I just watched one of the craziest at bats I’ve ever seen in a baseball game. Alex Cora, one of the weakest hitters in baseball, was facing Matt Clement, a pretty good pitcher. After the count ran to 2-1, Cora fouled off 14 consecutive pitches. After the first 7 the commentators were talking about how absurd it was to see all these consecutive foul balls. By 14 they didn’t even have any cliches left. The really surprising thing was that almost all the fouls were close to the lines – hardly any of them went into the stands.

Then on the 18th pitch of the at bat, Alex Cora, in one of the toughest parks to homer in in baseball, hit one into the bullpens beyond right field. Long at bats are fun to watch, but they often end anti-climactically. But Alex Cora hitting a home run, that was a nice ending. I do feel bad for the Cubs fans, because they seem cursed this game, but I’m pretty pleased I got to see something like that.

I just watched one of the craziest at bats I’ve ever seen in a baseball game. Alex Cora, one of the weakest hitters in baseball, was facing Matt Clement, a pretty good pitcher. After the count ran to 2-1, Cora fouled off 14 consecutive pitches. After the first 7 the commentators were talking about how absurd it was to see all these consecutive foul balls. By 14 they didn’t even have any cliches left. The really surprising thing was that almost all the fouls were close to the lines – hardly any of them went into the stands.

Then on the 18th pitch of the at bat, Alex Cora, in one of the toughest parks to homer in in baseball, hit one into the bullpens beyond right field. Long at bats are fun to watch, but they often end anti-climactically. But Alex Cora hitting a home run, that was a nice ending. I do feel bad for the Cubs fans, because they seem cursed this game, but I’m pretty pleased I got to see something like that.

I’ve never understood the appeal to direct realism as a way of meeting the sceptical challenges. Let’s stipulate that direct realism can explain how I know that there’s a desk in front of me. There’s still a lot of my knowledge left unexplained. For instance, I know the Devil Rays didn’t win the World Series any year in the last 100, and they won’t win it this year. (I know this is a little like saying I know they’ll lose the lottery, but I don’t care. I’ve got a better chance of winning Powerball than the Rays have of winning the series, and I ain’t got a ticket. It’s a little odd saying the Rays didn’t win the years before they existed, but I think it’s still true.)

Maybe through a direct realist theory of testimony I can be directly acquainted with the Rays having not won the Series in the last century. I’m sceptical, but maybe. But there’s no plausible direct realist theory where I can be directly acquained with the Rays losing *this* year, when they haven’t yet been mathematically eliminated. It’s just induction. But induction can surely give me knowledge of things like this.

If you think I’m going out on a limb here with the prediction that the Rays won’t win the Series, I’ll back down a bit and say they won’t win the National League pennant. Right now they’re in the American League, but I think it’s logically possible that their affiliation gets changed mid-season, they go on a 25 game win streak as a result, and they wind up NL champs. Ain’t gonna happen though. How do I know? Not by direct acquaintance with this not happening, nor even by acquaintance with any _natural laws_ that prevent it. It’s a nomic possibility that the lords of baseball could come up with a plan as stupid as moving the Rays between leagues midseason. And, though this is a stretch, it’s a nomic possibility the Rays could win 25 straight. Still, it ain’t gonna happen. How do I know? Induction.

Now here’s why I’ve always been puzzled about the direct realist response to scepticism. If all we know is what we can directly perceive, then we have a very impoverished range of knowledge. We fail to know things that are Moorean facts. (I think it’s a Moorean fact that the Rays won’t win the NL pennant this year. I’m more confident of that than I am of Moore’s having had hands.) So even if direct acquaintance given us knowledge of some things, we still need induction to give us all the knowledge we take ourselves to have. But once we allow that knowledge can be extended by induction, then direct realism can do little epistemological work. For the inductive argument from sense data to the existence of an external world is very strong.

Now this isn’t to say that there are any reasons to believe in sense data, or that there are no other reasons to be direct realists. All I’m saying is the very weak point that we get little epistemological help from direct realism. That’s not bad news for direct realism, because we get little epistemological help from all manner of true theories. Perdurantism doesn’t help us respond to the sceptic either, and it’s still true. But unless we think knowledge of our immediate surrounds is knowledge enough, or the inductive argument from facts about our surrounds to facts about the wider world is good while the inductive argument from sense data to facts about the wide world is not, direct realism doesn’t help deal with scepticism. And that’s especially true if you think knowing how the baseball season will or won’t end is a more pressing epistemological matter than knowing whether one has hands. As, it turns out, I do.

