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February 27, 2006
Camillus, Caeso, Volesus
Expressions that were once current have gone out of use nowadays. Names, too, that were formally household words are virtually archaisms today; Camillus, Caeso, Volesus, Dentatus; or a little later, Scipio and Cato; Augustus too, and even Hadrian and Antoninus. All things fade into the storied past, and in a little while are shrouded in oblivion. (section 33, book 4 of the Meditations)
Marcus Aurelius does a little socio-linguistics. (For more recent analysis see chapter 6 of Freakonomics
Posted by logican at 11:15 AM | Comments (3) | TrackBack
February 10, 2006
A Solution to a Problem about Inexpressible Propositions?
Jeff King's claims for his view of propositional structure in the introduction to "Structured Propositions and Complex Predicates" are pretty exciting. He writes:
I shall show that the account of propositions that results from my account of propositional structure has two highly desirable features. First, it is virtually undeniable that propositions as I shall construe them exist. Second, my account makes comprehensible how propositions manage to represent the world. It seems to me that these results are important.
It seems to me that he's right in thinking that those virtues are important, but further reading of the paper reveals that the view also has an terrible vice: it seems that in order for a proposition to exist, on King's view, it has to be the case that some sentence exists which expresses it.
King is well aware of this, though he doesn't accept that this feature is a vice, and after acknowledging that it is a consequence of his view, he tries to make it a plausible consequence:
Thus on the present view, there may be propositions even in the absence of any public natural languages. However, without vehicles that express propositions, whether they be mental sentences or sentences of a public language, there are no propositions. For on the present view, the propositional relation binding together the constituents of a proposition is composed of the relation binding together the lexical constituents of a vehicle expressing it (i.e. the sentential relation of the vehicle) and the relations connecting the lexical constituents of the vehicle to their sv's. For the propositional constituents to stand in this propositional relation (i.e. for the proposition to exist) is for there to be lexical items that stand in the relevant sentential relation and that have the propositional constituents as their sv's . Thus for propositions to exist, there must be vehicles consisting of lexical items standing in some (sentential) relation, where these lexical items bear semantic relations to propositional constituents.
Unlike King, I think this is unquestionably a bad consequence, since it seems to me that there are true propositions which we cannot express. Consider the real numbers, for example. There will always be real numbers that we don't have natural language expressions for (even language of thought expressions), since there are more reals than there are natural language expressions. Though I can quantify over real numbers using expressions like `all the reals between 0 and 1', I cannot express the proposition that would be expressed by "x is a real number" if I were to replace 'x' with a name for one of those reals that I don't have a name for. And no matter how many names I introduce, there will always be examples of such propositions that I can't express.
But perhaps things get more interesting if we're more liberal about what we count as a language. It's hard to see that it really matters that the language is natural, right? And mathematicians have some pretty odd and abstract ideas about what we might count as a language. For example, why should the expressions of a language be words that we can write down or speak? Why not let numbers be expressions? (Not numerals, mind, but numbers.) There's loads of them. In fact, let every real number be a name for itself. Add those new names to English and now, for every real number, there is a sentence (not always one I can right down, unfortunately) which expresses the proposition expressed by the sentence "x is a real number' when the "x" is replace with a name of the number.
Expanding our conception of a language in this way would seem to solve the problem. So I'm wondering: why not?
Posted by logican at 06:36 PM | Comments (16) | TrackBack
February 09, 2006
Name Systems
In section IV of "On Referring" Strawson remarks that although names for people are usually arbitrary it "would be perfectly possible to have a thorough-going system of names, based e.g. on dates of birth, or on a minute classification of physiological and anatomical differences."
It seems to me that there's a reasonable case to be made that we already have such systems. There's the system we use for constructing names for the natural and rational numbers, and for some of the reals, there's a system for naming dates (e.g. "January 9th 1942"). I wonder if there's a system for naming stars? (The International Star Registry, which lets you pay to name a star after your hamster, doesn't count.) And I wonder if the expressions determined by such systems really count as names, and at what point we slip into the realm of descriptions.
Posted by logican at 12:28 AM | Comments (5) | TrackBack