```--- 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)

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