>[SB]...I feel impelled to hurl an insult at this point -
> > Platonist!
>> More seriously, it depends on your understanding of language - does
>> language model the world? or does it talk about the world? (Plato v.
>> Aristotle, or Tractatus v. Philosophical Investigations if you're in to
>> Wittgenstein)
>
>[WK] Not sure what you read. What I mean is that even if mvl or fuzzy logics
> explicitly involve truth-degrees, it may be a misnomer: these degrees
>reflect the degree of our certainty about the truth of a statement, not
>the degree of truth of the statement.
>
>Suppose that we have the linguistic variable 'tall'. Suppose you assign
>to it a fuzzy set with a membership function f such that f(x) = 0 if x <
>160, f(x) = 1 if x > 180, and f(x) is linearly increasing from 0 at 160
>to 1 at 180. Suppose my height h is 170. Thus, f(h) = 0.5. Would you
>say that it is 50% true that I am tall? That the truth of 'wk is tall'
>is a 50% truth? (01)
[KBL] There are some statements to which one can assign definite
truth-values. We may not KNOW the truth-values, but the statements
HAVE truth-values. An example is "The infinite sum 1 + 1/2 + 1/4 +
1/8 + 1/16 + 1/32 + ... converges to the value 2." This statement is
true. An example of an empirical statement with a definite
truth-value is: "At midnight EDT on 16 May, 2007, Kathryn Laskey's
university phone number is +1-703-993-1644." (02)
Statements with a definite truth-value are those which pass the
clarity test. You may recall my statement some time ago during this
thread that a proposition passes the clarity test if it can be stated
sufficiently clearly that it is possible in principle to verify
whether or not it is true in Reality. Of course, for future events,
such verification must be postponed until the date of occurrence or
non-occurrence. Thus, the statement, "At midnight EDT on 16 May,
2011, Kathryn Laskey's university phone number is +1-703-993-1644,"
does have a definite truth-value, but no one yet knows it. Depending
on one's metaphysical leanings, the truth-value may as yet be
undetermined, but it will be fixed as of 16 May, 2011. (03)
An example from this thread that some would say has a definite
truth-value is "Waclaw's height is between 169 and 171 centimeters."
However, there is a bit of a problem with this. A person's height
can change by as much as a centimeter during a day. A person's
measured height depends on how he or she is standing -- whether
slumped over a bit or with square shoulders and extended spine. If
we are talking EXACT height all the way down to the Planck level, it
isn't even well-defined. For many practical purposes we can act as
if this statement has a definite truth-value (time-qualified, of
course -- Waclaw was at one time much shorter than 169 centimeters).
If we specify a definite procedure for measuring Waclaw's height at a
particular time, and then apply this procedure, we will obtain a
definite answer. We can then assign a definite truth-value to his
measured height for that particular measurement event. (04)
This brings me to Waclaw's "degree of tallness". Fuzzy logic enables
us to attach a number "degree of tallness" to Waclaw's height, and to
relate Waclaw's degree of tallness to his degree of heaviness, to his
father and mother's degrees of tallness, etc. Fuzzy logic provides a
calculus for manipulating these "degrees of set membership"
(equivalently, "degrees of truth" or "degrees of having a property")
consistently. Actually, there isn't one single calculus -- there are
several, depending on what combination operators one chooses to
employ. There is an enormous literature on fuzzy logic, a number of
implemented fuzzy reasoning systems, and a proliferation of
applications of fuzzy logic. Many people find fuzzy logic
interesting and useful, and it has a passionate community of
adherents. (05)
The fuzzy logic community has agreed to use the terminology "degree
of membership", "degree of truth", etc. for the numbers fuzzy systems
manipulate. The fuzzy community has agreed to use this terminology
because things that have 100% "degree of truth" correspond to things
that satisfy the clarity-test definition of true statements, and the
terminology has intuitive resonance for many people. (06)
Suppose we say that Waclaw's degree of tallness is 0.73. Does this
mean Waclaw "really" has membership level 0.73 in the set of tall
people, or that it "really is" 73% true that he is tall? I don't know
what that means. Waclaw's "degree of tallness" doesn't satisfy the
clarity test. (07)
So then, should we follow Waclaw's suggestion and say that the number
0.73 reflects our uncertainty about whether he is tall? I would
argue against this. It is too easily confused with subjective
probability. Assigning a subjective probability of 73% to the
statement that Waclaw is tall is very different from assigning a
fuzzy degree of truth of 73%. In the former case, I am asserting
that: (1) there IS a fact of the matter, in the clarity test sense,
of whether or not Waclaw is tall; but (2) I am uncertain about the
facts; and (3) the odds at which I would bet that he is tall are
73:27; and (4) in principle, I could find out the truth of the matter
and settle the bet. But whether Waclaw is tall does not satisfy the
clarity test, because I have not provided a precise definition of
what it means for him to be tall, that could in principle be verified
by anyone with access to the facts of the matter. Therefore, it is
not appropriate to assign a probability to the statement that he is
tall. (08)
I personally think, therefore, that it is misleading to say I am
uncertain about whether Waclaw is tall. I think it is less
misleading to say that (according to a given system of assigning
fuzzy memberships) he has membership degree 0.73 in the set of tall
people. The consumer of such statements must, of course, bear in
mind the rules by which fuzzy memberships are assigned and
manipulated, and think carefully about whether the resulting
mathematics applies to the problem at hand. But this is the case
with any application of any theory. (09)
Kathy (010)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (011)
|