (It’s cute though to hear that this is their conception of what makes a living being happy: lots of hugs.) Coming to think of it, the only species that make any sense at all as pets are those that truly thrive in the company of humans, and as far as I can tell, this only holds of dogs and cats. (Maybe horses? Not sure.) Could it be that, just as I resist the idea of e.g. rabbits being ‘happy’ among humans, I should also resist the possibility of a human boy being happy among orangutans? My intuitions are clashing here.
What do readers think? I especially welcome comments by philosophers of biology, who may have more data on intraspecific vs. interspecific cohabitation among the different species of animals.
(PS There are of course lots of interesting implications for the nature/nurture debate in such scenarios, but I will leave them be for now.)