A Fuzzy Ship from Theseus

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

mi pu cusku di'e

>> I am becoming more certain that a new construct or usage idiom is necessary
>> to describe fuzzy sets/logic.

jorge pu cusku di'e
>I think I agree, if the goal is to describe fuzzy logic. What I'm not
>certain about is what we need it for...

>...A tanru is a composite
>selbri, where one component modifies the other, so:
>
>        ta mutce blanu
>        That is very blue.
>
>{mutce blanu} is the selbri. It is analogous to using adjectives
>in English. To say "this is quite blue" in lojban all you need
>is to find the right word for "quite".
>
>I know that is not very precise from a formal point of view, but
>what would be the benefits in terms of the use of the language
>of having a more formal way of saying it?

It is important to distinguish fuzziness from vagueness.  Fuzzy is a
word with both technical and plebeian connotations.  "Fuzzy-headed
liberal" or "a little fuzzy on the details" for example, imply not well
thought out, confused, or vague.  This is reflected in definition 3 & 4
of fuzzy given in the American Heritage Dictionary (my preferred source
for US English usage).  The etiology of the word is relevant; "warm
fuzzy feeling" is apparently a recent usage.

fuzz0y (f=EEz2T) adj. fuzz0i0er, fuzz0i0est.
1. Covered with fuzz.
2. Of or resembling fuzz.
3. Not clear; indistinct: a fuzzy recollection of past events.
4. Not coherent; confused: a fuzzy plan of action. [Perhaps from Low German
fussig, spongy. See p=F2- below.] -fuzz2i0ly adv. -fuzz2i0ness n.

?

p=F2-. Important derivatives are: foul, filth, defile1, fuzzy, putrid,
potpourri, putrefy, purulent, pus. .
p=F2-. To rot, decay.
1. Suffixed form *pu-lo-. a. FOUL, from Old English ful, unclean, rotten;
b. FULMAR, from Old Norse full, foul; c. FILTH, from Old English f=F9lth,
foulness, from Germanic abstract noun *fulith=C5; d. FILE3; DEFILE1, from Ol=
d
English f=F9lan, to sully, from Germanic denominative *fuljan, to soil,
dirty. a, b, c, and d all from Germanic *fulaz, rotten, filthy.
2. Extended form *pug-. FOG2, from Middle English fog, fogge, aftermath
grass, from a Scandinavian source probably akin to Icelandic fuki, rotten
sea grass, and Norwegian fogg, rank grass, from Germanic *fuk-.
3. Extended variant form *pous-. FUZZY, from Low German fussig, spongy,
from Germanic *fausa-.
4. Suffixed form *pu-tri-. PUTRESCENT, PUTRID; (OLLA PODRIDA), (POTPOURRI),
PUTREFY, from Latin puter (stem putri-), rotten.
5. Suffixed form *puw-os-. a. PURULENT, PUS; SUPPURATE, from Latin pus,
pus; b. PYO-, from Greek puon, puos, pus.
6. EMPYEMA, from Greek compound empuein, to suppurate (en-, in; see en).
[Pokorny 2. p=F2- 848.]

The technical use of fuzzy is distinct in that careless vagueness or
confusion are not implied.  (Fuzziness might be considered intentional
vagueness, but vagueness with an important purpose.)

I have done some work with a fuzzy neural-net approach to selecting drug
therapy of various diseases, (I am a physician who does clinical
pharmacology research) and I am convinced that there is great merit to
this approach.  Until recently, the availability of standard programming
tools for fuzzy logic programming has impeded progress, but the
introduction of fuzzy logic operators in the latest version of MatLab
may indicate this lack of tools will soon be remedied.

There are now thousands of applications of fuzzy logic in use.  For
example, I have a Zojrushi fuzzy logic rice cooker, which cleverly
steams my rice to perfection, and keeps it edible for up to four hours!
I understand the new Ford Taurus has fuzzy logic in its engine throttle
controller.  Thousands of scholarly articles have been published
regarding fuzzy logic.  I have on my bookshelf no less than 18 books
discussing the subject.

