Formal Philosophy for Dummies 5 of 5

This is the final installment of my answers to this survey which I've affectionate called "Formal Philosophy for Dummies" (the Dummies being people like me who treat the topics on the basis of more enthusiasm than understanding).

5. What are the most important open problems in philosophy and what are the prospects for progress?

I can only speak to my discipline which is epistemology but I think one of the greatest challenges is to relate current work in formal epistemology--especially probability theory--to fairly traditional epistemological concerns. I speak not of an analysis of knowledge, but rather an elucidation of the notions of epistemic justification and of evidence. It seems obvious there must be a connection between various formal results and, say, traditional theories like coherentism and evidentialism. However, relatively little work has been done in drawing the lines of connection. I'd like to think the prospects for this are quite good since I intend to pursue this project for at least the next decade.

Obviously, given my answer to question four I also think the semantics of probability theory is a very important open question. It's hard to be optimistic about it given that most bayesians seem only concerned with subjective probability--not that there's anything wrong with that. Still, given the great number of skilled probability theorists out there and the rise of metaphysics again surely attention will once again turn to an attempt to develop a theory of logical probability.

Relatedly, more attention needs to be paid to the integration of probability theory and first order logic. This is a fecund topic which has produced too few sufficiently clear treatments.

I also think that one of the most important open problems in philosophy is not necessarily related to formal philosophy: cognitive axiology. It is high time epistemologists spend some serious time thinking about what kinds of cognition matter to us. Surely it is the answers to these questions that should guide further research.

Formal Philosophy for Dummies 5 of 5

This is the final installment of my answers to this survey which I've affectionate called "Formal Philosophy for Dummies" (the Dummies being people like me who treat the topics on the basis of more enthusiasm than understanding).

5. What are the most important open problems in philosophy and what are the prospects for progress?

I can only speak to my discipline which is epistemology but I think one of the greatest challenges is to relate current work in formal epistemology--especially probability theory--to fairly traditional epistemological concerns. I speak not of an analysis of knowledge, but rather an elucidation of the notions of epistemic justification and of evidence. It seems obvious there must be a connection between various formal results and, say, traditional theories like coherentism and evidentialism. However, relatively little work has been done in drawing the lines of connection. I'd like to think the prospects for this are quite good since I intend to pursue this project for at least the next decade.

Obviously, given my answer to question four I also think the semantics of probability theory is a very important open question. It's hard to be optimistic about it given that most bayesians seem only concerned with subjective probability--not that there's anything wrong with that. Still, given the great number of skilled probability theorists out there and the rise of metaphysics again surely attention will once again turn to an attempt to develop a theory of logical probability.

Relatedly, more attention needs to be paid to the integration of probability theory and first order logic. This is a fecund topic which has produced too few sufficiently clear treatments.

I also think that one of the most important open problems in philosophy is not necessarily related to formal philosophy: cognitive axiology. It is high time epistemologists spend some serious time thinking about what kinds of cognition matter to us. Surely it is the answers to these questions that should guide further research.

Formal Philosophy for Dummies 4 of 5

4. What do you consider the most neglected topics and/or contributions in late 20th century philosophy?

Carnapian epistemology has fallen on hard times. I think the Carnapian project will be resumed because it must be resumed. As far as I’m concerned finding a materially adequate, formally well-behaved, non-arbitrary measure of confirmation is the Holy Grail of formal epistemology. I think Henry (Kyburg) might think this as well and he's certainly dedicated most of his academic life to finding a such a system though that would require reading the Carnapian project in much broader terms. I still have hopes for a semantics for logical probability more along the lines of Carnap.

I also think Joyce's non-pragmatic vindication of probabilism could be incredibly important. I think for this to be shown, though, not only would the technical results need to be defended, but some concerns of traditional epistemology would have to be brought to bear on them such as the relative value of avoiding falsehood and getting truth and the relative value of different degrees of conviction. Also, it's not clear to me that even if we knew that probablisticly coherent belief systems were objectively more likely to be more accurate than incoherent ones that achieving this would constitute progress toward certain epistemic goals. In short, I think that how important an argument it turns out to be will depend on what conclusions we come to about the nature of cognitive ideals.

Formal Philosophy for Dummies 3 of 5

3. What is the proper role of philosophy in relation to other disciplines?

Philosophy is a categorical discipline in that for every other discipline D there is the philosophy of D. Call this "categorical philosophy." One essential role for categorical philosophers is to be the goatherds of the other disciplines. We've got scientists run amok making blatantly philosophical statements for which there particular expertise gives them no authority (perhaps it's revenge for the reverse problem).

