A Fuzzy Ship from Theseus

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

>> > No ones skin is Platonic ideal blue, but is blue to a degree. Its seems
>> > artificial to specify that something is 89% blue. A fuzzy means of
>> > describing the degree of blueness would be most interesting. Has anyone
>> > thought about this?
>> That is supposed to be "le jei le skapi be ko'a cu blanu", the
>>degree-of-truth
>> of someone's skin being blue.  As far as "ni" goes, I'm as much at sea as
>> anyone.

ucleaar <ucleaar@UCL.AC.UK> said
>I suspected that, but was unsure. If truth is gradient, then is false
>a truth value of 0, and true a value of more than 0?
>I wonder whether {lo jei carmi gusni} is different from {lo ni carmi gusni}.
>Perhaps there is an upper limit on {lo jei c g} (e.g. a value of 1),
>but no upper limit on {lo ni carmi gusni} (allowing for infinite brightness).
>What do you reckon?

In Aristotelean or two valued logic, continuously valued things are
typically either rounded to one of the values (true or false) or a
"probability" of being true or false is assigned.  Although this
approach is nearly universally accepted, it is not the only possible
consistent logic one might construct.  IMHO the fuzzy logic construct is
more intuitive than the Aristotelean construct.

Consider the (frequently cited) example of birds.  Here is my
(arbitrary) list of things from most birdlike to least:

Eagle, Pigeon, Penguin, Ostrich, Bat, Flying Squirrel, Jack Rabbit.

Your ordering would probably be different, of course.  But we could
probably agree on a list of relevant properties ( flies, lays eggs,
genetic makeup, etc.)  For each of these properties a degree of birdness
could be assigned to each thing on the list.  The relative importance of
each property could then be assigned a weight and a degree of birdness
assigned.  If we were being analytical, then perhaps an eagle would be a
bird to the extent 0.95, a pigeon would be a bird to extent 0.77, a bat
would be a bird to extent 0.05, or whatever.  Inversely, an eagle would
not be a bird to the extent 0.05, a pigeon would not be a bird to the
extent 0.23.  The birdness of each thing would be true to a certain
extent (x) and false to a certain extent (y) where x,y>0 & x+y=1

In Rober Nozick's book, Philosophical Explanations, he describes the old
puzzle of the ship of Theseus.  The ship starts out from the port of
Theseus on a lengthy voyage.  During the voyage, the entire structure of
the ship is replaced, one plank at a time.  When the ship returns to its
home port, is it the same ship?  Depends on your definition of course.
But if you use an Aristotelean criteria, such as "The ship is the same
ship until half of its boards are replaced." you end up with inelegant
categorizations:  changing one board could convert the ship of Theuseus
to a non-ship of Theseus.  If we use an analogous fuzzy logic, then the
ship will merely have gone from a 50.1% membership in the set of Ships
of Theseus to a 49.9% membership in the set of Ships of Theseus.

There can be multiple overlapping (nonnumberical) categories as well.
Perhaps a ship could be non Thesean, slightly Thesean, somewhat Thesean,
moderately Thesean, quite Thesean, extremely Thesean, absolutely
Thesean.  These categories could be represented by isosceles triangles
along the unit truth axis with the peak of each at 1.0, and the base of
each at 0 of its neighbor.  Then a ship might be 25% somewhat Thesean
and 75% moderately Thesean.

Fuzzy logic is not fuzzy in the sense of being confused, but fuzzy in
the sense of being partially true and partially false. of course, x=1
and y=0 is a possible assignment of truthfulness & falseness.  But
perhaps a platonic ideal bird could not exist in reality, depending on
your criteria.

If there is no clear meaning for ni, perhaps implementing a rich syntax
for describing fuzzy sets with ni would be amusing and/or useful.
Perhaps the capability exists but is simply unrecognized.

Da is in the 3rd of 7 overlapping fuzzy sets along the Thesean scale.
Da lo ni ci paze botcu ra'i lo Teseus

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