A compressed history: Not so long ago, a department of statistics was a boring place to be and a department of computer science was no place at all. It was the philosophy department–a good one, at least–which employed the mathematically inclined who were interested in scientific methodology and foundations. One legacy from this post-war era is artificial intelligence, particularly machine learning; another is that statistics departments are now a lot more interesting.
A consequence of this success is that philosophy departments no longer corner the market on methodology and philosophical foundations. That kind of work can, and sometimes does, go on in other places. Curiously, this gentrification of the university coincided with a growing ambivalence within philosophy to formal methods. Philosophers of a stripe have always had a thing for precision, and for a long time Greek was considered the only language suitable for philosophy. Then it was German. Today it is colloquial English disfigured by a semester of logic. I digress.
Formal Epistemology designates a subject that involves work on epistemology informed by formal methods along with work on the formal methods themselves. These two parts to the job employ different skills, which can be illustrated by two current and still drafty papers. (I pick these two simply to illustrate the point, and to expose no one to embarrassment but myself.)
The first paper, which explores how to do AGM Revision in Classical Modal Logic, concerns development work. In this case, the paper shows how to add a capability (AGM belief revision) to a class of classical modal logics, some of which underpin a variety of knowledge representation frameworks. The intended audiences for this paper are modal logicians and computer scientists, along with other formal epistemologists. The second paper criticizes Scott Sturgeon’s character matching principle for Lockean belief by turning it inside out to form an Envelope of Belief. This paper is a short conference paper for the APA Pacific which applies some off-the-shelf machinery to address some current topics in mainstream epistemology. The intended audiences are epistemologists and formal epistemologists.
So, What is a formal epistemologist? It is someone who both works on the development of formal methods and applies those methods to epistemological problems, broadly construed to include the special sciences. There are plenty of philosophers that do the latter for problems within philosophy, and a large number of scientists in various special sciences that do the former. But formal epistemologists do both, or have the skills to work these two sides of knowledge representation and reasoning problems. That’s what makes formal epistemologists valuable to philosophers (e.g., to help cut down on wheel reinvention) and to the special sciences (e.g., correct a priori detection of a misalignment between method and problem is much cheaper than running experiments.) This pair of skills is also what distinguishes formal epistemologists from a previous generation of philosophers of science: thanks to those ancestors of ours, we now have several well-developed special sciences to collaborate with and react to.
Where does someone go to become one? To a place that has formal epistemologists, for starters, and good ones working on topics that interest you. There is some online carnival barking about emerging world leaders in formal epistemology that is, unfortunately, ill-informed. Just because the axiom of ordering applies to vacation destinations does not mean that it applies to entire academic fields. Formal Epistemology includes quite a few sub-areas, meaning that not all well-known FE departments are necessarily comparable, and there are terrific people to work with who are located in a variety of places. That said, here are some sound options, along with a reason for why they are sound, presented in no particular order:
The bottom line? When shopping around for a department to do formal epistemology, make sure the person or persons you’d like to work with are serious about both parts of the job description.
Posts
Maybe I’m just another carnival barker here, Greg; but, I would like to add some (perhaps orthogonal) advice to prospective students. I would encourage them to seek out departments and people who (1) encourage work on FE-related areas, and (2) who have a track-record of placement, and (3) are actively involved with various parts of the profession (i.e., those who have personal and professional connections with people and departments that students will want to visit — and maybe even get jobs at later). On these dimensions, I think it’s rather clear that MIT, Rutgers, Berkeley (and various other American departments who might not rank very highly on “Greg’s List”) should be considered very strong, indeed. This is not meant to discourage anyone from applying to the schools at the top of Greg’s List (or even to encourage applying to my own personal faves), but rather to encourage students to think about items (1)-(3) in addition to the considerations Greg raises.
First, I hope everyone enjoyed the holiday weekend. Second, I like Greg’s list quite a bit, which is no surprise. I think Branden’s comments point to the fact that there is more than one tradition in FE. It would be nice to have a handle on these different traditions so that we could advise students accordingly (e.g. Greg’s list or Branden’s list). As an example of a sort of observation that might help in teasing out these different traditions, I’ll mention that David Lewis has been much less significant than Pat Suppes in terms of my own education. I suspect that this not the case for many FE people.
