I’ve been writing up some thoughts on easy knowledge, but they got a little long for a regular blog post. So they’re in this PDF. But don’t think of this as a paper – it’s really a long blog post in PDF form!
bq. “Easy Knowledge and Other Epistemic Virtues”:http://brian.weatherson.org/ekoev3.pdf
Do you want to be my boss – or at least one of my bosses?
bq.. “The Rutgers Center for Cognitive Science (RuCCS)”:http://ruccs.rutgers.edu/ruccs/index.php at the New Brunswick Campus of Rutgers University is searching for a new director. We are looking for an outstanding scholar with proven administrative abilities and a vision for the future of cognitive science at Rutgers. Highly desirable is experience in obtaining and administering interdisciplinary, multi-investigator grants. Intellectual breadth—an ability to understand and articulate the contributions from the principal disciplines that compose cognitive science is important, as is the ability to effectively represent the interests of RuCCS inside and outside Rutgers. Fund raising ability and community/industry outreach also desired.
Description of Center
A primary goal of the Center is to foster research on the nature of symbolic processes constitutive of intelligent performance, emphasizing foundational and computational approaches. The goal is to understand such aspects of intelligent performance as perception, language processing, planning, problem solving, reasoning, learning and knowledge formation, in terms of the underlying computational processes. The Center’s mission is essentially multi-disciplinary. It promotes the integration of techniques and knowledge drawn from experimental psychology, computer science, neuroscience, philosophy, linguistics, mathematics, and engineering. The Center offers a Cognitive Science Certificate for graduate students and supports a minor and independent major for undergraduates. RuCCS has 22 jointly appointed faculty members at present. It also has an additional 30 associates housed in various departments who play an active role in the intellectual life of the Center. At the present time the principal contributing disciplines are psychology, computer science, linguistics and philosophy. The policies of the Center are set in consultation with an executive committee which has representation from several participating departments.
Candidates should be at the Full Professor level. Salary is negotiable. Consideration of applications will begin on March 29, 2010, but applications will be considered until the position is filled. Send a letter of interest that outlines your qualifications for the position as well as a CV to:
Search Committee Staff
Rutgers University
Center for Cognitive Science
152 Frelinghuysen Road, Psychology Building Addition
Piscataway, NJ 08854
OR
Fax: 732-445-6715
OR
Email to: “dirsearch@ruccs.rutgers.edu”:mailto:dirsearch@ruccs.rutgers.edu
It’s well known that it’s easy to ‘mix’ two unconditional probability functions and produce a third unconditional probability function. So if x ∈ [0, 1], and f1 and f2 are both unconditional probability functions, and for any proposition p in the domain of both f1 and f2, f3(p) = xf1(p) + (1-x)f2(p), then f3 will also be an unconditional probability function. (This is really immediate from the axioms for unconditional probability.) I thought the same kind of thing would work for conditional probability, but I can’t figure out how to do it.
It’s certainly not true that if f1 and f2 are both conditional probability functions, then the function f3 defined by f3(p|q) = xf1(p|q) + (1-x)f2(p|q) will be a conditional probability function. Here’s a counterexample.
If we just apply the above formula, we get this
One natural move is to say that when f1(q) = f2(q) = 1, then f3(p|q) = xf1(p|q) + (1-x)f2(p|q). That will deliver something that is a conditional probability function as far as it goes, but it won’t tell us what f3(p|q) is when f1(q) = f2(q) = 0. And I can’t figure out a sensible way to handle that case that doesn’t run into a version of the inconsistency I just mentioned.
It feels like this is a simple problem that should have a simple solution, but I’m not sure just what it is. There’s a lot of information about mixing probability functions in “this paper”:http://fitelson.org/ew.pdf by David Jehle and Branden Fitelson, but it doesn’t, as far as I can see, touch on just this issue. Any suggestions would be appreciated!
As you probably noticed, the comments section now includes pretty pictures. For some people, that will include their own picture. For most people it includes a randomly generated monster. I kinda like the monsters, but if you would rather not be represented by one, here’s the instructions for creating your own picture.
That picture should then show up as your avatar in TAR, and in other blogs with this feature turned on. I’ve noticed, for instance, that it also works on “Feminist Philosophers”:http://feministphilosophers.wordpress.com/, and I’m sure it works elsewhere as well.
Two days ago I mentioned that I was impressed by the typesetting that “Anders Schoubye”:http://www.schoubye.org/papers.html has done, which apparently set off a flood of people to download his papers. I thought I should update that post to note that one of these papers, “Intuitions in Question”:http://www.schoubye.org/papers/IiQ.pdf has now been accepted for publication at _Linguistics and Philosophy_. Well done Anders, and I highly recommend getting the paper for both the form and the content!