Well, that was a bit of a rant, but I thought it was worth saying. I also thought most of the premises in my rant were fairly uncontroversial. But maybe not. If I recall correctly at the INPC Ram Neta reported to me that someone had said that on one reading Aristotle seems to endorse a direct realist solution to the problem of induction. And in the latest “No{u^}s”:http://www.blackwell-synergy.com/links/toc/nous/38/2 we see Marc Lange in his paper “Would “Direct Realism” Resolve the Classical Problem of Induction” doing something similar. Or at least that’s what he appears to be doing at first glance. Another paper to add to the ‘to be read carefully pile’. Maybe I’ll have to change my views on the relationship between perception and knowledge. (Of course it would be way cool if I could really _see_ that the Rays won’t win this year. It would be cooler still if I could see that the Yankees won’t win, but I think we need more than philosophy for that.)

I’ve never understood the appeal to direct realism as a way of meeting the sceptical challenges. Let’s stipulate that direct realism can explain how I know that there’s a desk in front of me. There’s still a lot of my knowledge left unexplained. For instance, I know the Devil Rays didn’t win the World Series any year in the last 100, and they won’t win it this year. (I know this is a little like saying I know they’ll lose the lottery, but I don’t care. I’ve got a better chance of winning Powerball than the Rays have of winning the series, and I ain’t got a ticket. It’s a little odd saying the Rays didn’t win the years before they existed, but I think it’s still true.)

Maybe through a direct realist theory of testimony I can be directly acquainted with the Rays having not won the Series in the last century. I’m sceptical, but maybe. But there’s no plausible direct realist theory where I can be directly acquained with the Rays losing *this* year, when they haven’t yet been mathematically eliminated. It’s just induction. But induction can surely give me knowledge of things like this.

If you think I’m going out on a limb here with the prediction that the Rays won’t win the Series, I’ll back down a bit and say they won’t win the National League pennant. Right now they’re in the American League, but I think it’s logically possible that their affiliation gets changed mid-season, they go on a 25 game win streak as a result, and they wind up NL champs. Ain’t gonna happen though. How do I know? Not by direct acquaintance with this not happening, nor even by acquaintance with any _natural laws_ that prevent it. It’s a nomic possibility that the lords of baseball could come up with a plan as stupid as moving the Rays between leagues midseason. And, though this is a stretch, it’s a nomic possibility the Rays could win 25 straight. Still, it ain’t gonna happen. How do I know? Induction.

Now here’s why I’ve always been puzzled about the direct realist response to scepticism. If all we know is what we can directly perceive, then we have a very impoverished range of knowledge. We fail to know things that are Moorean facts. (I think it’s a Moorean fact that the Rays won’t win the NL pennant this year. I’m more confident of that than I am of Moore’s having had hands.) So even if direct acquaintance given us knowledge of some things, we still need induction to give us all the knowledge we take ourselves to have. But once we allow that knowledge can be extended by induction, then direct realism can do little epistemological work. For the inductive argument from sense data to the existence of an external world is very strong.

Now this isn’t to say that there are any reasons to believe in sense data, or that there are no other reasons to be direct realists. All I’m saying is the very weak point that we get little epistemological help from direct realism. That’s not bad news for direct realism, because we get little epistemological help from all manner of true theories. Perdurantism doesn’t help us respond to the sceptic either, and it’s still true. But unless we think knowledge of our immediate surrounds is knowledge enough, or the inductive argument from facts about our surrounds to facts about the wider world is good while the inductive argument from sense data to facts about the wide world is not, direct realism doesn’t help deal with scepticism. And that’s especially true if you think knowing how the baseball season will or won’t end is a more pressing epistemological matter than knowing whether one has hands. As, it turns out, I do.

Well, that was a bit of a rant, but I thought it was worth saying. I also thought most of the premises in my rant were fairly uncontroversial. But maybe not. If I recall correctly at the INPC Ram Neta reported to me that someone had said that on one reading Aristotle seems to endorse a direct realist solution to the problem of induction. And in the latest “No{u^}s”:http://www.blackwell-synergy.com/links/toc/nous/38/2 we see Marc Lange in his paper “Would “Direct Realism” Resolve the Classical Problem of Induction” doing something similar. Or at least that’s what he appears to be doing at first glance. Another paper to add to the ‘to be read carefully pile’. Maybe I’ll have to change my views on the relationship between perception and knowledge. (Of course it would be way cool if I could really _see_ that the Rays won’t win this year. It would be cooler still if I could see that the Yankees won’t win, but I think we need more than philosophy for that.)

