From edward.cherlin.sy.67@aya.yale.edu Mon Jul 02 02:25:35 2001 Return-Path: X-Sender: Edward.Cherlin.SY.67@aya.yale.edu X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_2_0); 2 Jul 2001 09:25:35 -0000 Received: (qmail 2524 invoked from network); 2 Jul 2001 09:25:35 -0000 Received: from unknown (10.1.10.26) by l8.egroups.com with QMQP; 2 Jul 2001 09:25:35 -0000 Received: from unknown (HELO pltn13.pbi.net) (64.164.98.22) by mta1 with SMTP; 2 Jul 2001 09:25:35 -0000 Received: from mcp.aya.yale.edu ([216.103.90.93]) by mta8.pltn13.pbi.net (iPlanet Messaging Server 5.1 (built May 7 2001)) with ESMTP id <0GFU00LI7A6JZN@mta8.pltn13.pbi.net> for lojban@yahoogroups.com; Mon, 02 Jul 2001 02:25:32 -0700 (PDT) Date: Mon, 02 Jul 2001 02:40:35 -0700 Subject: Re: [lojban] Not talking about imaginary worlds In-reply-to: X-Sender: cherlin@postoffice.pacbell.net To: pycyn@aol.com Cc: lojban@yahoogroups.com Message-id: <5.1.0.14.0.20010702020333.00b12dd0@postoffice.pacbell.net> MIME-version: 1.0 X-Mailer: QUALCOMM Windows Eudora Version 5.1 Content-type: text/plain; format=flowed; charset=us-ascii From: Edward Cherlin At 07:35 PM 7/1/2001, pycyn@aol.com wrote: >One reason for not trying to discuss the current problem in terms of >imaginary worlds or possible worlds and the like is that we often talk about >such worlds in a completely assertive, non-hypothetical way: "Sherlock Holmes >lived at 221B Baker Street." This is a true statement, asserted as such, >without any subjunctive or contrary-to-fact fididddling, Which reminds me--What's the Lojban for fiddle-dee-dee? Do we have an attitudinal for it? >yet there never was >such a person or such an address in the real world; it is all literally >contrary to fact. Worse, within such discussion we can also deal with the >real world in a "contrary-to-fact, subjunctive," way: "If Holmes had pursued >Jack the Ripper, the gracious lady would have taken back the emerald." And if your grandmother had had wheels, she would have been a trolley-car. 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." >What is crucial, then, is not the nature of the world involved, but of >what we are doing with it. In one case we are attempting to describe it >correctly and we simply assert that it is thus-and-so and face the >consequences of being right or wrong. And in the other case, the >"subjunctive, contrary-to-fact"? At least some of the time, the act is >speculation -- abstraction, extra-or-interpolation. I am not sure that this >covers all the cases of sentences that are not now true but are not >recommended nor preferred, but it covers many of them. 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?" >I am also unsure just >what "speculation" means in practical terms. Arguments suggest that there are >specultive truths and falsehoods, but history suggests that, outside of the >hard sciences, where the speculation can be realized, I don't understand this clause. 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. >determining which is >which is not easy. In general, the rules are rather unclear, moore or less >like the rules of interpretation rather than experiment. Indeed one common >use for such speculation is to build on an interpretation toward possible >experiment. She gives me a look, which I interpret in a certain way. >Assuming that that interpretation is correct, then, if I were to do >so-and-so, she would do such-and-such. Descartes remarked how astonishing it always was when people explained his writings to him in terms which he never would have thought of. >Now, so-and-so is something I can do >without too much commitment, so I can now test my interpretation (assuming my >speculation is reasonably correct). >What is missing -- and always has been except in special cases -- is good >rules for when speculation is correct. Outside of the hard sciences, we have >to rely on imprecise terms (about a person's character, say), vague and >uncertain generalities (about what people of that sort do in certain types of >situations -- and [rarely explicit] what situations they will see as of that >type) and the like. We don't actually have hard and fast rules in the hard sciences or in math either, other than "Check it again!" Occasionally a long-established proof will be overthrown--not necessarily because it was wrong, but possibly because we have found a new way of doing things. The best example I know of is Peano's proof that all models of his axioms for the natural numbers are isomorphic. I have mentioned before that we have constructed non-standard models of the natural numbers, leading to non-standard real and complex numbers and a new, significantly simpler way of doing analysis using infinitesimals. 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. >And these generalizations -- an even the personality >types (to stick with that kind of case) -- are themselves often presented as >speculative: "If type x is in situation y, he would... ." Some of this may be >inherently a closed language game, without a necessary return to the real >world, of the sort that logic gives with closing the indirect proof or >science gives with an actual experiment. > So how do we mark speculation in Lojban? > Are there other non-assertive uses not dealt with? 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. Edward Cherlin Generalist "A knot! Oh, do let me help to undo it." Alice in Wonderland