Thanks, Jeff. Allow me to clarify the point of my original post. It was not to add more rhetoric to the discussion. It was simply to add some considerations that I think can be pragmatically useful for students who want to do FE-stuff (professionally, in a philosophy department). I don’t think the rhetoric of Greg’s post (“carnival barkers”) or yours (“Suppes v. Lewis”) is very useful for students in these senses. Moreover, I don’t think it’s useful for us to “break into camps”. That’s just divisive and (as far as I can tell) not pragmatically useful for anyone. One of the purposes behind the Formal Epistemology Workshops (FEWs) has been to include people from various FE-traditions AND also to include TE-people who are interested in how FE can be useful to them (qua traditional epistemologists). I prefer this inclusive approach. So, as I said in my previous post, I’m just trying to add pragmatically useful considerations to the discussion here — I’m not trying to take issue with Greg’s comments (or yours). [Although, I will add that I have learned a ton from both Pat Suppes and David Lewis!]
Hey Branden,
Thanks for the reply. I’m not sure that I understand what you mean in the following passage:
“It was simply to add some considerations that I think can be pragmatically useful for students who want to do FE-stuff (professionally, in a philosophy department). I don’t think the rhetoric of Greg’s post (”carnival barkers”) or yours (”Suppes v. Lewis”) is very useful for students in these senses.”
What is this sense in which your comment is useful whereas mine is not? I’m not doubting you. I’m just not sure what you mean. I can think of some relevant contexts where my comment could be useful to a student: e.g., the student mentions that she has read a good amount written by both philosophers, would like to learn more about one rather than the other, and would like to know suggestions about where such learning is likely to take place. That sounds pragmatically useful to me. I apologize, but I just don’t know what you have in mind.
Also, I don’t mean to be divisive. Sometimes it is helpful to make distinctions — I take it that you regard “formal epistemology” as signifying such a distinction.
Thanks for the clarification, Jeff. Sorry — I guess I misread your “Suppes v. Lewis” remark as implying something (normatively) comparative about the relative worth (for prospective FE students) of studying Suppes v. studying Lewis — and not merely as an autobiographical (and purely descriptive) remark about the “tradition of FE in which you happened to be immersed as a graduate student”. Be that as it may, I still prefer not to focus on “camps” or “traditions” in this (teaching/advising) context. As an adviser, I try to encourage students to work on all kinds of projects they find interesting — even if they “cross traditions” (or if they involve “traditions” with which I’m not very familiar, or ones that my own advisers didn’t pay much attention to). So, I guess I just don’t see how productive the “tradition talk” is in this context. Although, I grant it could be of some use to prospective students — especially if certain people in certain departments tended to discourage work on certain “traditions” (esp. ones in which the student in question is interested). But, that, too, seems to speak in favor of an “inclusive FE-world-view”, which is what I was trying to endorse with my last remark.
Some remarks on the on-going discussion. I agree with Branden that divisiveness is not a nice attitude. And I applaud the attempt to unify the discussion in epistemology. FEW has tried to do this with some success. And many of the places listed by Greg have supported FEW. At CMU we have done so quite strongly for example. But it seems that the declarations of world dominance that antedated Greg post are not precisely very unifying. I find these declarations considerably more divisive than Greg’s remarks and to some extent frivolous.
