Re: A Fuzzy Ship from Theseus

[jorge@PHYAST.PITT.EDU]

la stiv,n cusku di'e
> 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.

I never meant to say that fuzzy logic is not useful.  I only questioned
its usefulness with regard to everyday use of language.  The same
happens with Boolean logic, it is very useful in programing computers
for example, but not much in everyday use of language.

> 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.

But that's exactly the same in Lojban. You can say very precisely:

        le jei ta blanu cu du pibimu
        The truth value of "that's blue" is 0.85

or less precisely:

        ta mutce blanu
        That's quite blue.

You could even say:

        le jei ta cmima lo'i blanu cu du pibimu
        The truth of "that belongs to the set of blue things" is 0.85

My point is that neither in English nor in Lojban would I like to
normally say something involving the number .85 in this context.  I have
no problem with a computer program that assigns such a truth value to a
statement like that.  It's just that I never want to do something like
that when using everyday language.

> 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
> =3D 0.15 member of set of blue things.

I guess that would give something like {tolmutce} in Lojban:

        ta tolmutce blanu
        That's very little blue.

> 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

Why not:

traji cipni
mutce cipni
milxe cipni
tolmutce cipni
na'e cipni

I suppose one could think of more intermediate extents.

Also, you have the {je'ucai} to {je'unaicai} attitudinals to qualify any
statement.

> 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.

ta cmima le remoi be lu'i ze nalsatci selcmi noi lo'i cipni cu fatri
ke'a lo dunli

Not much more concise than the English version, but then, why would you
ever want to say that instead of {ta mutce cipni}?

> 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.

But the assigning of numbers is totally arbitrary, isn't it?  Why would
an ostrich get a .652 instead of a .7513 in the bird scale?  Saying that
it is .652 true bird makes as much (or as little) sense as saying that
it is .7513 true bird.  There is nothing wrong with assigning to it that
or any other number for a particular computer application, but it
wouldn't make any sense to talk like that, especially because we would
never reach an agreement on how much a bird an ostrich really is.  One
thing is to say that an ostrich is more birdish than a bat, with which
probably most people will agree, but a different thing is to actually
assign them numbers.

...
> 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.

How many points does an eagle get on the "it flies" sub-property, and
how many does the pigeon get?  You say that the eagle gets more, but
that's very subjective, and how many more?  We would never agree on some
universal scale.  Also, different eagles should supposedly get different
degrees of birdishness.

> 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.

You can explain that in Lojban as well as you are doing it in English.
When I say {mi pu klama le zarci} I am not claiming that the atoms that
now compose {mi}, the speaker, went to the store in the past.  Many of
them weren't there and many of those that were are no longer with me.
That's because the referent of {mi} is not a bunch of atoms.  It is an
entity that only tangentially has to do with atoms.  The same happens
with the ship, it is not the planks that are important to identify the
referent.  I still don't see how fuzzy logic helps us here.  Are you
saying that if half of my atoms have been replaced since then, then {mi
pu klama le zarci} would have a truth value of .5?  (Actually, I would
also need to consider the atoms of the store, maybe even more difficult,
not to mention the unstated sumti!)

Jorge