In seminar yesterday we were discussing the following argument, which purports to be an a priori argument that if most Xs are Ys, then all Xs are Ys. (This is a slightly simplified version of the argument in “Induction and Supposition”:http://brian.weatherson.org/IaS.pdf, but I think the simplifications are irrelevant to what I’m saying here.)

1. Assume most Xs are Ys, for conditional proof.
2. Assume a is an X.
3. Then a is a Y. (By statistical syllogism.)
4. So if a is an X, then a is a Y. (By conditional proof, discharging assumption 2.)
5. So for all x, if x is an X, then x is a Y. I.e., all Xs are Ys. (By universal introduction, since ‘a’ was arbitrary.)
6. So if most Xs are Ys, then all Xs are Ys. (By conditional proof, discharging assumption 1.)

The conclusion is absurd, so the issue is which is the mistaken step. My conclusion is that the mistake is to apply ampliative inference rules, like statistical syllogism, inside the scope of a supposition. Indeed, I think the core mistake is to think that we can formalise inference rules as being things that can slot into natural deduction proofs. Proofs are things that tell you about implication, and inference rules are things that tell you about good inference, and implication is not, after all, inference.

But the conclusion of the last paragraph would be better supported if I could claim there is nothing else wrong with the proof, save for the use of an inference rule at a point in the proof where only a rule of implication is permitted. And that was being disputed.

We know that statistical syllogism has defeaters. It isn’t good to infer that a is Y from Most Xs are Ys and a is X, if you have strong independent evidence that a is not Y. I wanted to reason as follows. The inference from Most Xs are Ys and a is X to a is Y goes through in the absence of any reason to think that a is especially likely to be not Y. You don’t need to have a positive reason to think that a is a ‘normal’ X (with respect to Y-hood). You just need an absence of reason to think it is abnormal. And of course you have an absence of such a reason. We’re doing this all a priori, and we don’t know anything about a. So the conditions for using statistical syllogism in *inference* are met.

The reply that my students came up with was two-fold. (I think the reply was primarily due to Una Stojnic, Lisa Miracchi and Tom Donaldson, though there was a fairly wide ranging discussion.) First, if ‘a’ is a dummy name, or as it were the name of an arbitrary object, then we can’t really say that this condition is satisfied. We know that it’s not true that the arbitrary object is not normal. After all, some Xs are not Ys. Or, at least, we have no reason to think they all are. So we must be treating ‘a’ as the name of a real object, not a ‘dummy name’, or the name of an ‘arbitrary object’. But there’s an issue about which kinds of objects we can even refer to in a priori reasoning. Perhaps the only objects we can refer to a priori are abstract mathematical objects (like the null set, or the number 2). And the problem then is that we may well have reason to defeat the statistical inference from 1 and 2 to 3, since a priori we may know that a is a special case. For instance, the following reasoning is bad a priori.

1. Assume most primes are odd.
2. Assume two is prime.
3. So two is odd. (By statistical syllogism.)
4. So if two is prime, two is odd.
5. Since two is arbitrary, all primes are odd.
6. So if most primes are odd, all primes are odd.

That’s bad reasoning because (perhaps inter alia) it’s a bad use of statistical syllogism. And it’s a bad use of statistical syllogism because even a priori we have reason to think that two is an ‘abnormal’ prime with respect to parity.

So there’s a dilemma for the reasoning I was using. If ‘a’ is a genuinely referring expression, then it isn’t clear that the preconditions for statistical syllogism are satisfied, because the only things it could refer to in a priori reasoning are things that we have a priori knowledge about. But if ‘a’ isn’t a referring expression, then it seems surely true that the step from 1 and 2 to 3 fails. Either way, we have reason to think the argument to 3 is bad, and that reason is independent of my general view that you can’t use ampliative inference rules (if such things exist) in suppositional reasoning.

I’ve uploaded three papers that I’ve been working on over the last year or so to my website. All of these are very much in draft form.

• Knowledge, Bets and Interests. I set out my preferred version of interest-relative invariantism, which links knowledge closely to decision theory. In particular, I argue that the things we write on the decision table for a choice facing an agent are all and only the things the agent knows, and this only makes sense if a version of interest-relative invariantism is true.
• Defending Interest-Relative Invariantism. This is a companion paper to Knowledge, Bets and Interests. I argue that something like my preferred version of interest-relative invariantism is immune to a wide variety of criticisms that have been sent in the direction of interest-relative invariatism in recent years.
• Disagreements, Philosophical and Otherwise. I’ve tried to turn Disagreeing about Disagreement into something ready to be published. This has involved adding length afterthoughts, saying more clearly than I could in the earlier paper where the regress objection fits into the broader debate about the equal weight view of disagreement.