Categorical philosophy investigates primarily the ontology, epistemology, and axiology of other disciplines. Science provides the easiest examples in the realism/anti-realism debate, the problem of induction, and inquiry into what questions science should attempt to answer (think of Kitcher's recent work on this third (not that I agree with his conclusions)). However, I think the epistemology of the social sciences and of history and theology are all very fruitful contributes philosophers make in other disciplines.

Question #2

2. What example(s) from your work (or the work of others) illustrates the role formal methods can play in philosophy?

In epistemology I have worked hard to integrate probability and more traditional epistemology in two areas: evidence and explanation. I am working hard on a phenomenal theory of evidence which satisfies essential bayesian theorems. Less originally I have both argued that traditional critiques of Orthodox Bayesianism are less than persuasive and that there are strong Neo-Bayesian strategies for evading them at any rate.

The twin pillars of the classical opposition to Orthodox Bayesianism are the problem of the priors and the weakness of a mere coherence constraint. The reply--which really needs to be shot back more forcefully than it has beenis that probability theory is a form of logic. It is, from a formal standpoint, no different than First Order Logic. FOL can't tell you what values you should have for the p's and q's--you must mind your p's and q's yourself--logic isn't the whole of epistemology (granted, many Orthodox Bayesians talk as if it is). Or if it is, then it isn't the whole story about rational belief (cognitive psychology has much to say). And ultimately all FOL can do is tell you when you're inconsistent (and in a much coarser granularity than probability theory). So though I think claims that probability theory exhaust epistemolog--has anybody really ever said just that--are clearly mistaken, I think the parallel between probability theory and first order logic is closer than most people appreciate.

A book which very nicely pursues this project is David Christensen's Putting Logic in its Place, though I disagree with him on keeping a closure constraint. One of my main projects is applying the theory of idealizations Weirich devised for decision theory in Realistic Decision Theory to probability theory. The proposed monograph is to be called _Realistic Bayesianism_.

Nevertheless there are ways of addressing the problems which have been developed but under-appreciated. Rather than rehearse them let me give an example which I have adapted from Kvanvig. Kvanvig and Riggs have suggested that traditional coherentists have missed the boat in not including non-doxastic--but still contentful--mental states (such as perceptions, memories, and appearance states generally) among the elements which must cohere. There's no reason Bayesian coherentists can't adopt this same strategy.

In fact, I think it makes perfect sense: I think we do often assign confidence levels to appearance states, as when we judge that we are seeing an optical illusion. I don't think this can be reduced to merely refusing to believe what is reported. We express a degree of confidence in the veracity of the appearance state itself. I think further analysis will bear this out.

I also would like to defend a limited form of Inference to the Best Explanation as a form of "poor man's bayesianism." That is, IBE is the way boundedly rational agents approximate bayesian inference. Often, the results of formal epistemology are judged to be inapplicable due to idealization. I agree and am keenly interested in adapting formal methods to cases of bounded rationality.

Formal Philosophy for Dummies

For dummies like me, that is.

Inspired by the populist orientation of the new "Masses of Formal Philosophy" project, I'll be serially posting my answers to the survey questions over the next five days.

1. Why were you initially drawn to formal methods?

I always loved math as a kid. Part of the draw was that it was definitive: unlike literature and social studies classes we could propose a definitive answer. It's not at all that I thought there weren't definitive answers in those other fields, it's just that we couldn't often give them.

So mathematics was my first introduction to the notion of formal reasoning, reasoning that was precise and canonical. Both the answers and the reasons could be stated crisply and clearly (in the range of math we did). Most importantly, the answers could be verified or refuted. Perhaps my interest was and is the result of an overly retentive or competitive personality (wouldn't be the first time that answer was proposed), but I thoroughly enjoyed the closure of coming to the solution of an equation.

On the other hand, there was plenty of mystery there as well. Even to a seventh-grader in a school in one of the most rural sections of the Midwest--the school was literally (in the literal sense of "literal") on grounds which were a block carved out of a corn field, and farm kids were bussed in from miles around from all four directions--as I say, even to one in my limited circumstances it was clear that the world of mathematics promised plenty of intrigue.

When I accidentally discovered non-Euclidian Geometry trying to solve a puzzle in seventh grade I was told to stay in from recess until I would stop being a smartass. (I don't recall the exact words, but the teacher thought I was toying with her and then it got heated.)

When I started poking around I found that--rather than being moribund--mathematics was full of mysteries, paradoxes, unsolved problems, and unexplored territory I was at first shocked--"how can there be disagreement or ambiguity even here"--but then fascinated.

Both aspects of formal methods fascinate me today in my study of philosophical logic and probability theory (motivated by the same problems as but coming to different conclusions than my teacher Henry Kyburg for whom the notion of a *canonical* proof is very important). I am fascinated by the obvious success of probability theory in an almost total absence of a solid semantic theory.