I cannot but infer from Branden’s posts that the criteria used to rank universities by special area (in this case formal epistemology) are not based (and perhaps should not be based) centrally on academic excellence but on some capacity for placement and for `having professional connections in the profession’ (his criteria (2) and (3)). Is this really used as a criterion to rank departments in any of the usual rankings? CMU ranks very high in areas like Logic or Decision Theory in a report like Leiter (where we do not have representatives at all and therefore no capacity to influence the discussion in any way). I do not think that this is due to the criteria that Branden mentions (having professional connections, etc). We are a young department with a reasonable placement record not only in philosophy but also in areas like computer science and statistics. If we have any merit in these areas is due centrally to academic excellence measured by objective facts like number of publications, citations, and the scientific recognition of some members of the faculty. I think that this is justified and that it should be the central criterion to rank special areas in philosophy (especially areas that are naturally connected with mathematics and the sciences). Having a good placement record is also important and perhaps should be considered when one ranks departments as a whole, but I do not think that this should be the determinant factor ranking special areas. Even at the level of the department as a whole there are rankings like the rank provided by the Chronicle of Higher Education that use objective measures when it comes to issues like scholarly productivity (CMU ranks 5th according to this ranking in the USA). In any case, perhaps Branden has something else in mind when he mentioned his points (2) and (3) as salient to determine which are the best departments in this area.
In any case, there is an aspect of Greg’s post that has been neglected. He mentioned that in many cases the ranks by special area should be taken only as indicative of the general strength of the department but that these ranks might not be very useful for students who have formed preferences regarding doctoral studies. These type of students are more common now in a market where students have usually masters degrees in philosophy or the sciences when they apply to doctoral programs. For example, if one is interested in the use of formal methods in the study of causality clearly the best place for pursuing studies is CMU (especially now that Woodward is moving to Pittsburgh). But if one student is interested in studying evolutionary game theory (a topic recently represented in FEW), perhaps the best place for this is Irvine. We have for example good people working in this area, like Kevin Zollman, but Brian Skyrms is without doubt the leading expert in this field in philosophy (as a matter of fact Kevin studied under Skyrms). CMU is very strong in various areas of logic, but if one is interested in modal logic and/or applications of game theory to logic and applications of logic to game theory perhaps the best place to go is Stanford (or Amsterdam) and study under van Benthem (CUNY could also be a good choice depending on the specific interests of the candidate). I do not know how good these places are placing people or how well connected these scholars are in the profession (by the way, probably both Stanford and Irvine have very good placement records) but these are not facts that I would consider as decisive when advising someone who has clear interests in studying in the aforementioned areas (MIT might be also quite strong in the second case). So, when one looks at issues in detail and when one considers informed decisions, the field of formal epistemology has many incomparabilities rather than a clear ordering ranking different places (this is one of the reasons why I think that declarations of world dominance are frivolous).
I think that it is important to inform undergraduate students about work in formal epistemology. This is the rationale behind the summer school in Logic at Formal Epistemology at CMU. So far, this is working nicely. The students usually emerge from the school with clearer ideas about their interests, and this is clearly good for the profession I think. Students well informed about scientific and philosophical facts will make better decisions regarding their professional future.
Finally a second element of Greg’s post that has been neglected in the previous discussion. I would think that a very important issue regarding leadership in formal epistemology is the capacity of developing new formal methods of philosophical relevance, not merely the capacity of applying preexisting formalisms. All the important philosophers that contributed in this area were pioneers in the development of new formal ideas (Carnap, Ramsey, Lewis, etc). Take for example the area of causality. The group of researchers associated with Clark Glymour at CMU developed much of the machinery (computational and mathematical) of Bayes networks and the pedagogical methods to teach the new material. Now statistics lists courses of graphical methods at CMU but these courses were to a large extent influenced by the pioneer work of philosophers in our department. Similar remarks apply to a few departments in the USA (Irvine, Stanford, etc) all of which are in Greg’s list. I think that this capacity for creative formal work of philosophical interest is the true mark of leadership in this area.
