New APPS: Art, Politics, Philosophy, Science

Easy as 1, 2, 3 ? -- Wittgenstein on counting

By Catarina Dutilh Novaes

(Cross-posted at M-Phi)

 

“A B C

It's easy as, 1 2 3

As simple as, do re mi

A B C, 1 2 3

Baby, you and me girl”

45 years ago, Michael Jackson and his troupe of brothers famously claimed that counting is easy peasy. But how easy is it really? (We’ll leave aside the matter of the simplicity of A B C and do re mi for present purposes!)

Counting and basic arithmetic operations are often viewed as paradigmatic cases of ‘easy’ mental operations. It might seem that we are all ‘born’ with the innate ability for basic arithmetic, given that we all seem to engage in the practice of counting effortlessly. However, as anyone who has cared for very young children knows, teaching a child how to count is typically a process requiring relentless training. The child may well know how to recite the order of numbers (‘one, two, three…’), but from that to associating each of them to specific quantities is a big step. Even when they start getting the hang of it, they typically do well with small quantities (say, up to 3), but things get mixed up when it comes to counting more items. For example, they need to resist the urge to point at the same item more than once in the counting process, something that is in no way straightforward! 

The later Wittgenstein was acutely aware of how much training is involved in mastering the practice of counting and basic arithmetic operations. (Recall that he was a schoolteacher for many years in the 1920s!) Indeed, counting and adding objects can be described as a specific and rather peculiar language game which must be learned by training, and which raises all kinds of philosophical questions pertaining to what it is exactly that we are doing when we count things. Perhaps my favorite passage in the whole of the Remarks on the Foundations of Mathematics is #37 in part I: 

Mary Wollstonecraft, Philosopher of Education

By: Samir Chopra

In 'Observations on the State of Degradation to which Woman is Reduced by Various Causes' (Chapter IV of A Vindication of the Rights of Woman), Mary Wollstonecraft writes:

Reason is...the simple power of improvement; or, more properly speaking, of discerning truth. Every individual is in this respect a world in itself. More or less may be conspicuous in one being than another; but the nature of reason must be the same in all...can that soul be stamped with the heavenly image, that is not perfected by the exercise of its own reason? Yet outwardly ornamented with elaborate care, and so adorned to delight man...the soul of woman is not allowed to have this distinction...But, dismissing these fanciful theories, and considering woman as a whole...the inquiry is whether she has reason or not. If she has, which, for a moment, I will take for granted, she was not created merely to be the solace of man...

Into this error men have, probably, been led by viewing education in a false light; not considering it as the first step to form a being advancing gradually towards perfection; but only as a preparation for life.

The power of generalizing ideas, of drawing comprehensive conclusions from individual observations, is the only acquirement, for an immortal being, that really deserves the name of knowledge. Merely to observe, without endeavouring to account for any thing, may (in a very incomplete manner) serve as the common sense of life; but where is the store laid up that is to clothe the soul when it leaves the body?

In the second para quoted above, Wollstonecraft, after asserting the existence of reason in women--via a theological claim--goes on to establish a normative standard for education: its function is not purely vocational but also a spiritual and moral one. The task of education is the development of reason, the business of bringing to full fruition the divine gift granted all human beings by their Creator. The task of education is not mere 'preparation' for a narrowly circumscribed sphere of profane responsibility; it is, rather, to elevate and uplift each human being by making it possible for them to exercise their reason--as part of a process of gradually 'perfecting' their souls. Education is not prelude to the 'real business'; it is the real business itself.

In the third para, Wollstonecraft asserts the importance of abstraction and generalization--implicit in these claims is the importance of pattern recognition. Humans cannot be content with particulars, with living from moment to moment; they must, through the mastery of these powerful intellectual tools, rise to a vantage point from which disparate phenomena can be tied together into explanatory wholes (and serve as the basis for future theory-building.) The 'common sense of life' is not the only standard that humans should aspire to; there are far loftier goals visible, the journey to which may only be made possible by the right kind of education.

