Oh dear.
Returning to philosophy, here is a remark by John Burgess about the possibility of translating ordinary sentences into sentences with seemingly less ontological commitment, as described in Prior's "Egocentric Logic" and Quine's "Variables Explained Away":
Thus whether one speaks of abstract objects or concrete objects, of simple objects or compound objects, or indeed of any objects at all, is optional. Or at least, this is so as regards "surface grammar". My claim is that if children who grew up speaking and arguing in Monist or Nihilist or some Benthemite hybrid between one or the other of these and English, it would be gratuitous to assume that the "depth grammar" of their language would nonetheless be just like that of English, with a full range of nouns and verbs denoting a full range of sorts of objects and connoting a corresponding range of kinds of properties. And any assumption that the divine logos has a grammar more like ours and less like theirs would be equally unfounded, I submit. It is in this sense that I claim any assumption as to whether ultimate metaphysical reality "as it is in itself" contains abstract objects or concrete objects, of simple objects or compound objects, or again any objects at all, would be gratuitous and unfounded. (p.18 of "Being Explained Away" -- Microsoft Word format, use Neevia to convert)
I'm not sure to what extent I agree with that. I do agree that there is something strange about asking whether numbers really exist. Burgess takes this to be the core question dividing nominalism and platonism about numbers. Thus he argues e.g. in "Nominalism Reconsidered" (MS Word again, coauthored with Gideon Rosen) that if nominalists agree that "there are numbers" is true -- while offering a nominalistically acceptable interpretation --, they have actually given up nominalism.
Philosophers like to paraphrase away ontological or ideological commitment: how can there be a lack of wine if there are no such
entities as lacks? Because "there is a lack of wine" is only a loose way of saying "there is not enough wine".
So do we suggest that "there is not enough wine" somehow gives the
underlying logical form or linguistic structure of "there is a lack of
wine"? One might think so: if there are no lacks, we can't honestly
use lacks as semantic values in our linguistic theory. So if 1) our
linguistic theory says that sentences of the form "there is an F" are
true iff the relevant semantic value of "F" is non-empty, and if 2)
"there is a lack of wine" has the form "there is an F", and if 3) the
members of a predicate's semantic value are things that (in some
intuitive sense) satisfy the predicate, then, given the truth of "there is a lack of wine", it follows that there are things satisfying "is a lack of wine". Which presumably we wanted to deny. Rejecting (2) seems to be a good way to block the argument: "there is a lack of wine" is
not really a sentence of the form "there is an F"; really, it
is a sentence of the form "there is not enough G".
Stalnaker's "Lewis on Intentionality" (AJP 82, 2004) is a very odd paper. The aim of the paper is to show that Lewis's account of intentional content as developed in "Putnam's Paradox" -- global discriptivism with naturalness constraints -- faces various problems and conficts with what Lewis says elsewhere.
The first thing that's odd about this is that in "Putnam's Paradox", Lewis doesn't develop an account of intentional content. Rather, he discusses Putnam's model-theoretic argument and suggests that if one holds something like global descriptivism about linguistic content, adding external naturalness constraints on the interpretation of predicates would be an attractive way to block Putnam's argument for underdetermination.
Sometimes I think it's unfortunate that advanced logic and metamathematics usually presuppose various mathematical truths. For instance, in discussions on mathematical realism I've heard people arguing that by the first incompleteness theorem, mathematical truth can't be identified with provability in a formal deductive system. For, those people argue, the first incompleteness theorem proves that for any reasonable formalized system of mathematics, there is a true arithmetical sentence G that is unprovable in the system.
I've written a little paper in German about the connections between metaphysical (modal) and analytical implication for the Olaf Müller-Kolloquium here at Humboldt University: "Fundamentale Wahrheiten" (PDF). It brings together some things I've already written about here. The main ideas are entirely due to Lewis, Jackson and Chalmers.
Since I haven't slept last night and feel unable to do anything productive, here is an abbreviated translation.
Skimming literature on the sociology of knowledge, I came
across Alfred Sohn-Rethel's "Soziologische Theorie der Erkenntnis",
which begins with the following definition
of "society" (sorry, no translation, as I have no idea what it means):
"Gesellschaft" ist, im Sinne dieser Untersuchung, ein Zusammenhang der
Menschen in bezug auf ihr Dasein, und zwar in der Ebene, in der ein
Stück Brot, das einer iÃt, den anderen nicht satt macht.
Which reminds me that a few years ago, I heard on BBC (Radio 3 if I recall correctly) a listener complaining about some modern classical music they had played. He suggested the following test for good music: If people listening to the piece for the first time don't notice that there's something wrong if random notes have been added or altered in the composition, it's bad music and shouldn't be broadcast.
Just for fun, I'm reading Peter Smith's draft of his new book on Gödel's Incompleteness Theorems. So far, it's quite enjoyable. I might say more about it later. But here is something of which I'm not sure it's correct. (I'm also not sure it's false, that's why I'm posting it here.)
Smith shows that not all computable functions are primitive recursive by proving that the antidiagonal of the p.r. functions can't be p.r., even though it is intuitively computable. Having
identified the p.r. functions with functions whose implementation
doesn't require unbounded loops, he then asks why the antidiagonal
function doesn't satisfy that condition:
Using my own weblog system, I usually don't get comment spam. But today a spam bot has posted a number of comments. From now on, comments containing HTML link tags will be rejected. They don't get rendered as links anyway, so this should only affect commenters who don't understand "No HTML allowed".
1. There is nowadays considerable evidence for the existence of pulsars. Still, it isn't incoherent to worry that the evidence might be misleading and pulsars don't exist after all. But it is incoherent to worry that pulsars might be the apple trees in my parents' garden. These apple trees aren't neutron stars, and they don't emit regular pulses of electromagnetic radiation, and things that don't do that don't deserve the name "pulsar".
2. Suppose we are convinced by van Inwagen's arguments that fictional characters are abstract entities created by authors and denoted by our fictional names. This suggests the following picture: Over and above our material universe there is a special realm of abstract fictional characters. Everytime an author writes a novel, new entities pop up in this fictional realm. There is no causal connection from the fictional realm to our world. But then how do we know about the fictional characters? How can we be sure for example that the creation of fictional characters is reliable? Couldn't it happen from time to time that a fictional character fails to be created? If so, perhaps Madame Bovary exists, but Sherlock Holmes doesn't. In which case it would be false (on the Kripke-van Inwagen account) that Sherlock Holmes was invented by Conan Doyle or that he is a widely known fictional character. Isn't our confidence in such assertions rather mysterious and irresponsible given that really we have no access at all to the fictional realm? At the very least, the exceptionless correspondence between what our authors do here on Earth and what happens in the fictional realm cries for explanation!
Metaphysical debates about causation, consciousness, chance, change, mathematics, or modality have a lot in common. In all cases, metaphysical theories try to tells us what, if anything, makes a certain class of statements true. Among the possible answers, we usually find suggestions to reject the alleged phenomena, to declare them as primitive, and to reduce them in various ways to something else. But on closer inspection, there appear to be big differences, in particular with respect to what is required for a reduction.