The faculty in the philosophy department at Rutgers University, New Brunswick, have sent the following letter to the administration at King’s College, London, protesting their proposed firing of three distinguished philosophers.
bq. The members of the Philosophy Department at Rutgers University hereby join the chorus of protest of your actions with regard to the Philosophy Department at King’s College and the outrageous treatment they have received from the College. The damage done to academia, to the Department, to the College, and most of all to the specific colleagues involved, is unconscionable. We urge you to reconsider, so as to contain the damage.
King’s decision seems to be both imprudent and unethical, and it’s in everyone’s best interests for it to be reversed very quickly.
UPDATE: Broken link fixed.
“Barack Obama”:http://www.whitehouse.gov/the-press-office/interview-president-youtube, from yesterday’s YouTube conference:
bq. And I’m a big believer that the most important thing that a kid can learn in school is how to learn and how to think. If Malia and Sasha, my two daughters, are asking questions, know how to poke holes in an argument, know how to make an argument themselves, know how to evaluate a complicated bunch of data, then I figure that they’re going to be okay regardless of the career path that they’re in. And I think that that requires more than just rote learning — although it certainly requires good habits and discipline in school — it also requires that in the classroom they’re getting the kind of creative teaching that’s so important.
I think the two things that could do the most to promote this aim are (a) a really good statistics course, to give people a feel for working with data, and (b) a really good critical thinking course, of the kind the best philosophy teachers deliver to college freshmen. If those courses were integral parts of the high school curriculum, then we’d see many more people who can make and evaluate arguments, especially arguments based around numerical data.
There have been intermittent attempts to bring philosophy in high school in various Australian states, but it would be great to see something similar attempted in America.
UPDATE: Via Larvatus Prodeo, I just saw this link to “an article about teaching philosophy in schools in Queensland”:http://education.qld.gov.au/learningplace/stories/articles/art-edviews-mar05-2.html. It seems there is much more philosophy going on in pre-tertiary education than I’d realised.
Here’s a puzzle for the E=K (i.e. all and only knowledge is evidence) theory.
bq. Jack is inspecting a new kind of balance made by Acme Corporation. He thoroughly inspects the first 10 (out of a batch of 1,000,000) that come off the assembly line. And each of them passes the inspection with flying colours. Each of them is more accurate than any balance Jack had tested before that day. So Acme is making good balances. He knows, by observation, that the first 10 balances are reliable. He also knows, by induction, that the next balance will be reliable. It’s not obvious that he knows the next one will be phenomenal, like the ones he has tested, but he knows it will be good enough for its intended usage. But he doesn’t know they all will be that good. Surprisingly, it will turn out that every balance made in this assembly line will be reliable. But you’d expect, given what we know about assembly lines, for there to be a badly made machine turn up somewhere along the way.
bq. So Jack knows the first 11 are reliable, and doesn’t know the first 1,000,000 are reliable. Let _n_ be the largest number such that Jack knows the first _n_ are reliable. (I’m assuming such an _n_ exists; those who want to hold on to E=K by giving up the least number theorem are free to ignore everything that follows.) For any _x_, let _R(x)_ be the proposition that the first _x_ are reliable. So Jack knows _R(n)_. Hence by E=K _R(x)_ is part of his evidence. But he doesn’t know _R(x+1)_. This is extremely odd. After all, _R(x)_ is excellent evidence for _R(x+1)_, assuming it is part of his evidence. And _R(x+1)_ is true. Indeed, by many measures it is safely true. So why doesn’t Jack know it?
It seems to me there is a mystery here that, given E=K, we can’t explain. If we have a more restrictive theory of evidence, then it is easy to explain what’s going on. If, for instance, evidence is perceptual knowledge, then Jack’s evidence is simply _R(10)_. And it might well be true, given the correct theory of what hypotheses are supported by what evidence, that _R(10)_ supports _R(84)_ but not _R(85)_. That explanation isn’t available to the E=K theorist. And we might well wonder what explanation could be available.
I have one idea that saves the letter of E=K, though at some cost I think to the spirit of it. Let’s say that evidence can be of better or worse _quality_. If you don’t know _p_, then _p_ is of no evidential use to you. But even if you do know it, how much evidential use is might depend on how you know it. For instance, if you infallibly know _p_, then _p_ is extremely useful evidence. More relevantly for today’s purposes, if you have *sensitive* knowledge that _p_, then _p_ is more useful than if you have *insensitive* knowledge that _p_.
