In the Ph.D. program at Stanford's Department of Philosophy, all of us first-year students are required to take a topical proseminar.  This year, Ken Taylor is teaching it and our topic is (really, topics are) "Content, Consciousness, and Reason".  This past week, we focused on an episode of a debate between broad and narrow mental content.  Although I won't really talk about any details of the debate, I should quickly define the terms.  Narrow content is content that depends only on properties of the individual.  Broad content is content that does not (for instance, it depends on socio-environmental factors).  Although Tyler Burge has given an influential argument in favor of broad content, some people (Fodor, Chalmers) still argue that some content must be narrow while others (Segal) argue that all content is narrow.

While I don't want to jump in to that debate here, I do want to talk briefly about a kind of argument that seemed to come to a few people in the seminar.  It's a kind of Kantian (I dare say transcendental) argument for the existence of at least some broad content.  The argument roughly goes like:

1. Disagreeing presupposes public contents that the disagreement is about.
2. We do disagree.
3. Therefore, some content is public.

Broadness follows because narrow content cannot be public.

One thing worth noting about this argument is that one cannot object to (2).  I would argue that "I disagree that there are disagreements" is in effect an instance of the liar paradox.

Although we were talking about disagreement in the seminar, the argument obviously generalizes:

1. Communication presupposes public contents that are being communicated.
2. We do communicate.
3. Therefore, some content is public.

To put (1) in more Kantian terms: Public contents are a necessary condition for the possibility of communication.

The real point that can be argued is (1).  I think it might be worthwhile to replace "communication" with "meaningful communication", but given that meaning is part of what's at stake here, that's a bit dicey.  It seemed like some students in the seminar wanted to push this line of thought by replacing "communication" with "philosophy" which provides a neat twist in that what we are doing while making this argument is philosophy.  That would make (2) equally irrefutable.  But it might put (1) in even more questionable territory.

In any event, I just wanted to put the argument out there to see what people make of it.  I'm personally unsure where I stand on the wide/narrow debate since I think some arguments from both sides are fairly convincing.  Of course, I've yet to see either side attempt to argue that the other notion of content in general is impossible.  Usually (both Segal and Sawyer do this in their entries in the Contemporary Debates in Philosophy of Mind anthology) one argues that the best current options for the kind of content at stake fail.  But that does not mean no future option will succeed.  This warning seems somewhat analogous to Kyle Stanford's argument that unconceived alternatives pose the biggest threat to scientific realism.

My article, "Lambda Calculi", has been accepted by and published at The Internet Encyclopedia of Philosophy.  Please do send me comments, criticisms, and suggestions.

R.J. Lipton just posted on his blog a very nice dedication to Alan Turing's famous paper "On Computable Numbers, with an Application to the Entscheidungsproblem". While I recommend both the blog post and the paper, I want to write about an episode from the comments section of the post.

In a comment, John Sidles takes an essay from the preface to General Victor Krulak's book First to Flight and replaces every occurrence of the word "US Marine" with "mathematician".  The result is breathtaking and somewhat awe-inspiring:

Why does the world need mathematicians?

Mathematics exists today—flourishes today—not because of what we know we are, or what we know we can do, but because of what the world believes we are and believes we can do.

Essentially, because of the unblemished achievements of mathematics over centuries, the world believes three things about mathematicians.

First, they believe that when trouble comes to the world, there will be mathematicians—somewhere—who through hard work have made themselves ready to do something about it, and do it at once. They picture mathematicians as mature individuals—dedicated members of a serious professional community.

Second, they believe that when mathematicians bend their minds to a task, they invariably turn in a performance that is dramatically and decisively successful—not most of the time, but always. The world’s faith and convictions in this regard are almost mystical. The mere association of the word “mathematics” to a challenge is an automatic source of encouragement and confidence everywhere.

The third thing that they believe is that training in mathematics is downright good for young people; that mathematicians are the masters of an unfailing alchemy that helps convert unoriented youths into proud, self-reliant stable citizens—citizens into whose hands the planet’s affairs may safely be entrusted.

The people believe these three things. They believe them deeply and honestly, so much that they are willing to pay for mathematicians to solve problems, and to teach young people.

Therefore, for reasons that completely transcend cold logic, the world wants mathematicians. These reasons are strong, they are honest, they are deep-rooted, and they are above question or criticism. So long as they exist—so long as people are convinced that mathematicians can really do the three things I have mentioned—we are going to have a mathematical profession.

And likewise, should people ever lose that conviction—as the result of the mathematics community’s failure to meet their high—almost spiritual—standards, the profession of mathematics will swiftly disappear.

