This morning, I read through (and very much enjoyed) Greg’s quick book review of Hendricks and Symon’s collection, Formal Philosophy: Aim, Scope, Direction - the review is hot off the presses in the new issue of Philosophy of science. Greg does a marvelous job of highlighting some of the most interesting ideas developed by the book’s contributors in a small amount of space. Here is one idea, which I found particularly fascinating, expressed by several of the contributors and – it seems – most emphatically by Clark Glymour. Quoting from Greg’s review:
The philosophy of science should work to advance the sciences … Real mathematical work with philosophical motivations is largely ignored, and a consequence is that many of what should be core concerns within contemporary philosophy of science have moved out of philosophy proper and into statistics and machine learning … [Consequently] much of philosophy of science is now occurring outside of the professional boundaries of philosophy.
This unfortunate point seems to be the result of another key idea found throughout this book:
The habit of contemporary philosophy of limiting the menu of structures to first-order logic, basic modal logic, and classical probability is akin to institutionally tying philosophers’ hands behind their backs.
The general denouncement of formal philosophy (as currently practiced) here goes something like this: formal philosophers, by and large, have become much too comfortable with a limited set of formal tools. Such formal tools have proven too simple in many important domains – thus, “one often finds a clash between imagined properties of a subject and the bad behavior of those properties within some structure.” The upshot is that formal philosophers for the most part offer results that have little to no applicability to science but instead are only of interest to formal philosophers themselves – “results that only a philosopher could love.”
The prescription then is that formal philosophers need to branch out; they need to become less satisfied with first-order logic and classical probability, and develop skills in a wider array of formal methods. Only then can the philosophy of science advance and become more relevant to the sciences. To quote Greg quoting Krister Segerberg: “To go beyond a great philosopher, go beyond his methods!”
These thoughts may well be dreary. But, at the same time, they are intended to be motivating.
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So once we move beyond “first-order logic, basic modal logic, and classical probability”, what formal tools would make the best additions to the philosopher’s “menu of structures”? I’m curious to hear opinions on this.
Two fairly obvious choices: graph theory for studying causation, and formal learning theory for formal epistemology.
Even within existing frameworks, like the use of probability theory in formal epistemology, there are formal tools like hierarchical Bayes models and Bayes nets that are under-utilized.
PGMs and learning theory are wonderful suggestions. I would add frameworks to deal with ‘time’ and ‘groups’, too, which might include temporal logics and systems for (iterative) revision / updating, under the former, and systems for group decision making under the latter.
I would also add something about bounded resources, including some thought to complexity. Not everyone is psychologistic about their logics, but some are, and for those it is sometimes handy to point out their their machinery resides in a complexity class far beyond the capabilities of either minds or machines.
All the previous suggestions seem nice. I would like to add a few. Although probability was mentioned above as one of the classical tools it seems to me that less attention in payed (unfortunately) to the use of probability in theories of decision both of normative and descriptive kind. It would be nice if a course in Rational Choice were thought everywhere at a mature level with the same regularity than courses of logic or advanced logic. Also there are certain areas of the theory of decision and games that have not been mentioned yet, like the theory of choice functions in social choice. This theory has been influenced by the work of Arrow and Sen among others. In its contemporary form it has applications in logic, ethics and political philosophy and epistemology (theories of belief revision, for example).
Some of the most important paradoxes threatening the received view about decision under uncertainty (like Ellsberg’s paradox) have indicated the interest of studying the theory of imprecise and indeterminate probabilities (and value). Now there is an international conference related to this issue (ISIPTA) and these topics are regularly studied usually in psychology and statistics. Unfortunately basic training about these topics is rare in philosophy programs. Most of the foundational work in decision theory of philosophers like Levi, Kyburg or Seidenfeld cannot be understood without basic training in the theory of imprecise probabilities.
Game theory as a general theory of interactive epistemology (the term was coined by Aumann) is also very important, and recently Skyrms and collaborators have done important work in evolutionary game theory. Both branches of game theory have many interesting applications in many areas, from biology to philosophy per se (recently Skyrms has been working in a general theory of signaling for example, which extends work done by Lewis in Convention).
As Greg pointed out there is a great deal of important literature on theories of bounded rationality deriving from the seminal work of Herb Simon. I think that some of the bounded techniques should now be part of the standard toolkit of a philosopher interested in formal epistemology or the foundations of cognitive science.
In logic there are entire areas that do not receive the attention they deserve. In philosophical logic, for example, the Kripkean paradigm used to deal with modality(which has been so influential in the second part of the last century) has been questioned and complemented by the use of alternative theories of possible world semantics (like neighborhood semantics) or by the use of algebraic, probabilistic, epistemic or categorial models. My impression is that this work in less known.
I entirely agree with pretty much all that has been said so far. I concur with Horacio regarding the relevance of the judgment aggregation literature, which clearly has a number of applications beyond the group case. Belief revision is indeed one such area (updating on incoming information amounts to merging two belief sets).
I would like to add, however, that the situation is not just regrettable for philosophers. There is far too much formal work being done in, e.g. AI, that proceeds from assumptions that are at worst entirely undefended and often at best backed up with an eyebrow-raising one-liner. This leads to too many results that are of no clear interest, or at least of no clear immediate applicability.
So you lament insular philosophers ignoring statistics, machine learning, game theory, etc? Consider that formal epistemology blogs like this one almost never cite papers or blog posts in those other areas. The obvious explanation, it seems to me, is that in general academics have little incentive to cite those outside their own field. I speak as an economist who has largely failed to get philosophers to pay attention to my formal work on the rationality of disagreement, and who does discuss philosophy papers on his blog (Overcoming Bias).
Hi Robin, thanks for coming by.
Incidentally, I’ve been an occasional, albeit interested, reader of Overcoming Bias ever since your talk at the workshop on disagreement in Oxford a couple of years ago.
Interesting, why do you think that academics lack an incentive to cite work outside their own fields?
In the case of philosophy, the issue may not be so much a lack of incentive, as a lack of competence. Many philosophy grads are ill-prepared to read further afield, especially in the more technically-demanding areas. In the UK at least, aside from a couple of logic courses and (with a hell of a lot of luck) the odd basic introduction to probability theory, philosophy students have very little exposure to the basic tools required. Those who wind up engaging with work in economics, mathematics or computer science have typically taken a first degree in one of those disciplines. Those who do not have that training face a somewhat steep learning curve.
Gregory, the obvious incentive issue is that academics are mainly rewarded for publishing in journals within their discipline. Authors who submit papers to such a journal know that its referees rarely read other journals. So there is little downside to failing to cite relevant work outside the discipline, and there can be a big a downside to using methods with which referees are not familiar.
Glad to have you as an OB reader. Hope you noticed this post.
Dear Robin – Considering that this formal epistemology blog is only about two months old, ‘almost never’ is true but easy enough to correct. I enjoyed and recommend Andrew Gelman’s recent posts at Statistical Modeling, Causal Inference, and Social Science.