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.
In "Tharp's Third Theorem", Lewis agrees with Jackson that "all of us are committed to the a priori deducibility of the manifest way things are from the fundamental way things are (whatever that may be)" (TTT, p.96). His somewhat cryptic argument isn't quite the same as Jackson's though, and it seems that he avoids the mistake I mentioned yesterday.
Note that Lewis doesn't say we're committed to the a priori deducibility of all truths from the fundamental truths. Instead, he speaks of the "fundamental way things are", or from "contingent truths, supervenient on the fundamental way things are" (TTT 96). (In case that's not clear: Like Lewis, I use "truth" for "true sentence", not e.g. for "true proposition".)
Let logicalism ("logicism" was already taken) be the claim that all truths supervene upon purely logical truths, where a purely logical truth is a truth that contains only logical terms, including terms from second order modal logic.
Logicalism immediately follows from this purely logical truth ('[]' is the box, 'ACT' the actually operator):
p <-> []((x)(F)(Fx <-> ACT(Fx)) -> p)
While all truths therefore supervene upon the purely logical truths, not all truths are a priori deducible from the purely logical truths. For instance, that water covers most of the earth isn't. So we have a counterexample to the claim that whenever all truths supervene on the F-truths, then all truths are a priori deducible from the F-truths.
Serious Metaphysics, in Jackson's sense, tries to identify a limited set of truths (i.e. true sentences) that entail (i.e. strictly imply) all truths. So what about
*) Everything is just as it actually is?
((p)(p <-> actually p), or (x)(F)(Fx <-> actually Fx))
(*) is true. It entails all other truths: whenever S is true, then so is "necessarily, if (*) then S". And it is fairly simple and economic: for instance, it doesn't contain macrophysical or phenomenal terms. Still, it's not serious metaphysics. What's wrong?
Apropos conceptual differences, Lewis didn't seem to care much about whether his
analyses exactly matched other people's semantic intuitions:
In "Veridical Halluzination and Prosthetic Vision", he claims that
prosthetic vision is properly called "seeing". He continues:
If you insist that "strictly speaking", prosthetic vision isn't really
seeing, then I'm prepared to concede you this much. Often we do leave
semantic questions unsettled when we have no practical need to settle
them. Perhaps this is such a case, and you are resolving a genuine
indeterminacy in the way you prefer. But if you are within your
rights, so, I insist, am I. I do not really think my favoured usage is
at all idiosyncratic. But it scarcely matters: I would like to
understand it whether it is idiosyncratic or not. (p.280 in Papers
II)
Another example: In Convention, he suggests that a regularity to dress in a particular way doesn't count as conventional if many people conforming to the regularity want others not to conform (so that they can poke fun at them). Realizing that this classification isn't obvious he notes:
If the reader disagrees, I can only remind him that I did not
undertake to analyze anyone's concept of convention but mine. (p.47)
He speaks of reminding the reader because he had already mentioned in the introduction that there might be no clear common concept of
convention. But, he adds, "what I call convention is an important
phenomenon under any name" (p.3).
In case anyone's interested, here is the preliminary study guide for my Wissenschaftstheorie course (postscript file, German). I've decided to spend a little time on constructivism and relativism because there's a parallel course on sociology of science, and at least in Germany it is common sociological practice to talk as if constructivism and relativism were true. (My principle of charity demands not to take this talk literally. It usually makes sense if one substitutes "theory" for "reality" and "belief" for "truth".)