I’ve also updated my collected online papers to include these, and updated the seminar notes for my scepticism graduate course.

A few quick links while worrying (even more) about global warming as a result of yesterday’s US elections:

• Gil Harman and Ernie Lepore are doing an “NEH Summer Seminar on Quine and Davidson”:http://www.princeton.edu/~harman/NEH/. Their course on Quine and Davidson a couple of years ago was great, so this is highly recommended.
• On a similar theme (sort of), Dean Zimmerman and Michael Rota are doing a “Seminar
  in Philosophy of Religion and Philosophical Theology”:http://www.stthomas.edu/philosophy/templeton/project.html at St. Thomas.
• I support Catarina Dutilh Novaes’s Gendered Conference Campaign.
• It was surprising to see Judy Thomson’s picture on a “front page NY Times article”:http://opinionator.blogs.nytimes.com/2010/10/31/philosophers-through-the-lens/?ref=opinion, but she does look like a paradigmatic philosopher.
• I’m really looking forward to the “The Key of Sea”:http://www.keyofsea.com.au/ record, and it is for a great cause too.
• The new “Philosophy Compass”:http://philosophy-compass.com/ site is much more user-friendly than the old one I think. And there are lots of articles I should write up here soon.
• I’m planning to write a book.
• Though it might take second priority to something else that just happened.

Via Zoe Corbyn’s “excellent twitter feed”:http://twitter.com/ZoeCorbyn, I saw this “disturbing article in the Chronicle of Higher Education”:http://chronicle.com/article/A-Modern-Scholars-Ailments-/124870/?key=TGl7dwU9ZHUVZHFgZGxBaGxQaHdpZkImMnFManxxblxTEw%3D%3D about link rot in journals.

bq. Authors and journal editors link to Web-based resources in citations meant to last, but the phenomenon of “link rot”—when links, or URL’s, stop working—can undermine the usefulness of those references. … Mr. Bugeja and Ms. Dimitrova studied online footnotes used over a four-year period, from 2000-3, in nine journals in their field, communication studies. Although the rate of “footnote flight” varied from journal to journal, the researchers write that they came up with “a collective half-life rate of 3.95 years, as only 1,083 (47 percent) of the 2,305 citations worked when checked in late 2006.”

In a sense, this is a big problem in philosophy. A lot of bibliographies these days feature links to articles on various personal websites. These links will, I’d bet, die very quickly. There are also links to blogs, and even blog comment threads, which also don’t feel particularly permanent. I haven’t seen anyone citing a Facebook discussion thread yet, but given how much discussion goes on there, I suspect it’s only a matter of time.

Now perhaps this isn’t a deep problem, since most of the papers will end up being published eventually, and citing the blogs/comment threads is no worse than citing ‘personal communication’, which is just what one would have cited had the conversation been via email rather than in a thread. But not all papers get published. And authors certainly don’t feel compelled to leave every version of a draft article on their website. More inconveniently, sometimes authors will change the title of a paper between online posting and publication, which could make tracking down a reference to the earlier, online-posted paper, very hard.

I’m not sure what the right solution to this problem is, or even how deep a problem it is. As the Chronicle article says, some of the problem can be averted with a good use of “document object identifiers”:http://www.doi.org/, or DOIs. Most of the commercially published journals in our field use DOIs for their online papers already, and it’s a good idea to incorporate those into one’s citations. (Many BibTeX styles already make allowance for DOIs, so this is easy to do if you use BibTeX.) But this won’t help with blogs, which don’t get DOIs normally.

And it requires that all electronic publications get DOIs for each article they post. That typically isn’t true in philosophy for things not hosted by a commercial publisher. As far as I can tell, the Stanford Encyclopaedia, Notre Dame Philosophical Reviews and the Journal of Philosophy all don’t use DOIs. Nor does the PhilSci archive, though perhaps that would be inappropriate given that work is not necessarily in final publication stage. Philosophers’ Imprint uses a different permanent URL, from “handle.net”:http://www.handle.net/, that I’m not familiar with but looks reasonably stable.

None of those sources have been subject to link-rot yet, as far as I know, but it would be good to have some redundancy here, to ensure that online work can persist as well as work on dead trees has persisted.

“Feminist Philosophers”:http://feministphilosophers.wordpress.com/2010/10/05/philosophy-at-howard-university-under-threat/ reports that the administration at Howard University is considering closing its philosophy department.

