| In a message dated 7/2/2001 4:25:58 AM Central Daylight Time,
edward.cherlin.sy.67@aya.yale.edu writes: Which reminds me--What's the Lojban for fiddle-dee-dee? Do we have an Which "fiddle-dee-dee?" There is the nonsense string for meter or rhyme ("... ... the fly has married the bumble-bee"), which is hard in Lojban, since so few syllables are nonsense. Or the dismissive one ("..., Tomorrow is another day!"), which is a {cu'i} of some sort, I think, but not clear what to attach it too -- maybe {ui} itself. Or the one that *says* "nonsense," maybe {ianai}. <And if your grandmother had had wheels, she would have been a trolley-car.> Not quite the same case both because it is facetious (and Lord knows what to do with that) and because it is not the contrary-to-fact use of the real world. <We can carry on such discussions either with a good deal of hand-waving, or by proposing a modal logical theory in which to carry on our discourse. We're not too keen on hand-waving here, and we certainly don't agree on a Lojbanic theory of modal logic sentence modifiers. This results in the typical infinite regress so familiar from the Tortoise and Achilles, where one of us says, "It's obvious!" and the other says, "No it isn't, it's impossible, and even if it were possible, I still wouldn't believe it."> Which is why I am suggesting turning to a "uses of language" approach, rather than trying to work this out in terms of other worlds, taking (almost) all language as descriptive. <The usual case is that we wish to suspend the operation of reductio ad absurdum (and excluded middle along with it) and use a somewhat limited form of positive, even constructive logic. "Let us suppose X" says the mathematician, physicist, or science fiction writer, "then ignoring the obvious contradictions, what happens?"> Classically one or the other version of relevance logic or some sort of paraconsistency, but I repeat that that is missing a useful alternative in favor of a nearly useless formalism in descriptive language. <Hard sciences, even math, use counterfactuals all the time, in circumstances where the outcome cannot be predicted with certainty. This is the stage of generation of productive hypotheses that make predictions. Later on, the predictions must be checked, if possible, by means of proof or experimentation. However, there can be a gap of decades, or in extreme cases centuries, between the formulation of a hypothesis, the working out of a prediction, and the verification or falsification of the prediction. Think of Fermat's Last Theorem, ( or the more interesting Riemann hypothesis, for the heavy-duty mathematicians here) or the atomic theory, proposed in Greek times and verified by Einstein's theory of Brownian motion and by X-ray diffraction in the early 20th century.> Pretty much my point (suppressing the bit about how long it sometimes takes to get it worked out). In the hard sciences, speculation leads to experimentation and thence to a decision on the hypothesis (eventually, to be sure). Other kinds of speculation are less controlled and lead less surely to tests and then to tests that are themselves less definitive. What can we work out about the situation where my grandmother had wheels? [I would ahve thought the atomic theory -- at least so far as it was formulated by the ancients -- was established by the early 19th century] <Descartes remarked how astonishing it always was when people explained his writings to him in terms which he never would have thought of.> Well, authors often misunderstand themselves, but-- more to the point -- interpretations (and thus ordinary speculations, too) are not so intimately tied to facts that we can easily discover them to have gone astray. This is part of the reason for not liking the descriptive language imp[lied by "possible worlds" and perferring to talk about language use, thus removing the question of truth from some of these kinds of speculations. <Building non-standard arithemetic and analysis requires that we work in two different logics simultaneously. Technically they are called first-order and second-order logic. We don't have a good way of describing this situation either in natural languages or in Lojban. If we did, I think it would go a long way toward clarifying the grammar puzzles that are exercising us today.> Well, Robinson's non-standard artihmetic does not involve second-order logic explicitly (or, any more than ordinary arithmetic does). It is more a matter of object language and metalanguage: The formulae look normal but what they mean is something else (Goedel's proof shows this more clearly, since we get interesting metalanguage readings of apparently uninteresting object language formulae. Well, you get that in Robinson, too, but the metalnaguage readings are a lot less clear). I don't think this has a lot to do with the present problem, though. <We will have to do what the mathematicians do--Work out how to express ourselves clumsily in the current language, and then invent a better one when we have a better idea of what we are doing.> Amen. |