--- Henrik Theiling & John Quijada wrote (many things) This discussion about scales is quite interesting I think, and it's one of my main concerns. I noticed several points on the way (or rather, some questions came to my mind when reading) : - why should a scalar concept be oriented one way and not the other one ? For ex, for a temperature scale, why should "cold" be at the lowest end, and "hot" at the highest ? If we naturally think so, that means that we think that the concepts or "hot / cold" and "high / low" are alike, and that if we consider those 2 pairs, "hot" is similar to "high" and "cold" similar to "low". Why is it so ? - if we also consider the concept of good / bad, or pleasant / unpleasant, than we have a tendency to consider "good" or "pleasant" to be at the highest end of the scale. So, logically, we consider that "hot" is good, and "cold" is bad. But clearly there is a flaw here somewhere, because "hot" cannot be good in any circumstance (ask a fireman). So where lies the flaw ? (When I say "the lowest, or the highest end", I mean that the vector is oriented like : origin ----->----- destination, and not like origin -----<----- destination, neither unoriented like origin -----!----- destination). - when considering a conceptual scale, we often think of a 3, 5 or maybe 7 degrees-scale. It's easy to understand why the number should be an odd one: so we have the possibility for an average value (although in some cases its is not so clever, for ex when asking people to give a judgement on something: if you allow an average value, this one will probably be unduely privileged). But why not 9, 11 or more ? Or 101 ? (from 0 to 100 included, average being 50). Because usually we don't need such a precision ? But they are cases where we would appreciate it. So clearly, there should not be a single, general scale in a language, but the possibility for several scales, depending on the context. Sometimes a 3 degree scale is enough, sometimes a 1001 one would be quite interesting. And I come back with my proposition of defining concepts like "warm" by a couple of parameters : 1/ the scale used; 2/ the value on that scale (ex: warm could be, in certain circumstances, expressed by : temperature (4;E5), meaning degree 4 on a defined scale E5, which could refer to: (1;2;3;4;5). (If this looks too abstract and mathematical to linguists, so let's suppose that in some language, "water" is "allonzenfan", "temperature" is called "tshakabums", "4" sounds like "gruobnenork" and "scale-E5" is uttered "pussypussypussy", so the sentence "Allonzenfan tshakabums gruobnenork pussypussypussy" (for ex) would mean "the water is warm", or more exactly "if I have the choice between: very cold, cold, tepid, warm, and hot, to qualify the water temperature, then I will describe it as warm"). - sometimes we have a tendency to define a scale, starting from 0 to n, sometimes from 1 to n, sometimes from -n to +n. Clearly all theses scales would be all right, provided we know which one we're talking about, of course. A scale should be defined by: 1/ minimum and maximum values; 2/ continuous, or discrete; 3/ if discrete, value of the step. For ex, on a continuous scale from 0 to 100, value 32.45783 would be all right. On a discrete scale from -2 to +2, with step 1, values -1, 0, +2 would be all right (if we come to a value of -1.6, we round it to the nearest authorized degree, so -2 in this case). - but we should also consider open scales, like Richter scales for earthquakes. In that case we have to know the mathematical function giving us the value of y depending on x (for ex, multiplying last value by 2 : 1, 2, 4, 8, 16...) Clearly, this is not very useful in common language, but I think the possibility should exist in a language, to be "at hand" when needed. In that case, the extreme values could be represented, when relevant, by: -infinite, +infinite, and we need the function used to be part of the definition of the scale. - can we consider that a closed, discrete scale having only 2 steps would be the definition of what we call polarity ? In other terms, is polarity just a particular case of scalarity ? If for ex I have a scale admitting only the values (1,2), or (0,1), or (-1,+1), then it looks very much like polarity: yes/no, positive/negative, male/female. So we could generalize and regroup the concepts of polarity and scalarity in a single concept. ===== Philippe Caquant "High thoughts must have high language." (Aristophanes, Frogs) __________________________________ Do you Yahoo!? Yahoo! Finance Tax Center - File online. File on time. http://taxes.yahoo.com/filing.html