kamkuspe

["Steven M. Belknap" <sbelknap@UIC.EDU>]

>If what you want to say is quantized logic, .e'u use {selka'u logji} =
>"logic of the thing which is quantized". The tanru mechanism takes care
>of this. If you said {kamkantu logji}, I would take it to mean "logic of
>the property of being a quant", not "logic with the property of being
>quantized"

As you point out, the tanru and lujvo mechanisms are somewhat flexible. So
far, I prefer <kamkuspe> and <kamkantu> to <selkuspe> and <selkantu>. I
remain unconvinced that these are wrong. But you use lojban more than me.
Is there some compelling reason you see for calling <kamkantu> "wrong"? You
haven't explained this yet.

>Let's build a simulation here. Let's simplify, and say we have a 2
>valued scale {0,1}.

Although you don't say so, I assume you mean a two-valued fuzzy scale,
something like "fuzzily true" and "fuzzily false"

>OK? Now, our patient says he feels 1 in his stomach.

OK. He means "I have fuzzy pain in my stomach." I assume you realise this
is a highly artificial situation.

>Then we punch him in his guts. His pain has doubtless increased, right?

Perhaps, but he can not explain this using the two valued scale. If he is
limited to this scale, he can only repeat "I have fuzzy pain in my
stomach."

>And he still says "I feel... nnngh... 1...". So, even though you set
>an arbitrary scale, (that it is two valued doesn't really matter, it is
>just for simplicity's sake), you have made a noticeable increment in the
>{ni broda}, while still reading the same value on your scale.

No noticeable increment in his pain can be expressed using your two valued
scale.

>Ergo, it
>is not "smallest measurable increment of property".

Actually, all that's happened is that our hero has become aware of the
inadequacy of his chosen fuzzy scale to express his pain. He miscalculated
the "maximal pain" upper end of his scale. He has learned something, and
will be better informed the next time he makes up such a scale; perhaps he
will make a better choice of scale the next time.

>>
>> What about cookies? I have three cookies in my lunchbox. What about
>> anything else you would describe using integers? Integers are quantizers
>> for things measured on a <kamkantu> scale.
>
>I eat a bit, and I am left with just half a cookie. I eat a bit more,
>and lo!, there are some crumbs left and not much more. Quantum? Not
>even integral. (excuse the pun)

You are alluding to a sorities paradox which results from claiming that a
thing is either a cookie or not a cookie. Start with a cookie, eat half. Is
it still a cookie? If no, repeat until you think its not a cookie. Using
true/false discrete logic, you can only escape the paradox by setting an
arbitrary number of steps after which you are left with a non-cookie. This
seems like a false dichotomy. One of the attractions of fuzzy logic/sets is
that such paradoxes can be avoided.

>No-one has ever successfully managed to measure sureness in an objective
>way. Maybe the guy is 90.1% sure, but he didn't bother to say so. When
>anybody tells me that something is 90% of something else, I
>automatically assume that they are working with a scale with 101 (or,
>maybe in informal speech, 11) classes. When I hear 90.0%, I envision
>scale with 1001 subcategories. And when somebody says fifty percent, I
>automatically visualise three categories. Not infinite. Just three.

You are welcome to visualize the meaning of these statements in any way you
wish. But what you are referring to are discrete, not fuzzy sets. Again,
you are welcome to do this, but you are not talking about fuzzy sets here.

>> >because we can't
>> >   calculate, or even measure things to infinite precision (which is
>> >   what a continuity of scale inspires in my mind)
>>
>> You are misunderstanding what fuzzy logic is. There is no need for infinite
>> precision. Perhaps you are confusing the number of fuzzy sets being used
>> with some requirement for infinite precision. I call the number of fuzzy
>> sets the "granularity" of fuzziness. If the granularity is 5 and we are
>> using an interval scale, then there are 6 sets, which I designate as:
>>
>> {0/5, 1/5, 2/5, 3/5, 4/5, 5/5}
>
>This is discrete, six-valued approximation of fuzzy logic.

No, this is wrong. {0/5, 1/5, 2/5, 3/5, 4/5, 5/5} are designations or
labels for the sets. As I explained, I am using the above six labels to
designate six *fuzzy* sets. Take the 2/5 label. Maximum membership in this
set occurs at the exact discrete value 2/5, extent of membership in this
set drops linearly to 0 at discrete value 1/5 and discrete value 3/5.
Again, you are welcome to use a six-valued discrete set if you prefer, but
do not confuse it with a six-valued fuzzy set, which is a different thing.

cohomihe la stivn


Steven M. Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria

email: sbelknap@uic.edu
Voice: 309/671-3403
Fax:   309/671-8413