(My Political Philosophy class and I read and discussed some excerpts from Vindication of the Rights of Woman yesterday; these two paragraphs led to a very interesting digression (ending up in computer science and binary numbers). Which is why I make note of them today.)

Note: This post was originally published--under the same title--at samirchopra.com. After posting a link to it on Facebook, I asked whether Mary Wollstonecraft features on philosophy of education reading lists. I would be very interested in responses. Thanks!

 

The Rainbow In My Roster

By: Samir Chopra

Two weeks ago, on 8 September, after finishing my morning stint my gym, I headed to the Brooklyn College campus. I arrived at 12:20, five minutes after the 11:00 AM to 12:15 PM classes had ended. The campus was overflowing with students: streaming out from classrooms and lecture halls, clogging the corridors, the walkways, the quadrangle, the benches outside the library and the library cafe. I walked among them, marveling once again at the splendid diversity--in the linguistic, cultural, ethnic, political dimensions--of our student body. I've been on this campus for just over thirteen years now, and these glimpses never lose their freshness.

I could hear, around me, Russian, Bengali, Urdu, Punjabi, Spanish, Chinese, Haitian Creole, Caribbean Patois, Hebrew; I could see headscarves and hijabs and chadors, yarmulkes, turbans, colored hair, ponytails, topknots, shaven heads. They walked in groups; they walked singly. They talked among themselves; they zoned out on their headphones. They sat; they stood; they sprawled out on the grass. Some rushed to the local Starbucks to refuel on caffeine; others began their lunch, outside, in the still gloriously warm weather, before the next round of classes began at 12:50. I walked on, through this riotous medley, feeling a curious melange of emotions surge through me; I felt protective, proud, and hopeful.

Like any teacher, I'm used to moaning and griping about my students: they don't do the readings; they're late for class; their writing sucks; they ask me questions whose answers are on the syllabus; they disappear for weeks on end and then show up, at the end of the semester, to ask whether they can still find redemption; they check their smartphones in class; they stare blankly at me when I ask them to show me they have understood the points made in last week's class; the list goes on and on. There is truth in all these complaints but there is much more to my students.

As I have noted on this blog, my students' interactions with me in the classroom are a constant source of intellectual enrichment for me; my understanding and appreciation of many philosophical works has been enhanced by my discussing it with my students; I might have a PhD in philosophy and the title of 'professor' but I'm still a student, and my teaching is how I continue to learn. It wouldn't work without my students; it takes two to tango and all that.

But the point I actually set out to make is that the diversity on display that day on campus reminded me that the sheer range of lives and experiences I encounter in my students is another education altogether. My students raise points in the classroom that are inextricably linked with their backgrounds: the Puerto Rican nationalist; the lesbian Orthodox Jew; the working single mother; the trans men and women; the young man struggling to break free of a family afflicted by alcoholism; the immigrants; the native New Yorkers; the senior citizens who audit; the first-generation students; the religious; the skeptical; the conservative; the politically radical; they all bring missives from worlds I only partially experience and understand. They are walking encyclopedias all on their own; they edify and enlighten. They make me realize that my life, varied and rich as it has been, is only the tiniest sliver of all in the giant mosaic of human experience. They point me to much more that lies beyond the narrow confines of my life. Every classroom holds a veritable United Nations, a pleasurable Babel of language, class, ethnicity and political orientation.

I remain ever grateful that I'm a teacher--especially when my students write me appreciative notes!--and that moreover, I'm a teacher here in Brooklyn, in New York City.

This post was originally published--under the same title--at samirchopra.com.

Vatter on Foucault on Hayek

A while ago, Daniel Zamora’s (re)publication of a series of essays designed to say that Foucault ended up embracing neoliberalism caused quite a stir in the blogosphere.  As one of those invited to contribute to a forum in An und für sich), I argued that Foucault saw both that neoliberalism realized the need to create markets (as opposed to liberalism’s assumption that they just happened), as well as the need to create homo economicus as a form of subjectification.  As I put it then:

Was Charlie Hebdo 'Mocking' The Death Of Alan Kurdi?