Why should lojban include fuzzy logic operators?  Well, we're talking
about the crown jewels here! lojban's first and foremost claim to fame
is that it is a powerful means of expressing predicate logic.  Even if
you are correct that fuzzy logic is not very useful, (and I hope to
convince you otherwise), there are many who believe that fuzzy logic is
to Aristotelean logic as rational numbers are to integers.  This gets at
my next point:

mi pu cusku di'e
>> This implies a blend of the property blue with the property or properties
>> non-blue, at least to this fuzzy speaker. The use of tanru seems to me to
>> be an example of the first type of fallacy I mentioned regarding fuzzy
>> sets/logic. It is an attempt to define an exact shade of blue which applies
>> to X. X is then in the set of things which are "much blue" or not in the
>> set of things which are "much blue" lojban seems stubbornly two-valued in
>> its logic.

jorge pu cusku di'e
>Well, but it's the same with your method. X will either be in the
>set of things that are .85 blue and .15 non-blue or it won't. No third
>possibility. It would be like defining {mutce} as .85 of the property
>and .15 of the non-property. Since using numbers is not really practical
>for everyday language, we are left with defining some "extent" words
>like {mutce} that do the equivalent job.

It is also true that we don't need decimal notation.  We can certainly
use the integers 2 & 3 to describe 2/3.  However, it is helpful to
express this number as 0.66666667 for comparative purposes.  Quick,
which is bigger 2/3 or 3985/5978?

The concept that you are glossing over is that of set membership.  When
you say that "X will either be in the set of things that are .85 blue
and .15 blue or not", you are assuming the law of the excluded middle-an
Aristotelean assumption.  The analogous fuzzy logic concept is
(appropriately enough) fuzzy set membership.  A thing can be partially
in a set and partially not in a set.  Thus X has fuzzy membership in the
set of blue things to extent 0.85, or (less precisely) X is quite blue.
There are a full set of operators analogous to the aristotelean
operators; for example, there is a negation operator NOT 0.85 member of
set of blue things 0.15 member of set of blue things.

>>>        le jei ti blanu cu du li pibimu
>>>        The extent of truth of "this is blue" is 0.85
>>>
>> I agree that this is in the spirit of what I mean by a fuzzy blueness, but
>> I also agree that it is far too contrived to be useful and it isn't quite
>> right anyway, being too abstract. Apparently it is as difficult or more
>> difficult to speak about fuzzy logic in lojban as in English.

>It depends what you want it for. If you want to use it for some technical
>function (like some artificial intelligence program) then you can assign
>a number to each sentence as a "degree of truth". For ordinary speech
>that doesn't work, but I don't think it is needed either. What would be
>the point of having a mathematically precise assignment of a fuzzy truth
>value to sentences?

The thing that I want fuzzy logic for is to move from common speech to
technical specifications.  If a fuzzy logic utility were built in it
would allow a speaker to use a sort of shorthand to express a complex
logical idea.

Imagine that we are describing birds, which (suppose for arguments sake)
I think of as being assigned to one of seven adjacent overlapping sets:

absolutely birdish
quite birdish
rather birdish
somewhat birdish
nearly birdish
slightly birdish
not-at-all birdish

It would be useful if in lojban one could say:

X is in the 2nd of 7 evenly spaced fuzzy sets along the truth vector
birdish.  If such sets were not evenly spaced, there could be a facility
for specifying the exact position of the 1.00 truth position of each
fuzzy set.

mi cusku di'e
>> ...
>> 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.

la dyl,n. cusku di'e
>Umm.. Yes.  Why is a pigeon less of a bird than an eagle?