Thanks for your post, Horacio. I think I basically agree with most of what you’re saying here. Again, just to clarify, I was merely trying to add some additional considerations that might be salient (prudentially) for prospective students in their deliberations about where to study. I was not making any comment about “overall rankings” of departments, etc. (whatever those are supposed to mean in the first place). I agree that statements of “world domination” (and the like) are not unifying (or terribly useful, probably, in any of the senses we’re discussing). Note that I’ve never made any such statements. nor do I plan to. [But, adding fuel to such rhetorical flames is also not going to help either. And, that was my complaint about Greg's use of the pejorative "carnival barkers" to describe some recent posts by certain graduate students and faculty] There is one thing I do regret about your remarks. They seem to suggest that students would be better off working with “creative FE-people”, as opposed to people who “merely apply old FE-stuff”. First, I’m not sure I really understand that distinction. Could you be more specific and give some concrete examples, please? Anyhow, even if I did understand this distinction, it’s unclear (to me) why graduate students are better served by working with the “creative types” as opposed to the “mere apply-ers” (or whatever other pejorative term you’d like to apply to them). Remember, I’m looking at this from the student’s perspective (qua budding professional philosopher), and not from “our” perspective. I’m not very interested in a chest-beating match about who “the best” formal epistemologists are (according to whatever standard you have in mind). I am (esp. in this “teaching section” context) more interested in seeing FE (broadly construed) thrive — in philosophy — through the success of FE students. And, I bet that some of the best teachers and advisers (i.e., those whose students have thrived in professional philosophy) have been “mere apply-ers” in your sense. So, I’m just not sure how useful that distinction is — for prospective students. Moreover, one must remember that philosophy — as a discipline — has an important historical and scholarly component. Students can ignore that if they like — but at their own peril. And, I’d advise against it. Having said all that, I should say — again — that my point was not to bring any people or departments down (e.g., CMU). Rather, I was trying to point out that students should take into account many factors when deciding where to study (and with whom to study). And, some of these factors are being neglected (or given too little weight) in Greg’s remarks (and yours).
BTW: I am, of course, a big fan of many of the people at CMU, Stanford, and the other departments you mention. But, I don’t see why we can’t also recognize the value of what people at other departments are doing (at least as teachers and advisers, if not as “bona fide leaders of research” in your sense). Thus, even if I were to agree with your assessment that “FE research excellence” is focused in the departments in your (and Greg’s) list(s), it wouldn’t undermine the importance of the considerations I’m raising (from the point of view of prospective FE students who aim to thrive as professional philosophers). But, as I said above, I’m not sure precisely what (or who) you have in mind when you talk about “ersatz” as opposed to “true” marks of leadership. Can you clarify?
Replies:
‘Carnival barking’: This may have died down since the thread started. If not, try rereading the post omitting ‘carnival barking’. Then return to the remaining comments.
‘Carnival barking’: My mild criticism was not in any way directed at Branden. On the contrary, I applaud Rutgers’ decision to hire him. My point instead is that this decision is an excellent down-payment on an FE section, not a capstone.
Good professional connections: I agree that this is an important component to picking a place to study, particularly if one wishes to find work in a philosophy department. But the connections cart should be hitched to the research excellence horse, not the other way around. The former brings progress to philosophy and professional connections outside of philosophy, the latter insularity.
Ordering : The list was unordered, as I stated. Places that immediately come to mind as strong in FE are those which have more than one strong FE scholar. Given the nature of the job, clusters of excellent people tend to form in a particular sub-area. Innovation in these areas contributes more rather than less reasons to the failure of comparability of departments, which is the reason the list is, and should be, unordered.
Rather than fret over who is above whom, Amsterdam or CMU, Rutgers or Oxford, I think our long-term professional interests are served by ensuring that innovation continues in formal epistemology. And that means that people and places should be recognized foremost for the excellent and innovative work they are doing, and the significance of those innovations needs to be explained to our colleagues who are not specialists. In other words, the importance and benefits to philosophy of what I called development work needs to be explained to non-specialists.
Thanks, Greg! I really appreciate the clarifications (and also the tone) of your latest post. I couldn’t agree more with the gist of your remarks. Indeed, I never meant to disagree with them, really — just to add some other considerations into the mix (from a prospective student perspective). Thanks, also, for the kind words about me personally. I really appreciate that. I’m really excited to be moving to Rutgers, and I think it will be a fine place for students to study FE. As always, however, I will continue to view FE (and especially the advising/mentoring of FE students) as a profession-wide collaborative effort. Needless to say, I look forward to continuing my relationships with great FE people such as yourselves, and many others around the world (many of whom I hope are reading this blog!). I view these relationships as essential for the development and growth of the area, as well as the intellectual development of my (and all of our) students. I hope the feeling is mutual.
