Wolfgang Schwarz

Modal knowledge, counterfactuals and counterpossibles

Carrie, Joe and Brit have recently commented on Williamson's proposal that modal knowledge is based on counterfactual knowledge. I share their suspicion, partly for the reasons Carrie mentions: the mere fact that statements about necessity and possibility are equivalent to counterfactuals doesn't tell us that the route to knowing the former proceeds via the latter. In fact, the assumption that we have a special cognitive faculty for knowing counterfactuals already seems odd to me. After all, we don't have special faculties for knowing indicatives or negations or conjunctions.

Lovely spam

I remember the years when this blog, because I wrote the software myself, received zero comment spam. Now it's about 1500 spam comments a day, and some have recently made it through. So I've stepped up the measures again. Every submitted comment now gets assigned a score based on 1) whether the POST request matches up with a previous GET request of the form page by the same client, 2) whether the client has fetched an image embedded in the form, 3) whether the client supports JavaScript, 4) whether the client supports cookies, 5) whether it took more than 5 seconds and less than 24 hours to fill in the form, 6) whether all form fields (including hidden ones) are submitted, 7) whether several randomly inserted form fields that are turned invisible with CSS have been left blank, 8) whether the submitted text doesn't contain spammy words, and 9) whether the same IP has not recently sent me something with a high spam score. If the score is high, you get a warning; if it is very high, you get blacklisted for 10 minutes and sent into a (mild) tarpit. I hope this combination will trap all the spam while not blocking any legitimate users who have merely turned off, say, images and JavaScript. I've tried it with Lynx and it worked fine. Let me know if you run into any problems.

Tree Prover Bugfix

I've fixed a tricky bug in my tableau prover that messed up the displayed proof in cases where the expansions of an alpha or beta formula are different, but their negation normal form is the same (example). Thanks to Christoph Pfisterer for pointing out this problem to me.

I've also begun working on a new version that allows for easy switching and editing the algorithm, so that one can use different logics and try out different precedence rules etc. At the current rate of development, this version will probably be finished around 2012.

Might

Lewis once proposed that a 'might' counterfactual ("if A had been the case, C might have been the case") is true iff is true. This is sometimes used in defense of controversial philosophical claims, like in Al Hájek's "Most Counterfactuals are False" and in Boris Kment's "Counterfactuals and Explanation". But at least in some cases, the analysis doesn't seem right.

Hail

Everything is possible

Just when I thought all viruses are specific, I caught an 'unspecific virus' last weekend -- at least that's what the doctors at the hospital identified it as. So I've been knocked out for about a week, but now I'm back with an exciting new theory of modality.

The theory is simple. It says that everything is possible. Pace Kripke, there are possible worlds where Queen Elizabeth is a poached egg and where Hesperus isn't Phosphorus. And pace almost everybody else, there are possible worlds where squares are round, bachelors married and where Hesperus isn't even self-identical.

If it rains

This appears to be a problem for pure epistemic accounts of indicative conditionals (a la Weatherson and Chalmers), on which "if A then B" is true iff the [epistemically] closest worlds verifying A also verify B.

The match cannot be played if it rains; either it has to be postponed or canceled. Which of these will happen is regulated by the rule book, but nobody has looked up the relevant passages so far. All we know is that exactly one of these two conditionals is in the rule book, and therefore true, and the other false:

Against abstract identifications

Some philosophers believe that the second world war is a triple of a thing, a property and a time. Others have argued that my age is a pair of an equivalence class of possible individuals and a total ordering on such classes. It is also often assumed the number 2 is the set {{{}},{}}; that the meaning of "red" is a function from contexts to functions from possible individuals to functions from possible worlds to truth values; that possible worlds are sets of ... sets of properties; and that truth values are the numbers 0 and 1 (aka the sets {} and {{}}).

Diamond Implicature II

I've thought a little more about this thing I called 'diamond implicature', and I've come up with the following explanation. I don't know if it's original, and unfortunately, I don't see how exactly it applies to the antecedent of counterfactuals, which is what I am most interested in.

The explanandum is that in many contexts, appears to imply . For example,

Norms of rationality

My officemate Jens-Christian, my flatmate Weng Hong and his officemate Aidan have started a blog on bunnies probabilitiy, possibility and rationality. There's already a couple of good posts by Weng Hong.

We had a little chat about the normativity of rationality today. Unlike with moral norms, I cannot imagine people who vastly disgree with me on the norms of rationality and who actually act upon their different norms. Can you imagine people who usually infer "~P" from "P and Q", update their beliefs by counter-conditionalizing P'(H) = 1-P(H|E), and always try to minimize their expected utility? I can't. By contrast, I find it easy to imagine people who value torturing innocent people and do so. This indicates that so-called norms of rationality are to a large part not real norms at all, but conceptual necessities. So is the "ought" or "must" in "if you believe P and Q, you must/ought to also believe P" like the "must" in "if it is true that P and Q, then it must also be true that P"? I think it's more like the "ought" in "if you go 'File' -> 'Save', the program ought to save the current document". Software can be buggy and fail to do what it's supposed to do according to its design specification. It is inconceivable that a word processor generally doesn't do any of the things that characterize a word processor. But it is conceivable that it fails occasionally and under specific conditions. (Then perhaps what Dutch books arguments try to show is that if you don't obey the probability axioms, you do something -- viz. give different evaluations to the same states of affairs -- which, if you did the same thing on a large scale, would rob you of your status as an agent with beliefs and desires.)