Is there a chance that such a thing might happen? I think there is. I think that we ourselves can shake these convictions and the accompanying faith which really sustain us. By a lack of attention we can lose the inspirational personal relation that is shared between our senior members and our rank-and-file. Also, by carelessness or inordinate attention to less important things, we can lose the attributes of professional dedication and unfailing preparedness which, in centuries past, has deservedly made mathematics one of humanity’s treasures.

How serious it is, I don’t profess to estimate to you, but it certainly worries me. It does, because if the world wanted to try, she could get along without a profession of mathematics.

In this post, I primarily wanted to reproduce and share the above piece.  That being said, I will conclude with a few brief comments.  It seems to me that while all three things are generally believed about mathematicians, the second seems to be the most true.  Ever since the mathematization of the sciences in the time from Galileo to Newton, there seems to be a push to mathematize anything and everything. This push, I believe, rests on a belief that by mathematically modeling a phenomenon we imbue said phenomenon with the certainty of mathematical truth.

I do also wonder what other professions could be substituted into the passage for "US Marine".  Of course, given the career path that I will soon be embarking on (I am starting a Ph.D. in Philosophy at Stanford this Fall), I am most curious about whether "philosopher" fits.  Judging by my interactions with a variety of people, their reactions lead me to believe that none of the three beliefs listed above are held in any kind of generality by "the people".  Philosophers are not always associated with hard work, "dramatic and decisive" success is hard to define let alone achieve in philosophy, and not many people feel an urgent need for a philosophical education.  While I would disagree with these assessments (sans maybe the second one), I would like to point out one thing about hard work in philosophy: the same attributes that make one a successful philosopher in modern academia are the same attributes that make one successful in any industry.  Hard work---honest toil for those keen on the phrase---cannot be replaced.  Whether or not that's a good thing I leave for another time.

While it was very hard to turn down offers of admissions from many schools that I dearly wanted to attend with faculty who I really wanted to work with, I am nevertheless thrilled to have accepted an offer of admission to Stanford University.  I will be pursuing a Ph.D. in Philosophy (likely specializing in Symbolic Systems; see this page for more details on the program) starting in Fall 2011.

In other news, I have mostly completed the research project for which I was awarded a PURA grant.  A poster on the project, entitled Ontological Labels for Automated Diagnosis of Left Ventricular Remodeling, was presented on April 12. See my publications page to download the poster.  In theory, this work will now turn into a peer-reviewed publication.

In a somewhat odd move, I'm going to post the "abstract" of a paper that I have yet to write. This is because I have not had the time or reason to write the paper but have had the ideas fomenting for quite some time.  Although this brief paragraph won't contain many details, I do believe it outlines a project that can be carried out and that I may in fact carry out in graduate school.

In a paper forthcoming in Noûs, Otavio Bueno and Mark Colyvan outline and defend an extension of mapping accounts of the applicability of mathematics which they call the inferential conception. Despite the extensions made to mapping accounts, the inferential conception still agrees with mapping accounts on the necessity of starting from an "assumed structure" of the world. In Bueno and Colyvan's view, since any dissection of the world into objects and relations will be theory-laden (and such dissections are necessary for any form of correspondence between empirical and mathematical structures to exist), "there is no avoiding such an assumption." (They do, however, maintain that there may be a "natural candidate pre-theoretic structure", as in the case of a street map. More on this later.)  In this post, I will briefly sketch an argument that such an assumption can be avoided using results from the burgeoning subdiscipline of the cognitive science of mathematics.  In particular, by properly understanding the genesis of mathematical concepts from embodied experience and everyday cognitive capacities, I will argue that mathematical structures should be understood as being grounded in empirical ones. From this perspective, the applicability of mathematics is an inevitable feature of mathematics and the existence of it as a problem is an historical artifact.

Attached is a paper that I recently wrote for Eckart Förster's class on Kant's Critique of Pure Reason. This classic should be and has been ready by every serious student of philosophy at least once, and I consider it a privilege to be studying it with an eminent Kant scholar.

The paper is a short (8 page) argument that the Schematism can be given a coherent reading. Though it engages with the secondary literature in a substantive way, I should provide the caveat that at the time of writing, I had only read just past the Schematism and so did not (and still do not) have the perspective of the complete work at hand.

Here is a paper that was the midterm for a summer class on the foundations of modern political philosophy.  I know there are a few typos and I hoped to rework the paper a bit, but as the semester is well under way, it's clear that I won't have time to get to these.

The paper is a fairly straightforward philosophical paper, in which I offer a slightly nuanced defense of the quotation: “Locke sacrifices the stability and clarity of a Hobbesian account of sovereignty to an indeterminate, open-ended ‘appeal to heaven’ that obscures the nature of political freedom and authority.”

Enjoy, and feel free to discuss in the comments.