Will any of you be at the Eastern? If so, let me buy you a drink, and pick your brains further about how to best ensure a bright future for FE.
I’d definitely be up for a drink at the Eastern. I’m not a big fan of the APA in general or the Eastern in particular, but a beer with any of you is sufficient motivation for me to take the short subway ride downtown.
Since we’re on the topic of FE and related areas, let me mention that Vincent Hendricks just sent following list of invited speakers for the 2010 Synthese Conference that will take place at Columbia in April:
Alexandru Baltag (Oxford)
Adam Brandenburger (NYU)
Cristina Bicchieri (Penn)
Christian List (LSE)
Wlodek Rabinowicz (Lund)
In addition to these invited speakers, there will be space for at least five contributed papers. More information about the event can be found via the following link:
http://www.springer.com/philosophy/philosophy+of+sciences/journal/11229
First of all I agree with Greg that the previous criticisms were not directed at Branden and that it is obvious that Rutgers made a very good decision hiring him. It is also true that Branden has not made any of the divisive comments about world dominance alluded in previous posts. And I am glad to see that that Branden does not approve them either.
About my last comments. I did not want to imply that historical studies are not important. Many of my colleagues, for example, are involved in historical projects aside from their main areas of research (Steve in the Carnap project, Wilfried in the Hilbert project, Clark in various projects including a translation of Reichenbach, Teddy in work related to Fisher, and I am interested in De Finetti’s work, etc). This is important work, for sure. I also made clear in my post that it is important to achieve some sort of unification regarding formal and traditional epistemology, and this requires some historical work as well. But I think that innovative work of formal, conceptual and experimental kind should be a crucial component of contemporary formal epistemology. Traditionally philosophy has created new formal tools that then found applications inside and outside philosophy. In my post I mentioned as an example the work of my colleagues in Bayesian networks which helped to develop ideas that now found applications both in philosophy and in computer science and statistics. But examples of this capacity for innovation abound. For example, Kripke’s work in the semantics of modal logics or Scott’s work in the same area are clear examples. Perhaps though it is incrementally more difficult to sustain this capacity for innovation given the fact that specialization increases with the past of time. This is the reason why innovative work in this and related areas tends to be produced by academic units that concentrate resources, reward interdisciplinary work and have the capacity to expose students to a wide variety of formal tools. Many of the academic units in Greg’s list are of this type.
During the 80’s and 90’s much of the innovative work in various areas of formal epistemology was carried out outside philosophy (in computer science, mathematical economics and psychology). Logics of knowledge and common knowledge, formalisms for belief change, probabilistic methods and decision theoretic approaches to inductive logic initially proposed by philosophers since the 50’s were tested and further developed outside philosophy. Part of this work continues outside philosophy (work in machine learning, for example). But now theoretical work in computer science is less common (in part because of the economic crisis, in part due to an interest in applications). As a result we have many computer scientists publishing now in philosophy. Paradoxically this is a very good opportunity. If things are done in the right way we can have a decade or two of innovative work in the fundamental areas of formal epistemology ahead of us and this work will be carried out fundamentally inside philosophy. But in order for this to happen it is important to set priorities for research and be clear about high standards. More importantly it is also important not to lose contact with work in areas outside of philosophy to avoid insular developments.
Hope that this helps clarifying some of the ideas in my post. Hope also to see you all at the APA. I will then be in NYC working and I plan to attend if there is something interesting going on. As Jeff says seeing some of you would be enough motivation to take a short subway ride to midtown.
I will miss seeing all of you in NYC this month. Raincheck?