The mathematical theory of probability is straightforward but the interpretation and application of the formalism is a rich and diverse matter. And I am fascinated with the issue of how to adjudicate debates between alternative systems of logic, the so-called deviant logics and classical logic. I love fuzzy logic, but wonder if it isn't just a form of bayesianism by another name and I love supervaluationism and love the idea of setting fuzzy logic in a supervaluationist framework.

In some sense there is just One Logic underlying them all, I'm not a pure conventionalist. But on the other hand there are some domains of discourse which have different rules. Intuitionism might be appropriate for mathematics, but not for empirical discourse. How many more distinctions like this might there be? How to strike the balance between the absolute and the pragmatic still fascinates me the way it did when I was a kid.

Damned with Faint Praise: More on Epistemic Norms

This is in part a continuation of my discussion with Clayton here.
Compare the two norms.

(T) Believe the truth.

and

(E) Form your beliefs on the basis of evidence.

I'm interested in the Ethics of Belief, so I'm interested in praise and blame for epistemic states (I was going to say "acts" which is closer to my own view, but I want to remain neutral for just a sec). So here's the deal. You don't get credit in any sense interesting from the perspective of an epistemic ethicist for satisfying (T) unless you do so by satisfying (E).

If you satisfy (T) but not (E)--or some similar norm--you were just lucky and so don't get any credit for it. The only positive evaluation we can give is "She's lucky" which is not a very interesting epistemic evaluation. Even if someone satisfies (T) a lot without satisfying (E), we'd just say "She's *really* lucky." Not very interesting for the epistemic ethicist.

Now maybe, unlike me, you you're interested in Reliablist Virtue more than Responsiblist Virtue. Well, to each their own, but I don't see that animal knowledge has much of an ethics. I don't think talk of norms makes much sense for animal knowledge. We can praise someone's perception as accurate in the same way we praise a thoroughbred horse for being fast, but that's praise only by a faint analogy. I'm interested in the real thing.

Hume as Skeptic AND Causal-Inductive Realist

In a seminar on causation with Alyssa Ney we began, naturally enough, with Hume. In particular we came to consider differing interpretations of Hume according to whether he did or did not believe that causation was "out there" in the world, not *just* in our heads and whether he thought induction could yield warranted belief.

One piece of evidence offered on behalf of a more traditional interpretation which takes Hume to deprecate induction is the fact of the self-ascribed "skepticism". He calls his own results "skeptical". Some thought that should be the end of the matter, but I don't think so. It seems to me that Hume's main target is not common sense so much as *rationalism*. He is certainly skeptical of the claims of the rationalists. So "skeptical" could be used with restricted scope and be roughly equivalent to "empiricist". In support of that possibility here's one definition of "skeptic" from the OED.
"those who deny the competence of reason, or the existence of any justification for certitude, outside the limits of experience."

That's roughly equivalent to a species of "empiricism" and seems to indicate my hypothesis is at least thus far a live option. I think this lends support to Beauchamp and Rosenberg's take on Hume. Currently reading Winkler's "The New Hume".

Epistemic Role of Simplicity

Over at Certain Doubts Mike Huemer started a really interesting discussion of the epistemic use of simplicity. I wanted to fill out my comments there and in a bit propose another more inchoate response than I was willing to post there.

I suggested there that

(S1) When multiple theories cover the data, the simplest is the most reasonable to believe
is a priori in the sense that it is constitutive of our concept of reasonable belief. I think this is especially clear when it comes to a deontological conception of reasonable belief for the following seems clearly true to me.

(S2) We don't have a right to posit any more (kinds or tokens of) entities than are required to cover the data.

From this it follows that

(S3) To posit more (kinds or tokens of) entities than are required to cover the data is unjustified.

I think these are basic facts about rationality.

This suggests the following account of theory simplicity.
(S4) Theory H1 is simpler than theory H2 iff H1 postulates fewer (kinds and/or tokens of) entities than H2.

I think all these principles have the positive feature of being platitudinous. I think at one time they would have been accepted as platitudes by philosophers and surely are accepted as platitudes by the innocent folk (in this case a plus in my view).

The question of whether simple theories are more objectively likely to be true is, I think, of the same status of the question of the justification of induction and therefore a very very deep and difficult problem. I think the most interesting question in the present approach concerns (S4).

(SQ1) How many new tokens are worth a new type?

(S4) is quite indeterminate w.r.t. answers to (SQ1). The main options are

(A1) It is always better to postulate more tokens than a new type.(A2) At some (vague) point, it becomes better to postulate a new type than new tokens.
Here's the sort of conflict I envision: H1 covers the data by postulating many billions of particles of a single type, whereas H2 covers the data by postulating, say, *two* token particles of two different types. (A1) strikes me as right at first, but this consideration makes me pause to reconsider (A2).