I think of flying as an important part of birdness.  This is of course
arbitrary.  But the pigeons I know spend a lot of time walking about
among the sleeping street people, finding the popcorn.  I reject that
genetics is the be all and end all of birdness.  There are some stuffed
dead birds in the Thornton museum at Harvard.  You can go see them!
These specimens are genetically birds.  Do they seem as birdish to you
as the pigeons outside?  This is of course besides the point.  We could
probably agree on a set of 10 or 20 sub properties of birdness that
would give us mutually agreeable birdness scores.

>> ...
>> 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?

>I'd quibble and say yes; I'm the same person I was 5 years ago, even
>though all the atoms in my body may have changed since then.[1] It's
>the form, not the materials, that determines identity.  But this
>example could easily be changed to one that I wouldn't quibble with.
>(e.g., gradually change the shape until it becomes a house.)
>
>[1] Not entirely true, but the extent to which it's not true is mainly
>determined by my experiences since then, not the change in materials.

Yes ship to house is a cleaner example.  As a physician, I am constantly
struck by the ephemeral nature of our corporeal structure.  People are
processes more than they are things.  The Navajo seem to have a firmer
grasp on this than native English speakers.  The criteria for identity
you are using is the closest continuer criteria, which Nozick discusses
in Philosphical Explanations.

Suppose a persistent museum curator surreptitiously follows behind the
ship of Theseus and picks up each plank as it is discarded,
reconstructing the original ship in its entirety.  The entirely new ship
sails back into the port of Theseus at the end of the voyage.  It is
accepted as the closest continuer of the original ship, as the
activities of the museum curator are unknown.  Then out of the mist on
the horizon sails the curator's ship reconstructed from the original
planks!  Now this ship is the closest continuer!  (Or maybe not,
depending on details of definition...)  Closest continuer is a
reasonable criteria, but can lead to surprises.

The problem with an aristotelean approach is the unreasonable sharp
discontinuity in which of the ships is the closest continuer.  When more
than fifty percent of the curator's reconstruction contains original
planks it suddenly becomes the closest continuer.  The fuzzy logic
approach is continuous.  The increasingly ersatz ship of Theseus
gradually diminishes in its degree of originality.  The increasingly
reconstructed ship of Theseus gradually increases in its degree of
originality.  This seems mucho buono to me.

mi cusku di'e
>> 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.

la ucleaar cusku di'e
>I believe in fuzzy categories, and I recognize that this example is
>from time to time used to exemplify the notion, but I think it is
>not in the least fuzzy. Eagles, pigeons, penguins are all indubitably
>birds, and bats, squirrels are indubitably not birds. These are
>on a TYPICALITY GRADIENT [emphasis, not yelling] but not a
>MEMBERSHIP GRADIENT. Contrast this with the category Square: the
>further something is from having four sides of equal length and four
>angles of 90 degrees, the less it is a square, but it isn't possible
>to say when it becomes definitely not a square. A category has gradient
>membership iff it has defining features.
>
>This is not necessarily the standard view, but at any rate it's what I
>teach my students.

Sure, eagles, pigeons, penguins, and ostriches are genetically birds.  I
certainly think genetics are important.  But to me birdishness is more
than genes.  An eagle gets a higher birdish score, because it swoops
about so birdishly, displaying several different modes of
flight-soaring, diving, climbing.  Pigeons seem to fly mainly to avoid
being stepped on.  Penguins fly, sure, but underwater!  Ostriches just
run.  Bats and flying squirrels are gentically less birdish (although
there is actually a lot of similarity between avian and mammalian DNA!)
Hence my ordering.  Imagine that I incrementally replace an eagle's
genes with the analogous iguana genes.  With which substitution does the
eagle abruptly cease being a bird?

la dyl,n. cusku di'e
>Wow.  For a doctor, you sure sound like a mathematician.

Well, yes.  My mother was heartbroken; she always wanted to say, "My son
the algebraic topologist" :)

-Stiv.n

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
=46ax:   309/671-8413