I will choose free will
Hey folks. The Guerilla Radio Show returns to full power tonight with a show on Free Will. What is Free Will? How can I get some? If you choose not to decide, have you still made a choice? Check us out on KCSB 91.9 if you can get it on your radio. Unfortunately, as far as I can tell the KCSB webcast is currently not functioning, so if you're not in our radio listening area, you won't be able to hear the show until we archive it on the GRS website, which should be fairly soon after the broadcast.
And here's a quick philosophical/logical question for your blog-reading (dis)pleasure: if laws (of nature) are more than just regularities, but the laws of nature could have been different (e.g. E=mc2 might have been false), then is there a way to cash out physical necessity in terms of possible worlds? Here's the problem: Say we have a law of nature /\x(Fx->Gx), which is true in this world, but not necessary because in some worlds there are different laws. It looks like there's no way to make this law "necessary" in any weaker way that doesn't break down into making it a contingent regularity. If we say that it's physically necessary, in the sort of standard way of formalizing that ([](LP->/\x(Fx->Gx)), where LP is a proposition stating some specified set of laws of physics; thus, the laws of physics strictly imply the regularity), we end up with a proposition that's still contingently true, because making it "physically necessary" in this way just made it true in worlds where the laws of physics come out true. If it's contingent that these laws of physics hold, then it's no less contingent that our regularity holds, if it only holds where the laws of physics do. We seem to want to say: the laws could have been different, but given that they are such-and-such, this regularity necessarily follows. But the standard ways to formalize this can only render it as: there are regularities that hold in only some worlds (specifically, worlds where certain other regularities hold); this seems to lack entirely the "necessity" we're looking for. Unless I'm missing something, there doesn't seem to be an obvious way to formalize physical necessity in the non-Humean, "necessitarian" way that a lot of philosophers would like to assert it. If that's the case, then either this is a deficiency in possible worlds semantics (I believe, though I haven't here argued, that this problem generalizes to any semantics of modal logic given in an extensional metalanguage, including Lewis/Stalnaker counterfactuals), or it indicates an incoherency in "necessitarian" physical necessity: physical necessity either can't be cashed out in terms of truth in a certain set of worlds, or it can and it's thus nothing more than a contingent regularity. I hope this is stated clearly enough that you can see the problem; it's kind of off-the-cuff, though, so I wouldn't be surprised if it's obscure. Of course, you can leave a comment asking for clarification. :)
And here's a quick philosophical/logical question for your blog-reading (dis)pleasure: if laws (of nature) are more than just regularities, but the laws of nature could have been different (e.g. E=mc2 might have been false), then is there a way to cash out physical necessity in terms of possible worlds? Here's the problem: Say we have a law of nature /\x(Fx->Gx), which is true in this world, but not necessary because in some worlds there are different laws. It looks like there's no way to make this law "necessary" in any weaker way that doesn't break down into making it a contingent regularity. If we say that it's physically necessary, in the sort of standard way of formalizing that ([](LP->/\x(Fx->Gx)), where LP is a proposition stating some specified set of laws of physics; thus, the laws of physics strictly imply the regularity), we end up with a proposition that's still contingently true, because making it "physically necessary" in this way just made it true in worlds where the laws of physics come out true. If it's contingent that these laws of physics hold, then it's no less contingent that our regularity holds, if it only holds where the laws of physics do. We seem to want to say: the laws could have been different, but given that they are such-and-such, this regularity necessarily follows. But the standard ways to formalize this can only render it as: there are regularities that hold in only some worlds (specifically, worlds where certain other regularities hold); this seems to lack entirely the "necessity" we're looking for. Unless I'm missing something, there doesn't seem to be an obvious way to formalize physical necessity in the non-Humean, "necessitarian" way that a lot of philosophers would like to assert it. If that's the case, then either this is a deficiency in possible worlds semantics (I believe, though I haven't here argued, that this problem generalizes to any semantics of modal logic given in an extensional metalanguage, including Lewis/Stalnaker counterfactuals), or it indicates an incoherency in "necessitarian" physical necessity: physical necessity either can't be cashed out in terms of truth in a certain set of worlds, or it can and it's thus nothing more than a contingent regularity. I hope this is stated clearly enough that you can see the problem; it's kind of off-the-cuff, though, so I wouldn't be surprised if it's obscure. Of course, you can leave a comment asking for clarification. :)