By: Samir Chopra

Charlie Hebdo has offended again. A recently published cartoon titled “So Close to His Goal”, shows Alan Kurdi, the Syrian toddler whose tragic drowning death sharply focused the world's attention on the desperation of the migrant crisis in Europe, lying face down on the sand near a billboard featuring Ronald McDonald and advertising a 2-for-1 McDonald's Happy Meal with the legend: 'Two children's' meals for the price of one." The caption reads, 'So close to his goal.' And above it all, "Welcome to migrants.' A second cartoon titled “The Proof that Europe is Christian” shows a toddler drowning in the ocean. waters. Next to him a Christ-like figure walks on water. The caption reads, "Christians walk on waters… Muslims kids sink.”

Here is how I 'read' the cartoon, roughly: The West and Europe imagines itself the haven of liberal, secular ideals; it imagines itself the bastion of democracy, republicanism, and the social welfare state. In point of fact, it is as much in thrall to old-fashioned notions of Christian triumphalism and the blurring of the church and state as those regimes that it disdains. The West and Europe still fight holy wars; they still imagine themselves under attack from the 'Huns' and the 'Goths' and the 'barbarians' and the 'Moors.' The migrants might have thought they were escaping to this promised land where they would be welcomed with open arms and invited to make a new life. Little do they know that they were only heading for a vapid, shallow, xenophobic, insular, Islamophobic, consumerist culture, one whose patron saint is Ronald McDonald, and whose guiding slogans are not the call to arms of the great revolutions, but rather, sales pitches for cheap goods.

That's how I read it. I did not take these cartoons to be 'mocking' a dead child.  I do not claim to know the 'intent' of the cartoonist, but given Charlie Hebdo's history, and the current context, my interpretation strikes me as at least halfway plausible.

I am not going to offer a systematic defense here of Charlie Hebdo, but want to make note of a couple of what I think are relevant points:

1. The famous cartoon of Barack and Michelle Obama exchanging fist-bumps in the Oval Office, while wearing 'Arab dresses' and carrying guns, appeared on the cover of the New Yorker. Had it appeared on the cover of the National Review Online, complete with a comments section of gibbering right-wingers rubbing their hands in glee, reactions to it would have been considerably sharper.
2. The Onion once ran an article titled 'Redskins Kike Owner Refuses To Change Team's Offensive Name.' I did not think the article or its headline was anti-Semitic. Some Jewish friends of mine were offended.

Charlie Hebdo's cartoons are bound to offend many and their choice of vehicle for making their political points might be questioned. But they have ample material to choose from and ample opportunity to offend; this world and its dominant species' arrogance and continuing self-destructive behavior will ensure that. Satirists exist and find work because we are worthy targets of satire.

Note: This post was originally published--under the same title--at samirchopra.com.

A Proposed Heuristic For Academic Budgeting Decisions

It occurred to me, in the midst of a conversation where folks were marveling at the money being spent by a flagship state university on a marketing initiative, that it should, at this juncture,* be possible to formulate a very simple test for evaluating the wisdom of this and other university spending initiatives:

"How many part time lines could be made full time and / or how many adjunct lines could be made permanent with the money being spent on this**?"

 

*A conjuncture defined, let us say, by the circumstance that the majority—or even a significant portion—of  faculty at US universities continue to be employed, against their preferences, in contingent positions without the full measure of academic freedom and the full participation in shared governance afforded by tenure and / or in positions that, by virtue of low salaries, lack of benefits, etc., make their very material existence substantially precarious.

**Depending on the conversational context, one may wish to add something like "bullshit" here. Use your judgment.

PSA-WC's Highlighted PhilosopHer of Science: Merrilee Salmon

The PSA Women's Caucus is delighted to announce its first Highlighted PhilosopHer of Science, Merrilee Salmon. You can read about Merrilee's many-splendored career over at Science Visions. Congratulations, Merrilee!

APDA Final Report

In the coming weeks I hope to be updating you with more details and analyses, but for now I am simply announcing that the final report for APDA is complete. Feel free to ask questions or comment below.

*Update: we noticed an error in one of the charts and some potentially confusing language in that section, so we have updated the report at the link.