Howard University, as many of you will be aware, is a historically black university, and one which has played an important role in the history of the Civil Rights Movement in America. It is Thurgood Marshall’s alma mater. And its philosophy department was the academic home to “Alain Locke”:http://en.wikipedia.org/wiki/Alain_Locke for the vast majority of his career. It would be a horrible development for such an important university to have no philosophy department, and for such an important philosophy department to close.

The post at “Feminist Philosophers”:http://feministphilosophers.wordpress.com/2010/10/05/philosophy-at-howard-university-under-threat/ has a number of links for people you can write to in protest of this suggested move, and I’ll try to keep this post updated with more information as it comes to hand.

Here are two things I’ve been working on recently.

• Knowledge, Belief and Interests

This is a follow up to my 2005 paper “Can We Do Without Pragmatic Encroachment”:http://brian.weatherson.org/cwdwpe.pdf. I argue that thinking about decision theory gives us a new way to appreciate the argument for the interest-relativity of knowledge. I also argue, or perhaps I should say concede, that cases where agents have false beliefs about the decision they are facing provide a reason for thinking there is a kind of ‘basic’ interest-relativity to knowledge. That is, in these cases there is an aspect of interest-relativity to knowledge that cannot be explained by the interest-relativity of belief.

• Scepticism Notes

These are the notes for my grad seminar on scepticism that’s currently ongoing. I’ll update this link a few times during the semester. The notes are very drafty, but maybe they’ll be of some interest as a way of thinking about scepticism.

I’ve been thinking of trying to do a 100-level course on scepticism. Obviously that would involve very different levels of detail and explanation to a graduate course, but I’m starting to think that some of the material I’ve covered in this seminar could work at 100-level. I doubt it would be as popular as “Shelly Kagan lecturing on Death”:http://dailybulletin.yale.edu/article.aspx?id=7848, but it could I think be useful.

“Matt Yglesias”:http://yglesias.thinkprogress.org/2010/09/new-labour-and-inequality/ and “Brad DeLong”:http://delong.typepad.com/sdj/2010/09/in-which-matthew-yglesias-observes-that-innumeracy-is-an-awful-thing.html have argued that this graph, from “Lane Kenworthy”:http://lanekenworthy.net/2009/06/01/did-blair-and-brown-fail-on-inequality/, shows that we shouldn’t be too critical of Labour’s performance with respect to inequality over their 12 years of government in Britain.

Both Matt and Brad are pushing back against “Chris Bertram’s post at Crooked Timber”:http://crookedtimber.org/2010/09/30/its-about-the-distribution-stupid/, which argued that Labour had done very little about equality. (Although in his remark on my comment on his post, Brad now seems to suggest that his post was a pre-emptive strike against what Chris would go on to write in comments.) There’s a natural rejoinder on behalf of Chris, which has been well made in both Matt and Brad’s comments threads. Namely, if the graph really showed that things had gotten better, equality-wise, the Gini coefficient for the UK would have fallen. But in fact it rose, somewhat significantly, over Labour’s term. Indeed, the “IFS Report”:http://www.ifs.org.uk/publications/4524 that the graph is based on shows quite clearly that it rose markedly towards the end of Labour’s term.

So I got to thinking about how good a measure “Gini coefficients”:http://en.wikipedia.org/wiki/Gini_coefficient are of equality. I think the upshot of what I’ll say below is that Chris’s point is right – if things were really going well, you’d expect Gini coefficients to fall. But it’s messy, particularly because Gini’s are much more sensitive to changes at the top than the bottom.

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Does anyone know where I could find literature on the relationship between Hume’s epistemological views (especially his views on induction) and his political views? Reading through some of the relevant material makes me suspect there should be a close connection – roughly that in each case past theorists have erred by expecting too much of reason, and in giving too little weight to Custom and Habit. But I’m a rank amateur, and I suspect this is the kind of thing on which experts have written valuable things.

I’m generally sceptical of the value of surveys, as currently conducted by practitioners of ‘experimental philosophy’ as a way of getting clear about what’s going on in philosophically interesting thought experiments. The most systematic reason for this scepticism comes from thinking about what exactly is going on in thought experiments.

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There was a fair bit of back and forth in the “previous thread”:http://tar.weatherson.org/2010/08/20/philosophy-in-the-new-york-times/ on just what us stakes-sensitive folks were claiming to be stakes-sensitive. So I thought I’d list what *I* thought was stakes-sensitive, and perhaps others who thought there is stakes-sensitivity somewhere can chime in either in comments or on their blogs/sites.

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