Brian Leiter has recently posted a pointer to a collection of photos of philosophers by Steven Pyke, largely taken for use by Oxford University Press.  While the photos themselves are gorgeous, Pyke also asked each philosopher to provide a 50 word account of their personal conception of philosophy.  Some do not have a remark; many are longer than 50 words; all of them are fascinating.

To me, the take home message of these remarks is that the philosophical enterprise is a very personal one. Every philosopher gets into the discipline for slightly different reasons and these reasons manifest themselves in terms of who they read, how they interpret works, and ultimately in what they publish. These personal differences come out in the remarks.

Ruth Millikan quotes a famous passage from Sellars:

The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term.

Steven Stich provides a largely naturalistic conception:

The idea that philosophy could be kept apart from the sciences would have been dismissed out of hand by most of the great philosophers of the 17th and 18th centuries. But many contemporary philosophers believe they can practice their craft without knowing what is going on in the natural and social sciences. If facts are needed, they rely on their "intuition", or they simply invent them. The results of philosophy done in this way are typically sterile and often silly. There are no proprietary philosophical questions that are worth answering, nor is there any productive philosophical method that does not engage the sciences. But there are lots of deeply important (and fascinating and frustrating) questions about minds, morals, language, culture and more. To make progress on them we need to use anything that science can tell us, and any method that works.

Leiter points out that Michael Dummett, John McDowell and Delia Graff Fara hold completely antithetical views. Writes Fara:

By doing philosophy we can discover eternal and mind-independent truths about the real nature of the world by investigating our own conceptions of it, and by subjecting our most commonly or firmly held beliefs to what would otherwise be perversely strict scrutiny.

Arthur Danto emphasizes the historical component of philosophy. Iris Murdoch calls for a revival of moral theory, which has taken a backseat to post-Nietzschean determinism in her view.

Unsurprisingly, Rorty makes note of philosophy in the conversation of mankind (to borrow a phrase from Philosophy and the Mirror of Nature):

Just as poetry in English is a conversation between Chaucer, Shakespeare, Milton, Wordsworth, Yeats, and the rest, so philosophy in the West is a conversation between Parmenides, Plato, Augustine, Hume, Hegel, Heidegger, Wittgenstein, and the rest. To be a philosopher in our part of the world is to get in on that conversation.

But enough summary; you can read all the comments in the above link.

The point I want to make is this: the variety of these conceptions of philosophy supports the metaphilosophical thesis that philosophy has no distinctive subject matter. If such a subject matter existed, we would expect much more agreement in these remarks than we do in fact see.  Obviously this analysis is very far from scientific, but I believe the evidence strong enough to falsify the claim that philosophy does have a distinctive subject matter.

Compare this to mathematics. While many practicing mathematicians are platonists at heart, there would still be some disagreements in their philosophies of math: why they do math, what they believe mathematical objects to be, etc. But mathematicians know mathematics when they see it.  There is no dispute whether something is mathematical or not (although I've heard a practicing mathematician describe logicians as "weaving spiderwebs in the basement of a cathedral").

Such is not the case for philosophy. While there are obviously texts that everyone would agree are philosophical, there is no clear demarcation between philosophy and non-philosophy as there is for many other disciplines. Do literary works such as Slaughterhouse Five count? Certainly there are philosophical viewpoints about (among other things) war, politics, and the nature of time. One easy approach would be to adopt a naturalistic criterion, a la Ross and Ladyman on science: philosophy is what gets recognized by journals, departments, etc. This approach, however, will fail for even more reasons than it does in science.

At this point, I am rambling (and may revise the post a bit in the future). I personally find great comfort in Epicurus' conception, quoted by Martha Nussbaum: "Philosophy is an activity that uses reasoning and rigorous argument to promote human flourishing." To me, philosophy is more of a mindset than a discipline: every philosopher I've met has similar dispositions and a similar desire to find answers to big questions. Perhaps this view will change as I encounter more and more philosophy, but let this be a snapshot in time.

I am attaching a final paper that I have recently written.  While I will not name the professor or the course, it should be pretty easy to guess with a bit of investigation.

At any rate, this paper is something of a literature review focused on Republic 527d-530c. Readings of Plato's astronomy by Vlastos, Mourelatos, and Gregory are examined both for internal consistency and accuracy with the text.

Click here to read the paper.

I have delivered two talks in the past three days.

1. On Saturday May 1, at the Johns Hopkins Undergraduate Philosophy Conference, I delivered a talk on "Limiting Idealizations in the Inferential Conception of the Applicability of Mathematics."  Because this presentation was not based on anything I'd written or given a talk on in the past, it was a bit rough at spots, but went fairly well (except for the projector overheating and shutting down 5-10 minutes in!).
2. Today (Monday May 3), as part of a student seminar series in Abstract Algebra II, I delivered a lecture on "Injective Resolutions in Abelian Categories."

Slides for both of these talks have been posted under "Invited Talks" on the publications page.