I agree with Horacio’s analysis about the recent history of innovation in formal epistemology (a.k.a., theoretical aspects of knowledge representation and reasoning), and that there is a good opportunity, particularly in the US, for philosophy departments to make a strong move back into this area of scholarship. But here institutional structure is important (another point that was made), because theory and practice need to work together for FE to be innovative and to be maximally relevant.
But there is a nice opportunity here. Knowledge-based systems, or more abstractly, reasoning with graphical structures, is an idea that has taken root in the sciences. But scientists do not typically treat these things as pure graph problems to be solved, as their colleagues in the math department implore; they instead supply them with causal, temporal, or broad epistemic interpretations. That’s us! Adopt these languages to talk philosophy, and you’ll have more science students in the philosophy classrooms. Do it right, and the special sciences would beat a path to your door for that service.
Boy, that would be exciting!
Thanks, guys! This is all super-helpful and illuminating. I have a much better sense of what you all have in mind. And, I think we’re all on the same page now. That was just what I was hoping would happen! These blogs sure can be useful (I need to participate in them more, and I also need to get better at this — I haven’t done that much blogging, and it’s a medium I still need to master!).
Thanks, Jeff, for the reminder and link(s) for the Synthese conference. That looks like it’ll be an awesome meeting! I might be able to make it (we’ll be looking for housing in the spring, and we may be in the area then). Meanwhile, I hope that you, Horacio, and I can get together for a drink at the Eastern. I’m chairing an FE-session (featuring Matt Kotzen and Roger White) — I hope you guys can make it.
I’ll definitely take that raincheck, Greg! I’ll be at the Pacific, and I hope to see you there!
One last remark — pertaining to “standards” and “relevance to the sciences”. I think all of the scholars in all of the departments we’ve been talking about here have very high standards (in both their research and their teaching), and that they all do really good work. I also think that philosophers (especially those at top philosophy departments) have a non-trivial obligation to their students to prepare them for (and give them the proper tools for succeeding at) jobs in philosophy departments. I, for one, think that is a top priority, teaching-wise. Having said that, I also think it would be great for people working on FE to do work that is relevant and useful to the sciences. So, while I agree with the gist of the remarks made here about “standards” and “relevance to the sciences”, I also think we have to be prudent and realistic about how we prioritize our research and teaching energies (qua philosophers, which is — after all — what we are).
Branden, in your comment from 11/29 at 10:29 you wrote that “I was not making any comment about “overall rankings” of departments, etc. (whatever those are supposed to mean in the first place). ” I read this as you registering doubts about the meaning of overall rankings. If this is the correct reading of your statement, then what is meant by your reference to the obligations of “top philosophy departments” in your most recent post? Was that a reference to “top” with respect specialty rankings or the overall rankings mentioned in your earlier post?
Regarding the last sentence of your most recent post, I’m assuming that you do not take “philosopher” to indicate those and only those who made (make) a career in a philosophy department.
I think that we all agree on the central importance of research excellence in FE, and those of us in the field clearly understand the vital contributions that continue to be made to the field from people working outside of philosophy. This is one of the many things that makes FE so exciting and vibrant at the moment, and it is encouraging that interest in the field is on the rise in US philosophy departments. This is a terrific development!
Sorry, Jeff. By “top” I just meant — by whatever standards one wishes to impose (you could remove “top” if you like). And, the “philisopher” remark was only meant to be taken from the perspective of someone who is advising students who plan to go on to jobs in philosophy departments. That’s the only “Teaching” perspective from which I am qualified to speak.
Just to re-iterate — I am in full agreement with Greg about recognizing
excellence and importance of FE work being done by people not in philosophy departments (and the importance of influencing and interacting with such researchers). I just think we (qua teachers and advisers of philosophy students) have to balance the interactions and contributions “outside” philosophy with our duties “inside” philosophy. I, for one, think the latter has greater weight (prudentially, for philosophy advisers and teachers) than the former. But, that’s not a fundamental disagreement (at least, I don’t think it is).
I think we agree but maybe there is a disagreement. Let’s see.