The “papers blog”:http://opp.weatherson.org is posted with three new papers. There are also several conference announcements to pass on below the fold.
Continue reading →

The “papers blog”:http://opp.weatherson.org is posted with three new papers. There are also several conference announcements to pass on below the fold.
Continue reading →

I just wrote the following sentence in a draft of the (infamous) probability paper.

bq. On nonadditive theories, it is possible to get evidence for a disjunction without getting evidence for either disjunct, which seems odd.

Then I realised, on classical Bayesian theory it is possible to get evidence for a disjunction without getting evidence for either disjunct. At least I think it is. The following looks to me to be consistent.

Pr(p v q) = 0.6
Pr(p) = 0.4
Pr(q) = 0.4
Pr(p & q) = 0.2
Pr(p v q | e) = 0.64
Pr(p | e) = 0.4
Pr(q | e) = 0.4
Pr(p & q | e) = 0.16

In that case, e looks like it is evidence for p v q, but not evidence for either disjunct. But could there be a realistic case like that? Presumably there could – in this case we could just find out that p and q are probabilistically independent.

Of course what I should have written was that on these nonadditive approaches we can get evidence for an _exclusive_ disjunction without getting evidence for either disjunct. And that still seems somewhat odd. But it looks less forceful now that the claim is qualified.

UPDATE: This post used to contain a conjecture that turns out to be false, as I realised about 2 minutes after writing the post.

Did I mention I’m enjoying doing logic work less than I usually enjoy philosophy? Of course that’s in part because in logic there are rules, and if you’re wrong telling an amusing anecdote won’t do much to cover up that fact. Which is, on the whole, a good thing about logic. But not so much when you’re so often wrong.

The “papers blog”:http://opp.weatherson.org is up for the day, the first day for a while there’s been any news to report.

Geek note about something I discovered while doing the report. In IE you can put subscripts on superscripts, as in 2^x₀. In Firefox that comes out as (practically indistinguishable from) 2^x0. I’ve got no idea how those look on Mac browsers. I thought it was analytic that anything IE did that Firefox didn’t do was bad, but I also thought subscripts on superscripts were good. So now I’m confused.

This should be really obvious, but I can’t find any convenient link, and I can’t see how to do this myself – at least not easily.

Say you wanted to mix probability theory and modal logic in the following way. The language of the sentences over which the probability function is defined includes a box, here written L. Whenever p is a sentence, Lp is a sentence, so all the usual formation rules apply. The logic for the box is S4. (We can substitute in other logics later once we figure out how S4 works.) We want the probability functions to be all and only the measure functions on Kripke models for S4. So Pr is an S4-probability function iff there is a Kripke model [W, R, V] and a measure function m defined over W such that for any sentence A, Pr(A) = m({w: A is true in [W, R, V] at w}). (Note I’m using square brackets around W, R, V because angle brackets confuse the HTML coder.)

Anyway, say you wanted to do all of that. How would you go about drawing up axioms to characterise the class of probability functions so isolated? Here’s one hypothesis. You’d simply take the axioms for classical probability theory, which always include (often tacitly, but always) some reference to either an entailment function or a class of logical truths. You then interpret that reference as a reference to S4-entailment, or S4-logical truth. And there’s your axiom system.

Does it work? I’ve got no idea. One of the things I proved in my paper on “intuitionist probability logic”:http://brian.weatherson.org/conprob.pdf is that this approach really won’t work when you want to move from classical logic to intuitionist logic. The problem is that classically equivalent axiomatisations of the probability calculus turn out to be inequivalent when ‘re-interpreted’ in an intuitionist way. (I.e. the references to entailment or logical truth are taken to be references to _intuitionist_ entailment or _intuitionist_ logical truth.) Could the same thing happen for the move from classical logic to S4? I don’t know. I thought it might be possible to generalise by claim about intuitionist logic to show that the answer to this question was _no_, but on a little reflection I rather doubt this is true. I think this is just an open question.

A (very brief!) lit search reveals very little on the intersection between probability theory and modal logic. Williamson’s 1998 BJPS paper has some relevant material, but it’s not exactly on point. The probabilistic semantics literature also has interesting material (esp by Cross and by Morgan) but it doesn’t seem (from what I can find from here late at night) to be exactly relevant either. (In all cases this lack of relevance is not due to shortcomings of the authors, but just because they were asking and answering different questions. I can sometimes appear overly critical here, so I should be clear that _in this case_ no criticism is intended!) But probability and modality are such big topics one would think there’d be _something_ on their intersection, and I don’t think the way I’ve framed the problem is _entirely_ idiosyncratic.