Let’s go through how this plays out in Jack’s case. Although he knows _R(11)_, this knowledge is insensitive. If _R(11)_ were false, he would still believe it. Had the production system malfunctioned when making the 11th balance, for instance, then the 11th machine would have been unreliable, but Jack would have still believed it. The only sensitive evidence he has is _R(11)_. By the time he gets to _R(n)_, his knowledge is extremely insensitive. There are all sorts of ways that _R(n)_ could have been false, in many fairly near worlds, and yet he would still have believed it.
So here’s a hypothesis. The more insensitive your evidence is, the less inductive knowledge it grounds. If Jack had sensitive knowledge that _R(n)_, he would be in a position to infer, and thereby know _R(n+1)_. The reason he can’t know _R(n+1)_ is not that he doesn’t have enough evidence, but rather that the evidence he has is not of a high enough quality. That’s an explanation for why Jack can’t infer _R(n+1)_ that neither leads to inductive scepticism, nor violates the letter of E=K. I’m not sure that E=K was meant to go along with the view that how you know something is evidentially relevant, not just whether you know it, so I don’t think this keeps the spirit of E=K. But perhaps the letter of E=K is more defensible than the spirit of it.
One other suggestion that came up over dinner in Barcelona was that we should be doing something to create online versions of important books of the last few decades that have fallen out of print. The classic example of this is “Science without Numbers”, but Frank Jackson’s “Conditionals” also counts. (In fact both the book he wrote with that title and the book he edited with that title probably count.)
What would need to happen to create online versions of these books? I think we need four steps.
Unless I’m missing something, those are the main steps that would be needed. And they don’t seem unmanageable. I’m no expert though on copyright law, so I might be quite wrong about how easy it would be for authors to get the right to republish their out of print books. And of course authors might not want to republish electronically. But I was wondering whether people thought this would be a good project to investigate, and if so, which books would be candidates for republishing?
I really enjoyed the Vagueness and Metaphysics workshop in Barcelona. I learned a lot from all the papers, and it got me interested in working on these topics in much more detail. Maybe I’ll even revive the idea of a writing a short book on vagueness, somehow melding “stuff”:http://brian.weatherson.org/manymany.PDF “from”:http://brian.weatherson.org/ttt.pdf “these”:http://brian.weatherson.org/vai.pdf “five”:http://brian.weatherson.org/Ch_8.pdf “papers”:http://brian.weatherson.org/VEatPoM.pdf. But first I wanted to touch on a point Robbie Williams made there.
In his “Truth and Paradox”:http://www.amazon.com/Truth-Paradox-Solving-Tim-Maudlin/dp/0199203911, Tim Maudlin argues that when we are dealing with ungrounded claims like the Liar, the norms of assertion do not include truth. Indeed, it is possible to assert the Liar (i.e., that the Liar is not true), even though it’s not true (and not assertable) that the Liar is not true. Robbie’s idea (I believe closely based on Tim’s) is that in ‘difficult’ areas, such as when we’re dealing with future contingents, vagueness, or the paradoxes, we should be looking for ‘local’ norms of assertion, not ‘global’ norms of assertion. A global norm is something like “Assert only what you know”, or “Assert only what is true”. A local norm might be something like “Assert a future contingent only if you know it”, or “Assert a vague sentence only if it is not determinately false”.
I’m not sure whether I agree with all these claims. I’d hoped to sit down with Tim’s book to read it more carefully, but sadly the Rutgers library doesn’t seem to stock it. (This is a little appalling – it’s an OUP book published by a Rutgers faculty member! Maybe I’ll head up to 42nd Street later this week and work in the public library for a day; they do have the book in stock.) But I do think they are interesting, and worth taking seriously. And that’s exactly what hasn’t happened in the existing norms of assertion literature. As far as I can tell, more or less no one in that literature cites Tim’s book at all, or for that matter worries about any of the paradoxes.
That’s bad, because I think there’s a fairly compelling argument that the knowledge norm can’t survive the paradoxes, even if a paradox-based argument against the truth norm succeeds. Consider (1).
(1) Brian does not know (1).
Assume I know (1). Then by the very plausible principle: Ksp → p, it follows that I don’t know (1). Contradiction. So I don’t know (1).
That argument looks perfectly sound. It certainly doesn’t look like I violated any norms of assertion in presenting it. But the last sentence is one that, as we just proved, I don’t know. So it’s perfectly OK to assert some things one does not know.
I’ve mentioned before that my outlook on a lot of philosophical questions has been changed by “Kevin Klement’s Compass papers”:http://people.umass.edu/klement/works.html on Russell’s paradox and Russell’s reactions to them. I think I might have to write up a short paper on the number of areas of contemporary philosophy where there has been insufficient attention paid to the paradoxes, with norms of assertion being one of the case studies.