I think boundaries and divisions between philosophy and non-philosophy are hard to apply in the case of formal epistemology, and that there is potential harm introduced by doing so. There are garbled and poor facsimiles in philosophy of FE ideas originating outside of philosophy, and vice versa. (It goes both ways.) It would be a disservice to any student to be constrained by disciplinary labels if better material (which is often the original material) exists in another field. It is one thing if someone doesn’t know any better; but then that person isn’t a leader in the field. It is quite another if a person does know better, since that would be to compromise the education of the next generation of scholars and the future of the field.
I am not claiming that anybody is doing this, intentionally or otherwise; rather, I am just stressing that in the long run, we all will be served best by embracing research excellence and aligning all of our institutions and practices with those ideals. There really is no other way.
I think we’re in agreement here, Greg. “demarcation” is always treacherous. I’d prefer not to do it at all. But, Universities are still broken down into departments, and — as an adviser — I can ignore these conventional demarcations only at the considerable peril of my students…
Greetings; I just came across this site in an old e-mail I’d entirely forgotten about. I’m obviously out of the loop in this discussion, but just wished to note that given how “formal epistemology” is being used here, it seems we need another tern to identify the study of a cluster of general methods and problems relating to finding things out/learning about the world. These general methods might be seen to fall under a broad conception of statistical science: roughly methods for planning, collecting, modeling and learning from data. Understanding these methods would also also be needed to make progress wrt philosophical problems involving the modeling methods often mentioned in this discussion, e.g., causal modeling CMU-style. But that is just one facet of the larger domain that I have in mind.
Well, this is just a “hello”, don’t even know if it will take….!
Dear Deborah,
This is an excellent point. FE is a nice legacy from one part of philosophy of science that focuses on formal methods for knowledge representation and reasoning. Now there is serious counterparts in the special sciences to interact with, and people of good conscience can disagree about what that means for the field. Your remark on methodology (for lack of a better term) is an excellent reminder that there are other legacies of the philosophy of science that impinge upon epistemology which enjoy serious engagement with the special sciences, statistics and machine learning in this case.
It seems natural to me to see these two topics as closely aligned, whatever we call it, and wherever those who do it happen to be employed.
Hi Greg:
There’s surely something right about your remark that “FE is a nice legacy from one part of philosophy of science that focuses on formal methods for knowledge representation and reasoning”. From this perspective, FE is essentially on a par with analytic epistemology, the goal being to represent/define concepts and/or reconstruct knowledge claims or inferences from given evidence claims. The shortcomings/limitations of this kind of appeal (to analytics or formal methods, respectively) is that it doesn’t open the door to understanding the basis for ampliative inference, for teaching us how we manage to successfully obtain reliable knowledge, and how we (humans) can do it better (faster, deeper, more reliably). One might call these goals “forward looking” (rather than reconstructions of cases).
Statistical science, roughly, deals with the study of methods for the planning, collection, modeling and learning from data to make “error-prone” inferences, and find things out. It is not surprising that statistics has been called “applied philosophy of science”. Now statistical methods themselves have long been the subject of philosophical debate, and by studying these we can both improve the foundations and interpretations of these methods and simultaneously set the stage for arriving at novel solutions to long-standing philosophical problems (e.g., about induction).
You put “statistics and machine learning” together, but it’s not at all clear to me how the goals machine learners set for themselves get at these philosophical issues (of the nature and justification of error-prone reasoning and strategies for human learning). I’m definitely no expert on machine learning, but base my claim on the varieties of tasks to which machine learners seem to set for themselves….insofar as these can be pinned down.
Hi Deborah,
I think we’re largely in agreement, although I don’t think that formal methods are restricted to case analysis. I see them working hand in hand with the special sciences, statistics included.
