A free-variable tableau with root
x(Fx & 
y~Fy)
closes after 4 nodes and 1 application of Closure. A standard tableau, on the other hand, will have at least 6 nodes because the root formula must be used twice. So translating free-variable tableaux into standard tableaux is not as easy as I once thought. I wonder if it would suffice to add a rule to the free-variable construction that forbids Closure to unify a variable with a constant that first appears after the variable on the branch.
I need to tidy up this part of my belief space. Once I complained that literal trans-world identity (as opposed to trans-world identity based on similarity) is implausible because it entails that there can be no vagueness about a thing's essential properties (for determinate properties): either the thing has the property at all worlds or not. On the other hand, I also believe that there is no big difference between individuating things as worldbound and individuating them as trans-world fusions of worldbound counterparts. Unfortunately, these two views can't both be correct.
I now have a 128 bit SSL certificate for umsu.de. For Postbote, you should now use the address https://www.umsu.de/post/ (with 'https' instead of 'http'), as that makes it is much harder for other people to access the transmitted data. (The same holds for Ned, but as far as I know I'm the only one who uses that.)
A few comments on Counterparts and Actuality by Michael Fara and Timothy Williamson (via Brian, of course).
Fara and Williamson argue that if Quantified Modal Logic is enriched by an "actually" operator, then given some further assumptions there is no correct translation scheme from QML to Counterpart Theory. Here, a correct translation scheme is one that translates theorems of QML into theorems of CT and non-theorems of QML into non-theorems of CT. (theorems of which QML? -- good question; read on.).
Lewis defends a kind of best system theory both with respect to laws of nature and with respect to mental content: something is a law of nature iff (roughly) it is part of the best theory about our world; somebody believes that snow is white iff (roughly) this is what best makes sense of his behaviour according to our belief-desire psychology.
In both cases, it looks on first sight as if the theory introduces an implausible relativity into its subject matter: We don't want to say that the laws of nature depend on what we happen to find simple (but simplicity is part of what makes a theory good), and we don't want to say that what someone believes and fears depends on what we think about his behaviour.
On page 305 of "Assertion Revisited" (in the latest issue of Phil.Studies), Robert Stalnaker suggests that the information conveyed by an utterance is the diagonal proposition associated with the utterance iff it is unclear in the relevant context which horizontal proposition the utterance expresses:
[T]he relevant maxim is that speakers presume that their addressees understand what they are saying. In terms of the two-dimensional apparatus, this presumption will be satisfied if and only if the propositional concept for the utterance [a function that assigns to every relevant possible context the horizontal proposition expressed by the utterance in that context] is constant, relative to the possible worlds that are compatible with the context. Our problematic example [of saying "Hesperus is Phosphorus" to O'Leary who doesn't yet know that Hesperus is Phosphorus], and all cases of necessary truths that would be informative (in the sense that the addressee does not already know that they are true) will be prima facie counterexamples to this maxim, and so will require reinterpretation [so that what is said is the diagonal, not the horizontal proposition].
Three comments:
I'm busy with lots of other things. Blogging will probably resume sometime next week.
(This is a follow-up to the previous post.) I think I've found a better way to provide for things like population-dependence in a Lewisian semantic framework. The trick is to regard it as a kind of index-dependence without explicitly introducing population-coordinates into the indices.
Recall, we want "pain*" to denote whatever state occupies the pain-role in the relevant population. Unfortunately, the relevant population isn't just the most salient population in the context of utterance, for we want to say things like
This is going to get a bit weird and technical. I wonder how a Lewisian semantics (along the lines of "Index, Context and Content" and "General Semantics") for terms like "pain" can make true everything Lewis says about such terms.
Assume that
1) Necessarily, for all x, x is in pain* iff x is in a state that plays the pain-role in normal members of the kind to which x belongs.
By "the pain-role" I mean the causal role attributed to pain by folk psychology. By "pain*" I mean whatever satisfies the condition expressed by (1). So (1) is more like a definition than an assumption. Lewis believes that our ordinary concept of pain roughly satisfies (1), but for what follows this doesn't matter. I think it's clear that we could have concepts for which something like (1) holds. Lewis's example of having a certain number stored in memory, as denoting a state of pocket calculators, sounds plausible to me (with the pain-role replaced by the role attributed to the state of having a certain number stored in memory by folk pocket calculator theory).
This comment by Gideon Rosen in the fascinating thread on IR at TAR made me smile:
Consider two opinionated journalistic essays on the same controversial topic ? say, the morality of Sharon-style extra-judicial killing, and suppose it's clear that both writers agree on the underlying facts. One says that the killings are unjustified because they violate a fundmental moral right to due process. The other says that there is natural rights are nonsense on stilts and that the killings are justified because they maximize utility. [...]