Let me try an example to draw together some threads. We know that a variety of statistical problems, particularly to do with causal graphs, can be reduced to so-called Tarski sentences expressed in the theory of real closed fields (RCF). Geiger and Meek have a nice UAI 1999 paper on this, “Quantifier Elimination for Statistical Problems”, where they discuss the problem of distinguishing Heywood models from a fully connected DAGs defined over the observed variables, but Tarski’s quantifier elimination methods are practical only for very small problem sets. Branden has a very nice package for Mathematic which is an easy to use implementation of this idea (PrSAT), but one can see the limitations Geiger and Meek allude to using this. (Indeed, that’s how I got interested in this problem.) One may instead turn to constraints programming techniques to investigate how to work on larger sets (there are pieces to a solution, but I know of no full system), or go whole hog and unleash genetically inspired learning algorithms on particular problem sets. Ant algorithms seem promising for multi-modal solution spaces.
My point with this (brief) example is that statistics, logic (or: real analysis), and computation are each extraordinarily powerful and can be harnessed in a variety of ways to attack problems of scientific interest as well as of philosophical interest. I also think that philosophy departments should be at the vanguard in promoting this kind of work.
As a student mainly educated in mainstream, non-formal analytic philosophy, where do you need to start if you want to improve your knowledge and skills in formal applications? Does one start with logic, with math, or something else? What are good books? Etc.
Dear Joost,
There are some nice suggestions here, but one idea that might be helpful would be to take (or sit in) a good undergraduate course in discrete mathematics, which I think is pretty common nowadays. This type of course covers a lot of ground, and doing all of the exercises (even those that seem too computationally oriented) with a class is a good start on obtaining “mathematical maturity”. A course like this will begin to give you a working feel for logics, sets, and ordering, which I think would pay out dividends for you.
I concur with Greg. I would add that if you’re interested in learning about probability and some of its applications in philosophy — you might want to look at my Probability & Induction course, which is entirely online (including all reading materials). See:
http://www.fitelson.org/probability/
I also have some other salient courses almost entirely online as well. See:
http://fitelson.org/teaching.htm
Hi!
I got an e-mail about some updates here, so came to check it out, whereas I hadn’t gotten the earlier reply to me by Wheeler. I really don’t see what reduction to Tarski sentences has to do with being able to employ statistical methods to answer questions about evidence, obtain reliable methods, etc. Maybe I’m missing…
But I do think philosophers have tended to see the role of probability in inference in terms of deductive probability theory whereas that doesn’t get you very far when it comes to inductive-statistical inference based on probabilistic models. With statistical inference, you don’t merely get out what you put in. Since this is a forum where hopefully we can say what we really think, however radical, I would recommend that philosophy of science students learn statistics in place of the usual smattering of probability theory/Bayes’ theory methods. Then they can get beyond reconstructing epistemological intuitions (that we’re supposed to start with) and actually see how reliable statistical inferences are made. We could then get beyond the “problem of induction” that seems such a stumbling block in philosophy, and get on to the business of finding/building reliable methods and inferences. Mayo
Thanks for the help and advice!
Joost
Joost,
Greg and Branden have given you some excellent suggestions. Let me add a few of a different flavor. First, you might enjoy taking a look at something like The Principles of Mathematics by Russell, or perhaps some selections from the Benacerraf and Putnam collection. Second, you might also want to look at something like Steve Awodey’s book on category theory, which provides a very nice introduction to the structural aspects of mathematics, and it does so in a way that should be accessible to many philosophers.
Being a student at Tilburg I already have been exposed to some formal stuff (especially Bayesian stuff). However, my mathematical and logical baggage is limited. Every time I am confronted with huge bodies of formal stuff I am overwhelmed. Drawing upon Neurath’s metaphor, it feels like I am out on the ocean, with a very small ship, or more precise, a shaky raft, and I have to start undoing this raft of its shakiness, and then built it up, while on the sea. In mathematics and logic, it probably will never be possible to start off from the shore and then gently walk your way into the water, but surely some ways are better than others in order to become master. So I guess what I was looking for with my question was a manual to prevent my ship from sinking every time. Now you guys gave me this nice set of tips. It makes me enthusiastic, hungry to improve my formal skills. Yet I also realize that this isn’t something you learn by doing it a few hours a week. So I guess I will take a year ‘off’ next academic year to plunge myself into the formal pool, so that I can return as a real captain of my ship. Thanks!